3.4: The Regression Equation
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Data rarely fit a straight line exactly. Usually, you must be satisfied with rough predictions. Typically, you have a set of data whose scatter plot appears to "fit" a straight line. This is called a Line of Best Fit or Least-Squares Line.
COLLABORATIVE EXERCISE
If you know a person's pinky (smallest) finger length, do you think you could predict that person's height? Collect data from your class (pinky finger length, in inches). The independent variable, \(x\), is pinky finger length and the dependent variable, \(y\), is height. For each set of data, plot the points on graph paper. Make your graph big enough and use a ruler . Then "by eye" draw a line that appears to "fit" the data. For your line, pick two convenient points and use them to find the slope of the line. Find the \(y\)-intercept of the line by extending your line so it crosses the \(y\)-axis. Using the slopes and the \(y\)-intercepts, write your equation of "best fit." Do you think everyone will have the same equation? Why or why not? According to your equation, what is the predicted height for a pinky length of 2.5 inches?
Example \(\PageIndex{1}\)
A random sample of 11 statistics students produced the following data, where \(x\) is the third exam score out of 80, and \(y\) is the final exam score out of 200. Can you predict the final exam score of a random student if you know the third exam score?
| \(x\) (third exam score) | \(y\) (final exam score) |
|---|---|
| 65 | 175 |
| 67 | 133 |
| 71 | 185 |
| 71 | 163 |
| 66 | 126 |
| 75 | 198 |
| 67 | 153 |
| 70 | 163 |
| 71 | 159 |
| 69 | 151 |
| 69 | 159 |
Scatter Plot, Regression line and equation, \(r\) and \(R^{2}\) Calculator
Create a scatter plot, the regression equation, \(r\) and \(r^{2}\) below by entering a point, click Plot Point and then continue until you are done.
| ( , ) |
Data:
| Regression Equation: | r: | \(r^{2}\): |
Exercise \(\PageIndex{1}\)
SCUBA divers have maximum dive times they cannot exceed when going to different depths. The data in Table show different depths with the maximum dive times in minutes. Use your calculator to find the least squares regression line and predict the maximum dive time for 110 feet.
| \(X\) (depth in feet) | \(Y\) (maximum dive time) |
|---|---|
| 50 | 80 |
| 60 | 55 |
| 70 | 45 |
| 80 | 35 |
| 90 | 25 |
| 100 | 22 |
Answer
\(\hat{y} = 127.24 – 1.11x\)
At 110 feet, a diver is predicted to dive for only five minutes.
The third exam score, \(x\), is the independent variable and the final exam score, \(y\), is the dependent variable. We will plot a regression line that best "fits" the data. If each of you were to fit a line "by eye," you would draw different lines. We can use what is called a least-squares regression line to obtain the best fit line.
Consider the following diagram. Each point of data is of the the form (\(x, y\)) and each point of the line of best fit using least-squares linear regression has the form (\(x, \hat{y}\)).
The \(\hat{y}\) is read " \(y\) hat" and is the estimated value of \(y\). It is the value of \(y\) obtained using the regression line. It is not generally equal to \(y\) from data.
Figure \(\PageIndex{2}\)The term \(y_{0} – \hat{y}_{0} = \varepsilon_{0}\) is called the "error" or residual. It is not an error in the sense of a mistake. The absolute value of a residual measures the vertical distance between the actual value of \(y\) and the estimated value of \(y\). In other words, it measures the vertical distance between the actual data point and the predicted point on the line.
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for \(y\). If the observed data point lies below the line, the residual is negative, and the line overestimates that actual data value for \(y\).
In the diagram in Figure, \(y_{0} – \hat{y}_{0} = \varepsilon_{0}\) is the residual for the point shown. Here the point lies above the line and the residual is positive.
\(\varepsilon =\) the Greek letter epsilon
For each data point, you can calculate the residuals or errors, \(y_{i} - \hat{y}_{i} = \varepsilon_{i}\) for \(i = 1, 2, 3, ..., 11\).
Each \(|\varepsilon|\) is a vertical distance.
For the example about the third exam scores and the final exam scores for the 11 statistics students, there are 11 data points. Therefore, there are 11 \(\varepsilon\) values. If you square each \(\varepsilon\) and add, you get
\[(\varepsilon_{1})^{2} + (\varepsilon_{2})^{2} + \dotso + (\varepsilon_{11})^{2} = \sum^{11}_{i = 1} \varepsilon^{2} \label{SSE}\]
Equation\ref{SSE} is called the Sum of Squared Errors (SSE) .
Using calculus, you can determine the values of \(a\) and \(b\) that make the SSE a minimum. When you make the SSE a minimum, you have determined the points that are on the line of best fit. It turns out that the line of best fit has the equation:
\[\hat{y} = a + bx\]
where
- \(a = \bar{y} - b\bar{x}\) and
- \(b = \dfrac{\sum(x - \bar{x})(y - \bar{y})}{\sum(x - \bar{x})^{2}}\).
The sample means of the \(x\) values and the \(x\) values are \(\bar{x}\) and \(\bar{y}\), respectively. The best fit line always passes through the point \((\bar{x}, \bar{y})\).
The slope \(b\) can be written as \(b = r\left(\dfrac{s_{y}}{s_{x}}\right)\) where \(s_{y} =\) the standard deviation of the \(y\) values and \(s_{x} =\) the standard deviation of the \(x\) values. \(r\) is the correlation coefficient, which is discussed in the next section.
Least Square Criteria for Best Fit
The process of fitting the best-fit line is called linear regression . The idea behind finding the best-fit line is based on the assumption that the data are scattered about a straight line. The criteria for the best fit line is that the sum of the squared errors (SSE) is minimized, that is, made as small as possible. Any other line you might choose would have a higher SSE than the best fit line. This best fit line is called the least-squares regression line .
THIRD EXAM vs FINAL EXAM EXAMPLE:
The graph of the line of best fit for the third-exam/final-exam example is as follows:
Figure \(\PageIndex{3}\)The least squares regression line (best-fit line) for the third-exam/final-exam example has the equation:
\[\hat{y} = -173.51 + 4.83x\]
REMINDER
Remember, it is always important to plot a scatter diagram first. If the scatter plot indicates that there is a linear relationship between the variables, then it is reasonable to use a best fit line to make predictions for \(y\) given \(x\) within the domain of \(x\)-values in the sample data, but not necessarily for x -values outside that domain. You could use the line to predict the final exam score for a student who earned a grade of 73 on the third exam. You should NOT use the line to predict the final exam score for a student who earned a grade of 50 on the third exam, because 50 is not within the domain of the \(x\)-values in the sample data, which are between 65 and 75.
Understanding Slope
The slope of the line, \(b\), describes how changes in the variables are related. It is important to interpret the slope of the line in the context of the situation represented by the data. You should be able to write a sentence interpreting the slope in plain English.
INTERPRETATION OF THE SLOPE: The slope of the best-fit line tells us how the dependent variable (\(y\)) changes for every one unit increase in the independent (\(x\)) variable, on average.
THIRD EXAM vs FINAL EXAM EXAMPLE
Slope: The slope of the line is \(b = 4.83\).
Interpretation: For a one-point increase in the score on the third exam, the final exam score increases by 4.83 points, on average.
The Correlation Coefficient \(r\)
Besides looking at the scatter plot and seeing that a line seems reasonable, how can you tell if the line is a good predictor? Use the correlation coefficient as another indicator (besides the scatterplot) of the strength of the relationship between \(x\) and \(y\). The correlation coefficient, \(r\) , developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable \(x\) and the dependent variable \(y\).
The correlation coefficient is calculated as
\[r = \dfrac{n \sum(xy) - \left(\sum x\right)\left(\sum y\right)}{\sqrt{\left[n \sum x^{2} - \left(\sum x\right)^{2}\right] \left[n \sum y^{2} - \left(\sum y\right)^{2}\right]}}\]
where \(n =\) the number of data points.
If you suspect a linear relationship between \(x\) and \(y\), then \(r\) can measure how strong the linear relationship is.
What the VALUE of \(r\) tells us:
- The value of \(r\) is always between –1 and +1: –1 ≤ r ≤ 1.
- The size of the correlation \(r\) indicates the strength of the linear relationship between \(x\) and \(y\). Values of \(r\) close to –1 or to +1 indicate a stronger linear relationship between \(x\) and \(y\).
- If \(r = 0\) there is absolutely no linear relationship between \(x\) and \(y\) (no linear correlation) .
- If \(r = 1\), there is perfect positive correlation. If \(r = -1\), there is perfect negative correlation. In both these cases, all of the original data points lie on a straight line. Of course,in the real world, this will not generally happen.
What the SIGN of \(r\) tells us:
- A positive value of \(r\) means that when \(x\) increases, \(y\) tends to increase and when \(x\) decreases, \(y\) tends to decrease (positive correlation) .
- A negative value of \(r\) means that when \(x\) increases, \(y\) tends to decrease and when \(x\) decreases, \(y\) tends to increase (negative correlation) .
- The sign of \(r\) is the same as the sign of the slope, \(b\), of the best-fit line.
Note
Strong correlation does not suggest that \(x\) causes \(y\) or \(y\) causes \(x\). We say "correlation does not imply causation."
Shoot Down Money at the Correct Correlation Game
You will be given a correlation and your money will be flying through the air. You must keep shooting down your money until the correlation for that scatter plot is within 0.1 of the correlation goal that is shown. You can destroy your money by shooting it down, but when you do you will lose that much money and the bill will turn into a point that becomes part of a scatter plot. You start with $100. Try to end with as much money as you can. Click on Start to start the game. Use the buttons below or the left and right arrow keys to rotate your gun and the up key to shoot. Good Luck!
| r | r Goal | Money Left |
The formula for \(r\) looks formidable. However, the LibreTexts Regression Analysis calculator can quickly calculate \(r\).
The Coefficient of Determination
The variable \(r^{2}\) is called the coefficient of determination and is the square of the correlation coefficient, but is usually stated as a percent, rather than in decimal form. It has an interpretation in the context of the data:
- \(r^{2}\), when expressed as a percent, represents the percent of variation in the dependent (predicted) variable \(y\) that can be explained by variation in the independent (explanatory) variable \(x\) using the regression (best-fit) line.
- \(1 - r^{2}\), when expressed as a percentage, represents the percent of variation in \(y\) that is NOT explained by variation in \(x\) using the regression line. This can be seen as the scattering of the observed data points about the regression line.
Consider the third exam/final exam example introduced in the previous section
- The line of best fit is: \(\hat{y} = -173.51 + 4.83x\)
- The correlation coefficient is \(r = 0.6631\)
- The coefficient of determination is \(r^{2} = 0.6631^{2} = 0.4397\)
- Interpretation of \(r^{2}\) in the context of this example:
- Approximately 44% of the variation (0.4397 is approximately 0.44) in the final-exam grades can be explained by the variation in the grades on the third exam, using the best-fit regression line.
- Therefore, approximately 56% of the variation (\(1 - 0.44 = 0.56\)) in the final exam grades can NOT be explained by the variation in the grades on the third exam, using the best-fit regression line. (This is seen as the scattering of the points about the line.)
Summary
A regression line, or a line of best fit, can be drawn on a scatter plot and used to predict outcomes for the \(x\) and \(y\) variables in a given data set or sample data. There are several ways to find a regression line, but usually the least-squares regression line is used because it creates a uniform line. Residuals, also called “errors,” measure the distance from the actual value of \(y\) and the estimated value of \(y\). The Sum of Squared Errors, when set to its minimum, calculates the points on the line of best fit. Regression lines can be used to predict values within the given set of data, but should not be used to make predictions for values outside the set of data.
The correlation coefficient \(r\) measures the strength of the linear association between \(x\) and \(y\). The variable \(r\) has to be between –1 and +1. When \(r\) is positive, the \(x\) and \(y\) will tend to increase and decrease together. When \(r\) is negative, \(x\) will increase and \(y\) will decrease, or the opposite, \(x\) will decrease and \(y\) will increase. The coefficient of determination \(r^{2}\), is equal to the square of the correlation coefficient. When expressed as a percent, \(r^{2}\) represents the percent of variation in the dependent variable \(y\) that can be explained by variation in the independent variable \(x\) using the regression line.
Glossary
- Coefficient of Correlation
-
a measure developed by Karl Pearson (early 1900s) that gives the strength of association between the independent variable and the dependent variable; the formula is:
\[r = \dfrac{n \sum xy - \left(\sum x\right) \left(\sum y\right)}{\sqrt{\left[n \sum x^{2} - \left(\sum x\right)^{2}\right] \left[n \sum y^{2} - \left(\sum y\right)^{2}\right]}}\]
where \(n\) is the number of data points. The coefficient cannot be more then 1 and less then –1. The closer the coefficient is to \(\pm 1\), the stronger the evidence of a significant linear relationship between \(x\) and \(y\).
Contributors and Attributions
-
Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>.


1.5.3: Windows Start Menu
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Please move your mouse cursor over to the bottom left of the computer display and click on the Start button . After clicking on the start button, the start menu will display. The start menu consists of a list of shortcuts to applications that allow the user to run applications on the computer. When the start menu launches, your user account name and optional picture appear at the top. The menu shows a list of often-used programs and other controls on the left, and variously-sized shaded rectangles called tiles on the right. Each tile represents an app, short for an application program. Some titles show updated content using a feature called a live tile the updates the application with relevant information to share with the user. You may categorize these shortcuts by dragging them into different areas and changing the file folder names to suit your preferences. Apps may also be resized if you right-click on the shortcut and select “resize”. You may also “pin” applications you use often to start menu shortcuts area on the right by dragging and dropping them to the start menu shortcuts menu. or by right-clicking, selecting “more” and then “pin to taskbar.
You can click on “All Apps” to display and scroll through all applications on your computer using the slider. Take some time to navigate and explore the start menu. You will find folders and subfolders and applications on this menu along with helpful shortcuts to several applications and navigation menus on your computer to increase your productivity.
You may also “pin” applications in the start menu to the taskbar, the bar on the lower part of the screen. To do so, right-click on the start menu icon, select “more” and “pin to taskbar” The application will now be always displayed on the Windows Taskbar.


5.13.7: Alfred Lord Tennyson's "The Lady of Shalott" (1832-42)
"The Lady of Shalott"
"Illustration to Tennyson's 'The Lady of Shalott'" by W. E. F. Britten (1901) is in the public domain
I
On either side the river lie
Long fields of barley and of rye,
That clothe the wold and meet the sky;
And through the field the road runs by
To many-tower’d Camelot;
And up and down the people go,
Gazing where the lilies blow
Round an island there below,
The island of Shalott,
Willows whiten, aspens quiver,
Little breezes dusk and shiver
Through the wave that runs for ever
By the island in the river
Flowing down to Camelot.
Four gray walls, and for gray towers
Overlook a space of flowers,
And the silent isle embowers
The Lady of Shalott.
By the margin, willow-veil’d,
Slide the heavy barges trail’d
By slow horses; and unhail’d
The shallop flitteth silken-sail’d
Skimming down to Camelot:
But who hath seen her wave her hand?
Or at the casement seen her stand?
Or is she known in all the land,
The Lady of Shalott?
Only reapers, reaping early
In among the bearded barley,
Hear a song that echoes cheerly
From the river winding clearly
Down to tower’d Camelot:
And by the moon the reaper weary,
Piling sheaves in uplands airy,
Listening, whispers, “’Tis the fairy
Lady of Shalott.
II
There she weaves by night and day
A magic web with colours gay.
She has heard a whisper say
A curse is on her if she stay
To look down on Camelot.
She know not what the curse may be
And so she weaveth steadily,
And little other care hath she,
The Lady of Shalott.
And moving through a mirror clear
That hangs before her all the year,
Shadows of the world appear.
There she sees the highway near
Winding down to Camelot:
There the river eddy whirls,
And there the surly village-churls
And the red cloaks of market girls,
Pass onward from Shalott.
Sometimes a troop of damsels glad,
An abbot on an ambling pad,
Sometimes a curly shepherd-lad,
Or long-haired page in crimson clad,
Goes by to tower’d Camelot;
And sometimes through the mirror blue
The knights come riding two and two;
She hath no loyal knight and true,
The Lady of Shalott.
But in her web she still delights
To weave the mirror’s magic sights,
For often through the silent nights
A funeral with plumes and lights
And music, went to Camelot:
Or when the moon was overhead,
Came two young lovers lately wed;
“I am half sick of shadows,” said
The Lady of Shalott.
III
A bow-shot from her bower-eaves,
He rode between the barley-sheaves,
The sun came dazzling through the leaves
And flamed upon the brazen greaves
Of bold Sir Lancelot.
A red-cross knight for ever kneel’d
To a lady in his shield,
That sparkled on the yellow field,
Beside remote Shalott.
The gemmy bridle glittered free,
Like to some branch of stars we see
Hung in the golden Galaxy.
The bridle bells rang merrily
As he rode down to Camelot.
And from his blazon’d baldric slung
A mighty silver bugle hung,
And as he rode his armour rung,
Beside remote Shalott.
All in the blue unclouded weather
Thick-jewelled shone the saddle-leather;
The helmet and the helmet feather
Burned like one burning flame together.
As he rode down to Camelot.
As often through the purple night,
Below the starry clusters bright,
Some bearded meteor, trailing light,
Moves over still Shalott.
His broad clear brow in sunlight glowed;
On burnished hooves his war-horse trode;
From underneath his helmet flowed
His coal-black curls as on he rode,
As he rode down to Camelot.
From the bank and from the river
He flashed into the crystal mirror;
“Tirra lirra” by the river
Sang Sir Lancelot.
She left the web, she left the loom,
She made three paces through the room,
She saw the water-lily bloom,
She saw the helmet and the plume,
She looked down to Camelot.
Out flew the web and floated wide;
The mirror cracked from side to side;
“The curse is come upon me,” cried
The Lady of Shalott.
IV
In the stormy east-wind straining,
The pale yellow woods were waning,
The broad stream in his banks complaining,
Heavily the low sky raining
Over tower’d Camelot;
Down she came and found a boat
Beneath a willow left afloat,
And round about the prow she wrote
The Lady of Shalott.
And down the river’s dim expanse –
Like some bold seer in trance,
Seeing all his own mischance –
With a glassy countenance
Did she look to Camelot.
And at the closing of the day
She loosed the chain, and down she lay;
The broad stream bore her far away,
The Lady of Shalott.
Lying, robed in snowy white
That loosely flew to left and right –
The leaves upon her falling light –
Through the noises of the night
As she floated down to Camelot:
And as the boat-head wound along
The willowy hills and fields among,
They heard her singing her last song,
The Lady of Shalott.

For ere she reached upon the tide
The first house by the water-side,
Singing in her song she died,
The Lady of Shalott.
Under tower and balcony,
By garden-wall and gallery,
A gleaming shape she floated by,
Dead-pale between the houses high,
Silent into Camelot.
Out upon the wharfs they came,
Knight and burgher, lord and dame,
And round the prow they read her name,
The Lady of Shalott.
Who is this? And what is here?
And in the lighted palace near
Died the sound of royal cheer;
And they crossed themselves for fear,
All the knights at Camelot;
But Lancelot mused a little space;
He said, “She has a lovely face;
God in his mercy lend her grace,
The Lady of Shalott”.
Contributors and Attributions
- Adapted from "A.L.Tennyson: The Lady of Shalott" from NDLA by Jan-Louis Nagel (2018) CC BY-SA


8.1: Hydrosilylation of Alkenes
Asymmetric hydrosilylation and hydroboration of carbon-carbon double bonds followed by oxidative cleavage of the C-Si and C-B bonds give effective methods for the construction of optically active alcohols (Scheme \(\PageIndex{1}\)).
Asymmetric hydrosilylation of carbon-carbon unsaturated substrates provides effective methods for the synthesis of optically active organosilanes, which are versatile intermediates in organic synthesis. Chiral alkyl and aryl silanes can be converted into optically active alcohols with retention configuration by oxidative cleavage of a carbon-silicon bond into carbon-oxygen bond, while the diastereoselective reaction of chiral allyl- and allenyl silanes with C=O bond can give homoallylic and homopropargylic alcohols.
8.1.1 Reactions of Styrene and its Derivatives
Chiral Palladium-catalyzed asymmetric hydrosilylation of styrene with trichlorosilane has been extensively studied. The reaction proceeds with excellent regioselectivity to give 1-phenyl-1-silylethane via a stable π -benzyl palladium intermediate (Scheme \(\PageIndex{2}\)).
Scheme \(\PageIndex{3}\) illustrates the possible mechanism. Deuterium-labeling studies suggest that the β -hydrogen elimination is found to be much faster compared to the reductive elimination from the intermediate II . The involvement hydropalladation in the catalytic cycle has been revealed by the side product analysis from the reaction of o -allylstyrene.
The reaction has been utilized in the synthesis of 1-aryl-1,2-diols from arylacetylenes (Scheme \(\PageIndex{4}\)). Platinum-catalyzed hydrosilylation of arylacetylene gives ( E )-1-aryl-2-(trichlorosilyl)ethanes that could be further reacted with trichlorosilane in the presence of chiral palladium complex to afford optically active 1-aryl-1,2-bis(trichlorosilyl)ethanes. The latter could be transformed into optically active 1,2-diol via oxidative cleavage of the carbon-silicon bond into carbon oxygen bond.
Other chiral catalysts have also been employed for the asymmetric hydrosilylation of alkenes. The chiral bis (oxazolinyl)phenylrhodium complex catalyzes the asymmetric hydrosilylation of styrenes with hydro(alkoxy)silanes in high enantioselectivity, although the regioselectivity is found to be somewhat moderate (Scheme \(\PageIndex{5}\)).
α -Substituted styrenes proceed reaction with phenylsilane to afford benzylic tert -alkylsilanes in the presence chiral organolanthanide as catalyst in moderate enantioselectivity (Scheme \(\PageIndex{6}\)).
8.1.2 Reactions of 1,3-Dienes
The reaction of 1,3-dienes with hydrosilanes having electron-withdrawing groups on silicon affords synthetically useful optically active silanes in the presence of chiral palladium complex (Scheme \(\PageIndex{7}\)). The reaction proceeds in a 1,4-fashion providing chiral allylsilanes that could be converted into homoallylic alcohols on the reaction with aldehydes.
The use of ferrocenylphosphine and mop-phen ligands has been demonstrated for the hydrosilylation of cyclo-1,3-hexadiene in the presence of palladium salts (Scheme \(\PageIndex{8}\)). The reaction with phenyldifluorosilane afforded the highest enantioselectivity compared to that with trichlorsilane or methyldichlorosilane. Based on the reaction of with deuterium-labeled silane the involvement of π-allylpalladium intermediate and 1,4- cis -addition has been proposed.
In case of linear 1,3-dienes, the regioselectivity has become an issue. In the reaction of 1-phenyl-1,3-butadiene using ferrocenyl ligand, ( R )-( S )-ppfa, the formation of a mixture of regioisomeric allylsilanes is observed (Scheme \(\PageIndex{9}\)). However, in the reaction of alkyl substituted 1,3-dienes, 1,3-hexadiene and 1,3-decadiene, a single regioisomer is obtained with moderate enantioselectivity. Improvement in the enantioselectivity is observed employing the bis (ferrocenyl)monophophine ligands a-d having two planar chiral ferrocenyl moieties on phosphorus atom.
The reaction of 1-buten-3-ynes substituted with bulky groups at the alkyne terminus affords enantiomerically enriched allenylsilanes in the presence of palladium complex (Scheme \(\PageIndex{10}\)). For example, the reaction of 5,5-dimethyl-1-hexen-3-yne using ( S )-( R )-bisppfOMe a proceeds in a 1,4-fashion to give allenyl(trichloro)silanes in high regio- and enantioselectivity. Further enhancement in the enantioselectivity is shown employing chiral phosphametallocene b having a sterically demanding η 5 -C 5 Me 5 moiety.
8.1.3 Reactions of Alkyl Substituted Alkenes
Hydrosilylation of simple terminal alkenes give branched products with high regioselectivity. The palladium systems show exceptional catalytic system compared to Pt, Ni and Rh based systems. For example, the hydrosilylation of 1-octene with trichlorosilane using palladium-(S)—MeO-mop gives a 93:7 mixture of 1-octylsilane and 2-octylsilane with 95% ee (Scheme \(\PageIndex{11}\)).
The above catalytic system is also effective for the hydrosilylation of cyclic alkenes, such as norbornene and bicyclo[2.2.2]octane, 2,5-dihydrofuran and norbornadiene. For example, the reaction of norbornene gives exo adduct exclusively (Scheme \(\PageIndex{12}\)). The hydrosilylated product can be transformed into exo -2-norbornanol or endo -2-bromonorbornane via the corresponding pentafluorosilicate. In addition, chiral ferrocenylmonophosphines a-d are too found to be effective for this process with excellent enantioselectivity.
Chiral yttrium hydride complex (d 0 metal complex) bearing non-Cp ligand catalyzes the hydrosilylation of norbornene with phenylsilane to produce exo -adduct with 90% ee (Scheme \(\PageIndex{13}\)). More recently, the first chirality transfer from silicon to carbon in a reagent-controlled reaction of norbornene is reported in the presence of achiral palladium complex. The hydrosilylation of norbornene with chiral silane A having 85% ee is found to form the hydrosilylated product B with 93% ee exhibiting asymmetric amplification (Scheme \(\PageIndex{14}\)).
8.1.4 Intramolecular Hydrosilylation
Synthesis of optically active polyols from allylic alcohols can be achieved using chiral Rh-catalyzed intramolecular hydrosilylation followed by oxidation of allyloxy hydrosilanes (Scheme \(\PageIndex{15}\)). For example, hydrosilyl ether of di(2-propenyl)methanol can be converted into optically active 1,3-diol using intramolecular hydrosilylation in the presence of chiral rhodium-(R,R)-diop followed by oxidation. Rh-BINAP is also found to be effective catalyst for the intramolecular hydrosilylation of hydrosilyl ethers of allyl alcohols.
8.1.5 Cyclization/Hydrosilylation
Asymmetric cyclization and hydrosilylation of a ,ω-diunsaturated compounds such as 1,6-dienes and 1,6-enynes affords powerful tool for the construction of optically active functionalized carbocycles. For example, the tandem reaction of diallylmalonate in the presence of cationic Pd complex bearing a chiral pyridine-oxazoline proceeds with high diastereoselectivity to yield the corresponding trans-substituted cyclopentane with 90% ee (Scheme \(\PageIndex{16}\)).
The reactions of 1,6-diynes using cationic Rh complexes bearing chiral bisphosphine gives the hydrosilylated alkylidenecyclopentanes with high enantioselectivity. For example, the 1,6-enyne proceeds reaction with triethylsilane in the presence of cationic Rh and ( R )-biphemp to give hydrosilylated alkylidene cyclopentane in 92% ee (Scheme \(\PageIndex{17}\)). Subsequently, chiral Rh complex containing spiro diphosphine ( R )-sdp is found to be effective for this process.
The synthesis of carbocycles can also be accomplished by the cyclization of ω-formyl-1,3-dienes in the presence of hydrosilanes and chiral nickel complex (Scheme \(\PageIndex{18}\)). For example, zerovalent nickel complex of (2 R ,5 R )-2,5-dimethyl-1-phenylphospholane catalyzes the cyclization of 1,3-dienes with a tethered formyl group in the presence of triethoxysilane to give five-membered carbocycle with 73% ee.


2.3: How to Educate a Gentleman?
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Selections from How to Educate a Gentleman?
John Locke
In this section Locke lays out several of his thoughts on the best way to educate a young gentleman. He speaks primarily of how a tutor should act toward a young pupil. Much of his attention is focused on how avoiding physical punishment and helping students develop their own motivation.
A sound mind in a sound body, is a short, but full description of a happy state in this world: He that has these two, has little more to wish for; and he that wants either of them, will be but little better for anything else. Men’s happiness or misery is most part of their own making. He, whose mind directs not wisely, will never take the right way; and he, whose body is crazy and feeble, will never be able to advance in it. I confess, there are some men’s constitutions of body and mind so vigorous, and well framed by nature, that they need not much assistance from others, but by the strength of their natural genius, they are from their cradles carried towards what is excellent; and by the privilege of their happy constitutions are able to do wonders: but examples of this kind are but few, and I think I may say, that of all the men we meet with, nine parts of ten are what they are, good or evil, useful or not, by their education. ‘Tis that which makes the great difference in mankind: the little, and almost insensible impressions on our tender infancies, have very important and lasting consequences: and there ‘tis, as in the fountains of some rivers, where a gentle application of the hand turns the flexible waters into channels, that make them quite contrary courses, and by this little direction given them at first in the source, they receive different tendencies and arrive at last, at very remote and distant places.
Reflection Question
Locke seems to be committing himself to societal determinism. Is this consistent with his other philosophical works?
1.[Physcial] punishment contributes not at all to the mastery of our natural propensity to indulge corporal and present pleasure, and to avoid pain at any rate, but rather encourages it; and so strengthens that in us, which is the root of all vicious and wrong actions. For what motives, I pray, does a child act by, but of such pleasure and pain, that drudges at his book against his inclination, or abstains from eating unwholesome fruit, that he takes pleasure in, only out of fear of whipping? He in this only prefers the greater corporal pleasure, or avoids the greater corporal pain; and what is it, to govern his actions, and direct his conduct, by such motives as these? What is it, I say, but to cherish that principle in him, which it is our business to root out and destroy? And therefore I cannot think any correction useful to a child, where the shame of suffering for having, done amiss does not work more upon him than the pain.
33. As the strength of the body lies chiefly able to endure hardships, so also does that of the mind. And the great principle and foundation of all virtue and worth is placed in this, that a man is able to deny himself his own desires, cross his own inclinations, and purely follow what reason directs as best, though the appetite lean the other way.
Reflection Question
What kind of ethical framework undergirds Locke's views of value and worth?
49. This sort of correction naturally breeds an aversion to that which it is the tutor's business to create a liking to. How obvious is it to observe, that children come to hate things liked at first, as soon as they come to be whipped, or chid, and teased about them? And it is not to be wondered at in them, when grown men would not be able to be reconciled to any thing by such ways. Who is there that would not be disgusted with any innocent recreation in itself indifferent to him, if he I should with blows, or ill language, be haled to it, when he had no mind? Or be constantly so treated, for some circumstance in his application to it? This is natural to be so. Offensive circumstances ordinarily infect innocent things which they are joined with: and the very sight of a cup, wherein any one uses to take nauseous physic, turns his stomach, so that nothing will relish well out of it, though the cup be never so clean and well-shaped, and of the richest materials.
50. Such a sort of slavish discipline makes a slavish temper. The child submits, and dissembles obedience, whilst the fear of the rod hangs over him; but when that is removed, and, by being out of sight, he can promise himself impunity, he gives the greater scope to his natural inclination, which by this way is. not at all altered, but on the contrary heightened and increased in him; and after such restraint, breaks out usually with the more violence. or,
51 4. If severity carried to the highest pitch does prevail, and works a cure upon the present unruly distemper, it is often bringing in the room of it a worse and more dangerous disease, by breaking the mind; and then, in the place of disorderly young fellow, you have a low-spirited, moped creature: who, however with his unnatural sobriety he may please silly people, who commend tame, unactive children because they make no noise, nor give them any trouble; yet, at last, will probably prove as uncomfortable a thing to his friends, as he will be, all his life, an useless thing to himself and others.
52 Beating them, and all other sorts o slavish and corporal punishments, are not the discipline fit to be used in the education of those we would have wise, good, and ingenuous men; and therefore very rarely to be applied, and that only in great occasions, and cases of extremity. On the other side, to flatter children by rewards of things that are pleasant to them, is as carefully to be avoided. He that will give to his son apples, or sugar-plums, or what else of this kind he is most delighted with, to make him learn his book, does but authorize his love of pleasure, and cocker up that dangerous propensity, which he ought by all means to subdue and stifle in him. You can never hope to teach him to master it whilst you compound for the check you give his inclination in one place, by the satisfaction you propose to it in another
Reflection Question
What about this course of action is wrong for Locke? Is it inconsistency, inefficiency, or something else entirely?
To make a good, a wise, and a virtuous man, it is fit he should learn to cross his appetite, and deny his inclination to riches, finery, or pleasing his palate, etc., whenever his reason advises the contrary, and his duty requires it. But when you draw him to do anything that is fit, by the offer of money or reward the pains of learning his book, by the pleasure of a luscious morsel; when you promise him a lace-cravat, or a fine new suit, upon performance of some of his little tasks; what do you, by proposing these as rewards, but allow them to be the good things he should aim at, and thereby encourage his longing for them, and accustom him to place his happiness in them? Thus people, to prevail with children to be industrious about their grammar, dancing, or some other such matter of no great moment to the happiness or usefulness of their lives by misapplied rewards and punishments, sacrifice their virtue, invert the order of their education, and teach them luxury, pride, or covetousness, etc. For in this way, flattering those wrong inclinations, which they should restrain and suppress, they lay the foundations of those future vices, which cannot be avoided, but by curbing our desires, and accustoming them early to submit to reason.
53. I say, not this, that I would have children kept from the conveniences or pleasures of life, that are not injurious to their health or virtue. On the contrary, I would have their lives made as pleasant, and as agreeable to them as may be, in a plentiful enjoyment of whatsoever might innocently delight them: provided it be with this caution, that they have those enjoyments only as the consequences of the state of esteem and acceptation they are in with their parents and governors; but they should never be offered or bestowed on them, as the reward of this or that particularly performance, that they show anaversion to, or to which they would not have applied themselves without that temptation.
54. But if you take away the rod on one hand, and these little encouragements, which they are taken with, on the other, How then (will you say) shall children be governed? Remove hope and fear, and there is an end of all discipline. I grant, that good and evil, reward and punishment, are the only motives to a rational creature; these are the spur and reins whereby all mankind are set on work and guided, and therefore they are to be made use of to children too. For I advise their parents and governors always to carry this in their minds, that they are to be treated as rational creatures.
55. I grant, and punishments must be proposed to children, if we intend to work upon them. The mistake, I imagine, is that those that are generally made use of, are ill chosen. The pains and pleasures of the body are, I think, of ill consequence, when made the rewards and punishments, whereby men would prevail on their children: for they serve but to increase and strengthen those appetites which 'tis our business to subdue and master. What principle of virtue do you lay in a child, if you will redeem his desires of one pleasure by the proposal of another? This is but to enlarge his appetite, and instruct it to wander. If a child cries for an unwholesome and dangerous fruit, you purchase his quiet by giving him a less hurtful sweetmeat; this perhaps may preserve his health, but spoils his mind, and sets that farther out of order. For here you only change the object, but flatter still his appetite, and allow that must be satisfied: wherein, as I have showed, lies the root of the mischief: and till you bring him to be able to bear a denial of that satisfaction, the child may at present be quiet and orderly, but the disease is not cured. By this way of proceeding you foment and cherish in him, that which is the spring from whence all the evil flows, which will be sure on the next occasion to break out again with more violence, give him stronger longings, and you more trouble.
65. ...Let therefore your rules to your son be as few as is possible, and rather fewer than more than seem absolutely necessary. For if you burden him with many rules, one of these two things must necessarily follow; that either he must be very often punished, which will be of ill consequence, by making punishment too frequent and familiar; or else you must let the transgressions of some of your rules go unpunished, whereby they will of course grow contemptible, and your authority become cheap to him. Make but few laws, but see they be well observed, when once made. Few years require but few laws; and as his age increases when one rule is by practice well established, you may add another.
70 ...What shall I do with my son? If I keep him always at home, he will be in danger to be my young master; and if I send him abroad, how is it possible to keep him from the contagion of rudeness and vice, which is so every where in fashion? In my house, he will perhaps be more innocent, but more ignorant, too, of the world, and being used constantly to the same faces, and little company will, when he comes abroad, be a sheepish or conceited creature... Virtue is harder to be got than a knowledge of the world; and if lost in a young man, is seldom recovered... A young man, before he leaves the shelter of his father's house, and the guard of a tutor, should be fortified with resolution, and made acquainted with men, to secure his virtue; lest he should be led into some ruinous course, or fatal precipice, before he is sufficiently acquainted with the dangers of conversation, and has steadiness enough not to yield to every temptation... But how any one's being put into a mixed herd of unruly boys, and then learning to wrangle at trap, or rook at span-farthing, fits him for civil conversation or business I do not see... I am sure, he who is able to be at the charge of a tutor at home, may there give his son a more genteel carriage, more manly thoughts, and a sense of what is worthy and becoming, with a greater proficiency in learning into the bargain, and ripen him up sooner into a man, than any at school can do... And if a young gentleman, bred at home, be not taught more of them than he could learn at school, his father has made a very ill choice of a tutor. Take a boy from the top of a grammar-school, and one of the same age, bred as he should be in his father's family, and bring them into good company together; and then see which of the two will have the more manly carriage, and address himself with the more becoming assurance to strangers....Vice, if we may believe the general complaint, ripens so fast now-a-days, and runs up to seed so early in young people, that it is impossible to keep a lad from the spreading contagion, if you will venture him abroad in the herd, and trust to chance, or his own inclination, for the choice of his company at school… It is virtue then, direct virtue, which is the hard and valuable part to be aimed at in education... And therefore I cannot but prefer breeding of a young gentleman at home in his father's sight, under a good governor, as much the best and safest way to this great and main end of education, when it can be had, and is ordered as it should be… This I am sure, a father that breeds his son at home, has the opportunity to have him more in his own company, and there give him what encouragement he thinks fit; and can keep him better from the taint of servants, and the meaner sort of people, than is possible to be done abroad. But what shall be resolved in the case, must in great measure be left to the parents…
73. None of the things they are to learn should ever be made a burden to them, or imposed on them as a task. Whatever is so proposed, presently becomes irksome: the mind takes an aversion to it, though before it were a thing of delight or indifferency. Let a child be but ordered to whip his top at a certain time every day, whether he has, or has not a mind to it; let this be but required of him as a duty, wherein he must spend so many hours morning and afternoon, and see whether he will not soon be weary of any play at this rate. Is it not so with grown men? What they do cheerfully of themselves, do they not presently grow sick of, and can no more endure, as soon as they find it is expected of them as a duty? Children have as much a mind to show that they are free, that their own good actions come front themselves, that they are absolute and independent, as any of the proudest of you grown men, think of them as you please.
Reflection Question
Is Locke right about the nature of tasks? If so, what implications would it have for the kinds of demands humans can make on each other?
102. Begin therefore betimes nicely to observe your son's temper, and that, when he is under least restraint. See what are his predominant passions and prevailing inclinations; whether he be fierce or mild, bold or bashful, compassionate or cruel, open or reserved, etc. For as these are different in him, so are your methods to be different, and your authority must hence take measures to apply it self [in] different ways to him. These native propensities, these prevalences of constitution, are not to be cured by rules, or a direct contest, especially those of them that are the humbler and meaner sort, which proceed from fear and lowness of spirit; though with art they may be much mended, and turned to good purposes. But of this be sure, after all is done, the bias will always hang on that side that nature first placed it: and, if you carefully observe the characters of his mind now in the first scenes of his life, you will ever after be able to judge which way his thoughts lean, and what he aims at even hereafter, when, as he grows up, the plot thickens, and he puts on several shapes to act it.
118 Curiosity in children (which I had occasion just to mention, section 108) is but an appetite after knowledge, and therefore ought to be encouraged in them, not only as a good sign, but as the great instrument nature has provided to remove that ignorance they were born with, and which, without this busy inquisitiveness, will make them dull and useless creatures. The ways to encourage it, and keep it active and vigorous, are, I suppose, these following: 1. Not to check or discountenance any inquiries he shall make, nor suffer them to be laughed at; but to answer all his questions, and explain the matters he desires to know, so as to make them as much intelligible to him. as suits the capacity of his age and knowledge... Mark what 'tis his mind aims at in the question, and not what words he expresses it in... For knowledge to the understanding is acceptable as light to the eyes: and children are please and delighted with it exceedingly, especially if they see that their inquiries are regarded, and that their desire of knowing is encouraged and commended. And I doubt not, but one great reason why many children abandon themselves wholly to silly sports; and trifle away all their time in trifling, is, because they have found their curiosity balked, and their inquiries neglected…
167. ...In teaching of children this too, I think, it is to be observed, that in most cases, where they stick, they are apt to be farther puzzled, by putting them upon finding it out themselves… Therefore, wherever they are at a stand, and are willing to go forward, help them presently over the difficulty, without any rebuke or chiding; remembering, that where harsher ways are taken, they are the effect only of pride and peevishness in the teacher, who expects children should instantly be masters of as much as he knows: whereas he should rather consider that his business is to settle in them habits, not angrily to inculcate rules, which serve for little in the conduct of our lives; at least are of no use to children, who forget them as soon as given. ...The great use and skill of a teacher is to make all as easy as he can....Passionate words or blows from the tutor, fill the child's mind with terror and affrightment, which immediately takes it wholly up, and leaves no room for other impressions....
180. ...But in this, as in all other parts of instruction, great care must be taken with children, to begin with that which is plain and simple, and to teach them as little as can be at once, and settle that well in their heads, before you proceed to the next, or anything new in that science.
Give them first one simple idea, and see that they take it right, and perfectly comprehend it, before you go any farther; and then add some other simple idea, which lies next in your way to what you aim it; and so proceeding by gentle and insensible steps, children, without confusion and amazement, will have their understandings opened, and their thoughts extended, farther than could have been expected. And when any one has learned any thing himself, there is no such way to fix it in his memory, and to encourage him to go on as to set him to teach it others.
Reflection Question
What are Locke's principal views about the ends and means of education?
Attributions
- You can find a complete version of this book on its WikiSource page.
- A special thanks to A. Legrand Richards for his assistance in selecting the texts for this abridgment.


12.4: Cutting and Pasting DNA- Restriction Digests and DNA Ligation
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- Ying Liu
- City College of San Francisco
Restriction Enzymes
Many bacteria have enzymes that recognize specific DNA sequences (usually 4 or 6 nucleotides) and then cut the double stranded DNA helix at this sequence (Figure \(\PageIndex{7}\)). These enzymes are called site-specific restriction endonucleases , or more simply “ restriction enzymes ”, and they naturally function as part of bacterial defenses against viruses and other sources of foreign DNA. To cut DNA at known locations, researchers use restriction enzymes that have been purified from various bacterial species, and which can be purchased from various commercial sources. These enzymes are usually named after the bacterium from which they were first isolated. For example, EcoRI and EcoRV are both enzymes from E. coli . EcoRI cuts double stranded DNA at the sequence GAATTC, but note that this enzyme, like many others, does not cut in exactly the middle of the restriction sequence (Figure \(\PageIndex{8}\)). The ends of a molecule cut by EcoRI have an overhanging region of single stranded DNA, and so are sometimes called sticky-ends . On the other hand, EcoRV is an example of an enzyme that cuts both strands in exactly the middle of its recognition sequence, producing what are called blunt-ends , which lack overhangs.
DNA Ligation
The process of DNA ligation occurs when DNA strands are covalently joined, end-to-end through the action of an enzyme called DNA ligase . Sticky-ended molecules with complementary overhanging sequences are said to have compatible ends , which facilitate their joining to form recombinant DNA. Likewise, two blunt-ended sequences are also considered compatible to join together, although they do not ligate together as efficiently as sticky-ends. Note: sticky-ended molecules with non-complementary sequences will not ligate together with DNA ligase. Ligation is therefore central to the production of recombinant DNA, including the insertion of a double stranded DNA fragment into a plasmid vector.


12.3: Contract Components
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- Stuart H. Bartholomew
- Virginia Polytechnic & State University via Virginia Tech Libraries' Open Education Initiative
Learning Objectives
- Owner-contractor contracts
- Fixed-price, competitively bid contracts
- Standard forms-of-contract
- Federal government construction contract
- AIA contracts
- EJCDC contract
- State highway department contracts
- Other agency contracts
- One-of-a-kind contracts
- Bidding documents
- General conditions
- Supplementary conditions
- Specifications
- Drawings or plans
- Reports of investigations of physical conditions
Continuing the overview of construction-related prime contracts presented in Chapter 3, this chapter focuses on the particular construction-related prime contract of interest to construction contractors—that is, owner–contractor contracts for construction services. This focus will be concentrated even further by confining the discussion to fixed-price contracts arrived at by competitive bidding.
Generally, someone who is knowledgeable and comfortable operating in the competitively bid, fixed-price contract environment usually finds little difficulty when operating under other forms of construction contracts. The reverse is not always true.
Standard Forms of Contract
A number of standard forms-of-contract for fixed-price, competitively bid prime construction contracts are widely used today. A discussion of the more prominent of these follows.
Federal Government Construction Contract
Foremost among standard forms-of-contract is the federal government construction contract . This form of contract is normally used by all branches of the federal government for construction work. Prominent examples of different federal agencies using this contract include the General Services Administration, the Bureau of Reclamation, the U.S. Army Corps of Engineers, the U.S. Navy Facilities Engineering Command, the U.S. Bureau of Public Roads, and the National Park Service. The actual contracts, depending on the particular federal agency, all differ slightly in the wording of the basic provisions, and the titles used for the contract document divisions vary. However, the contracts are of the same type and contain the same basic provisions.
A typical instance where this form-of-contract was used is the U.S. Army Corps of Engineers Lock and Dam No. 26 project on the Mississippi River. This immense public works project. north of St. Louis, Missouri, involved a series of major contracts beginning in the early 1980s. Bids were taken for the third contract of the series on August 23, 1985, three to four months after it was advertised, so that bidding contractors would have time to prepare their fixed-price bids. The bidding documents consisted of two four-inch-thick volumes of technical specifications, four two-inch-thick volumes of drawings, and seven or eight extensive addendums, each of which made numerous changes in all of the other documents, including previously issued addendums. Obviously, preparing a fixed-price bid for this contract was a complicated matter requiring hundreds of hours. Smaller projects entail fewer documents and require less effort to prepare a bid. But regardless of the size of the federal project, the essential contract provisions under which the project is to be built will be the same. The larger, fixed-price federal contracts that contain a schedule of bid items are the most complex and offer the best example of the variety of problems that can occur. Five bids were received for this Lock and Dam No. 26 contract, ranging from a low bid of $227 million to a high of $288 million.
American Institute of Architects Contracts
A second important standard form-of-contract is the American Institute of Architects (AIA) Standard Form of Agreement Between Owner and Contractor . The two companion documents necessary to form the complete contract are AIA Form A-101 and AIA Form A-201. This contract is by far the most widely used form for fixed-price building construction work in both the public and private sectors, particularly the private sector. Entire texts have been written by legal scholars on this particular contract. [1]
Associated General Contractors Contracts
The AGC Standard Form Prime Contract Between Owner and Contractor is recommended for use by the Associated General Contractors of America (AGC). This contract is commonly used on private work and is suitable for both building construction and engineered construction projects. Its usage is less broad than that of the AIA contract.
Engineers Joint Contract Documents Committee Contract
Another form-of-contract, the Engineers Joint Contract Document Committee (EJCDC) Contract , is used primarily for engineered construction in the private sector. Its use has also been endorsed by the Associated General Contractors of America.
State Highway Department Contracts
Another broad class of competitively bid, fixed-price contracts consists of the state highway department contracts of the various states. These contracts tend to be similar in format, no doubt because the construction work within each state is similar. The influence of the Federal Highway Administration (FHWA) has forced this similarity. The format usually consists of an infrequently published “bible,” which contains all general provisions and standard technical specifications of the state. Often a revision manual will be periodically published with changes. Then, in addition to the “bible” and its revision manual, each particular project will have its own set of “special provisions” that apply to that particular project. The special provisions contain site-specific provisions and information and any further changes to the “bible” as it relates to that specific project. The technical requirements of these state highway department contracts tend to be similar, even though some general provisions may vary. These contracts, like most others, are written by the owner agencies. From the standpoint of the legal rights afforded the contractor, these contracts vary considerably. Contractors who bid frequently in a particular state are aware of the provisions of that state’s contract and know what to expect.
Other Agency Contracts
Many other agencies traditionally build infrastructure systems over time through a series of recurring contracts for similar construction work. Examples are the rapid transit districts and water and sewer districts of the large metropolitan centers, as well as state agencies (other than highway departments), such as the California Department of Water Resources and the California Department of Architecture. Each agency tends to create its own unique form of prime construction contract, often based on the federal government contract, which it then uses over and over. Construction contractors who frequently bid to one or more of these agencies become familiar with the terms of the particular form that each agency uses.
One-of-a-Kind Contracts
Occasionally, contracts are created for a particular project. These one-of-a kind contracts tend to vary widely. Little about them is standard or traditional, either in format or detailed provisions. Since contracting parties can agree to anything that is not contrary to law, these isolated, individual, one-of-a-kind contracts can take almost any hybrid form that the parties concoct. They are limited only by the imagination of the parties who draft them, each of whom attempts to secure the most favorable agreement possible from that party’s point of view. Disputes that arise from one-of-a-kind contracts are usually more difficult to resolve because there is no past pattern of experience, as is the case with one of the “tried-and-true” standard forms-of-contract.
Typical Documents Comprising the Contract
Fixed-price, competitively bid contracts are comprised of certain, fairly typical documents. With the exception of one-of-a-kind contracts, the major categories of most contracts of this type consist of the following list:
- Bidding documents, consisting of the “Invitation to Bid,” the “Instructions to Bidders,” and the “Bid Form”
- General Conditions of Contract
- Supplementary Conditions of Contract
- Specifications
- Drawings
- Reports of investigations of physical conditions
Some contracts may not contain all of these categories but, with the exception of one-of-a-kind contracts, none is likely to contain material that won’t logically fit into one category or another.
Bidding Documents
The first category, bidding documents , normally begins with an advertisement , originally discussed in Chapter 1. The back section of contemporary industry periodicals, such as the Engineering News Record , contains a plethora of bid advertisements with every new issue. The advertisement identifies the project for which bids are desired, the owner, the time and place of the bid opening, and instructions to potential bidders on how to obtain a full set of contract documents.
The second document in the bidding group is usually the Invitation for Bids (IFB) or, sometimes, a Request for Proposals (RFP) . The federal government and some other owners use the IFB when bidders must strictly conform to the drawings and specifications and the RFP when bidders may propose variations for the project. Both typically include the following:
- A description of the contract work
- The identity of the owner
- The place, date, and precise time of the bid opening
- The penal sum of the required bonds (bid bond, performance bond, and labor and material payment bond) [2]
- A description of the drawings and specifications, their cost, and where they may be obtained
- The length of time after bid opening that bids will be deemed good (duration of bids)
- Rules regarding the withdrawal or modification of bids and late bids
- Information regarding any planned pre-bid conferences and pre-bid site inspections
- Particular requirements of law of which the owner wants bidders to be aware
- Any special instructions, other requirements, or other information that the owner wants to point out to bidders
In addition to the IFB or RFP, the contract documents may also contain a section called Instructions to Bidders . When used, this section is an adjunct to the instruction portion of the IFB or RFP. Sometimes all necessary instructions are contained within the IFB or RFP, and there is no separate Instructions to Bidders section. More logically, the Instructions to Bidders is a separate document, and the IFB or RFP contains all of the other necessary but noninstructional information that a bidder needs.
In every case, the contract documents contain the Bid Form . Bidders complete this document, sign, seal, and turn it in at the appointed place, prior to the deadline set for the submittal of bids. The fully executed Bid Form constitutes the “offer” element necessary for contract formation, discussed in Chapter 2. Note that the Bid Form must be completely filled out, signed, and sealed, all in accordance with the IFB or RFP and the Instructions to Bidders to constitute a responsive bid. The con tents of the Bid Form usually include the following:
- A definitive statement of the general terms and conditions of the offer. This statement is normally unilaterally determined by the owner and is preprinted on the form.
- The format of the commercial terms applying to the offer. Again, this format is normally determined unilaterally by the owner either as a single lump sum total price or as a schedule of bid-item prices. In the first case, the bid form contains a single blank space in which the bidder is instructed to enter a single lump sum price for the entire project. In the second case, the form contains a numbered series of all bid items for the project, each consisting of a description of the work for discrete parts of the project and either blanks for unit prices and extensions against a preprinted quantity of work or a single blank for a lump sum price. The total bid in this case is the sum of the unit price extensions and lump sum prices. With either a single lump sum format or a schedule-of-bid-items format, the bidder fills in the blanks for defining the precise commercial terms of the bid.
- Supplementary information that the owner may want to know about the bidder. This usually consists of information about the bidder’s financial strength and past experience.
- Additional information for federal bids. The bid form for federal contracts contains a number of “Certifications and Representations” in affidavit form, such as noncollusion and nonsegregated facilities affidavits, required to comply with federal law.
- Affirmative action requirements for public projects. Bid Forms for public projects usually require written goals and timetables for meeting the requirements of equal opportunity legislation and minority business enterprise/women business enterprise requirements.
- Bid security. Finally, the Bid Form must contain the required bid security, usually in the form of a bid bond issued by an approved surety. Sometimes, a certified check must be presented for the bid security.
Oddly enough, private sector bids often require much more supplementary information on the Bid Form than do public sector bids. And, among public projects, Bid Forms for federal contracts usually require less supplementary information than the average.
A final interesting point concerning bidding documents is that the AIA approach excludes the bidding documents from the contract. Article 1 of AIA A-201, General Conditions of the Contract for Construction, states:
The Contract Documents do not include Bidding Documents such as the Advertisement or Invitation to Bid, the Instructions to Bidders, sample forms, the Contractor’s Bid or portions of Addenda relating to any of these, or any other documents, unless specifically enumerated in the Owner–Contractor Agreement.
Why would the AIA wish to exclude the bidding documents from the contract? The rationale seems to be that the eventual contract is considered to be the end result of a negotiation, not the result of a binding firm-price bid. The bid is regarded as merely the starting point for the ensuing negotiation. Most other forms-of-contract include the bidding documents as part of the contract.
General Conditions of Contract
The second section of the documents that normally comprise the contract is the General Conditions of Contract , often referred to simply as the General Conditions , or sometimes, General Provisions . Here are found very definitive statements, clause by clause, of all general terms and conditions that govern the performance of the contract work. In the case of the federal government and other agencies that frequently contract for construction work, the general concept of this section of the documents is to include all clauses that will remain the same, contract after contract, changing very infrequently. Many of these standard clauses in federal contracts pertain to the requirements of the Federal Acquisition Regulations, which by law must be included in every federal construction contract.
Supplementary Conditions of Contract
In addition to the General Conditions or General Provisions, most construction contracts contain a section called Supplementary Conditions or Special Conditions . The idea of this section is to include clauses dealing with general matters that apply to the instant contract only—that is, those that are either site-specific or in some other way apply only to the specific contract. Such matters might better be called “project-specific” matters. Some forms of contract do not have a Special (or Supplementary) Conditions section. Instead they include all general matters, whether standard or project-specific, in the General Provisions section. It is also common to include general project-specific matters in Division 1 of the Specifications section. In the Uniform Construction Index (UCI) form of technical specifications, which is widely used, Division 1 is titled “General Requirements.” Thus, to be entirely sure that nothing of a general nature has been overlooked in a particular case, it is necessary to carefully read the General Conditions, the Supplementary Conditions (if included), and Division 1 of the Technical Specifications.
One important area of the Supplementary Conditions for contracts where federal funds are involved is the Davis-Bacon Wage Determination originally discussed in Chapter 1. By federal law, wages paid the workers on any such project must be at least as high as listed in the Davis-Bacon Determination for each trade classification involved in the work. Even where federal funds are not required, many states require that prevailing wages be paid on public work. These rates are set by a commissioner on a project-to-project basis at a level he or she has determined through investigation to equal the “prevailing” wage for each classification of work in the locality of the project. This determination is obviously significant to contractors interested in submitting a bid. For example, if the determination is set at low “open-shop” rates, potential bidding contractors, bound by union labor agreements that require payment of higher rates, know that they are competing at a disadvantage and might be well advised not to bid at all. On the other hand, if the Davis-Bacon commissioner has determined the “prevailing” rates to be union labor agreement rates, all bidders are on a more equal footing. Open-shop or merit-shop contractors will have to pay the same rates as union contractors.
Specifications
The technical requirements for each division of work in the contract will be completely detailed in that section of the contract document called the Specifications . The format usually conforms to the Uniform Construction Index, which is understood by virtually every segment of the industry. Depending on size of contract, the Specifications can be voluminous. It is necessary that completely definitive requirements be carefully stated so that both parties to the contract have a mutual understanding of the precise technical standards the project work must meet.
Drawings
The next important section of the contract documents is the Drawings , which complement the Specifications. The Drawings must be sufficiently complete to adequately show exactly what is to be built. Certain features of the work may be shown in fairly general terms, with the requirement stated that the contractor must prepare detailed shop drawings that conform to and augment the general contract drawings. These must be submitted to the owner or the owner’s engineer for approval prior to fabrication of the material covered by the shop drawings. For example, a contractor may supply detailed bar-bending schedules and placing drawings for reinforcing steel and structural steel fabrication and erection drawings, including the connections. However, the basic contract drawings advertised for fixed-price bids must be sufficiently clear and accurate so that, if contractors carefully conform to them, a satisfactorily constructed product will result. If either the Drawings or Specifications do not meet this standard, the owner may incur severe liability under the Spearin Doctrine, which is discussed in Chapter 13.
Reports of Investigations of Physical Conditions
An additional and final section that may or may not be included as an integral part of the contract documents consists of various reports of investigations of physical conditions at the project site. These reports often concern geotechnical aspects of subsurface soil or rock conditions. They usually appear in the form of written evaluations and soil boring logs describing subsurface conditions. Other examples are weather records and, in the case of projects on or near streams and rivers, stream flow hydrographs. These reports are probably the more common examples of this type of information, but basically any included information describing physical conditions at the site falls into this category. A more detailed discussion of these kinds of reports and whether or not they are considered to be part of the contract is included in Chapter 5.
Conclusion
This chapter focused on the format and the general contents of the major component sections of prime contracts between owners and general contractors for the performance of construction work. The prominent forms-of-contract commonly used today were also briefly discussed.
Chapter 5 will show why contractors need to understand the nature of the potential contract before they commit to any particular construction project. Also, the details of the critical or “red flag” clauses contained in such contracts will also be analyzed from the point of view of the bidding contractor.
Questions and Problems
- What is the historic, traditional form of contract upon which the present-day construction industry is based? What are the seven forms of contract discussed in this chapter? Why might a one-of-a-kind contract cause later trouble?
- What major categories could you expect to find in the documents particularly related to bidding for a typical competitively bid fixed-price contract and what type of information or requirements are contained in each? Would every set of contract documents be likely to contain a General Conditions section? A Supplementary or Special Conditions section? In what three possible places in a set of typical contract documents would you look to be certain that all matters of general importance (other than technical matters and details on the drawings) were examined and noted? Which document part defines the offer element necessary for contract formation?
- Why is the Davis-Bacon Determination important in a set of contract documents? Where would you expect to find it? Would documents for every project be expected to contain a Davis-Bacon Determination? If not, in which category of projects would you expect to find it?
- What is the attitude concerning bidding documents held by the AIA? Do most other forms of contract reflect the AIA attitude? Questions 5 and 6 assume that the reader has access to a set of typical federal contract documents for an actual project and to AIA Document A-201 (General Conditions of Contract).
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With respect to the federal contract, determine the following and cite the section of the documents from which you obtained the answer (place the appropriate abbreviation from the following list in parentheses at the end of each answer):
[table id=1 /]- What is the date and time of bid opening?
- What is the penal sum of the required performance bond?
- Will there be a pre-bid conference?
- What is the number of days that bids must be held open for acceptance?

- Do bidders have to certify that they do not maintain segregated facilities?
- How many milestone completion dates are there?
- What is the amount of liquidated damages for each day that each milestone is late?
- Is there a clause pertaining to suspension of work?
- Does the government have the right to occupy a completed part of the work?
- Is there a clause dealing with variations in work quantities?
- What is the date of the Davis-Bacon Determination?
- How long does the contractor have to perform the entire project?
- How many bid items are there?
- Is there a clause pertaining to changes in the work?
- Is there a clause dealing with differing site conditions?
- How often can the contractor expect to receive progress payments?
- Is there a clause pertaining to default terminations and excusable delay?
- Is there a clause for termination of the contract for the convenience of the government?
- Is there a clause concerning contract disputes?
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With respect to the AIA document A-201 (General Conditions of Contract), determine the following and indicate where in the document you obtained the answer. At the end of each answer, cite the source in the document by writing in parentheses the article and subarticle.
- Is the owner empowered to stop the work?
- Is the owner empowered to terminate the contract?
- Does this form of contract contemplate or imply a fixed time for completion of the work?
- Is the contractor required to indemnify and hold harmless the owner?
- Does this contract contemplate changes in the work?
- Does this contract provide relief for the contractor’s failure to perform due to conditions beyond the contractor’s control?
- Does this contract provide that either the owner or contractor can make a claim against the other for damages suffered?
- Is the contractor likely to be liable to the owner for damages caused by late completion?
- Does the contract contain the equivalent of the differing site conditions clause found in a federal contract?
- Is the contractor required to carry insurance?
- Does the contract imply that there could be payments made to the contractor by the owner in the event of owner-caused delays?
- Does the contract provide for progress payments?


13.3: Venn Diagrams
To visualize the interaction of sets, John Venn in 1880 thought to use overlapping circles, building on a similar idea used by Leonhard Euler in the 18 th century. These illustrations now called Venn Diagrams .
A Venn diagram represents each set by a circle, usually drawn inside of a containing box representing the universal set. Overlapping areas indicate elements common to both sets.
Basic Venn diagrams can illustrate the interaction of two or three sets.
Create Venn diagrams to illustrate \(A \cup B, A \cap B,\) and \(A^{c} \cap B\)
\(A \cup B\) contains all elements in either set.
\(A \cup B\) contains all elements in either set.
\(A \cap B\) contains only those elements in both sets - in the overlap of the circles.
Use a Venn diagram to illustrate \((H \cap P)^{c} \cap W\)
We'll start by identifying everything in the set \(\mathrm{H} \cap P\)
Now, \((H \cap P)^{c} \cap W\) will contain everything not in the set identified above that is also in set \(W\)
Create an expression to represent the outlined part of the Venn diagram shown.
The elements in the outlined set are in sets \(\mathrm{H}\) and \(F\), but are not in set \(W\). So we could represent this set as \(H \cap F \cap W\)
Create an expression to represent the outlined portion of the Venn diagram shown
- Answer
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\(A \cup B \cap C^{c}\)


12.3: Reparations
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- Erika Gutierrez, Janét Hund, Shaheen Johnson, Carlos Ramos, Lisette Rodriguez, & Joy Tsuhako
- Long Beach City College, Cerritos College, & Saddleback College via ASCCC Open Educational Resources Initiative (OERI)
Racism has caused tremendous harm to many racial and ethnic groups in the United States. Many argue that in order to advance equity, this harm merits a response. One proposed solution involves providing compensation for victims of racism. Reparations refers to the act of repairing damage and providing restitution for past harms. One example of reparations in the United States is the Civil Liberties Act of 1988, which acknowledged that a great injustice had been committed against Japanese Americans when they were interned during World War II. The act mandated that Congress pay each living victim of internment $20,000 in reparations.
Although most of the discussion around reparations is focused on the financial aspect, it is important to note that there are other very important components to a program of reparations. The first of these is recognition. Recognition involves society’s acknowledgment of the anger, hurt, injustice and material loss caused by racism, and how these wrong doings continue to affect people’s lives today (Yamamoto, 2009). This recognition extends to the specific experiences of racial and ethnic groups in the United States, such as how African Americans feel about slavery, Native Americans about genocide, and Japanese Americans about internment.
The second component of reparations is responsibility. This involves acknowledging that someone is responsible for the harms inflicted on racial and ethnic groups in the United States (Yamamoto, 2009). The question of responsibility often comes up with regard to slavery. Who is responsible? Individual slave owners? Their descendants? The United States government? Many are calling for reparations for African Americans. Proponents claim this would not only address the harms of slavery, but also of Jim Crow laws and ongoing discrimination in employment, housing, education, the criminal justice system etc. Opponents argue that descendants of enslaved people did not experience the oppression of slavery, noting that reparations were given to Japanese American survivors of internment during WWII, not their descendants. Another argument against reparations suggests that reparations for one group (e.g. African Americans) will open up the door for other groups (e.g. Native Americans and Mexican Americans, groups who lost land during the expansion of Manifest Destiny).
Finally, there is the question of the reparations themselves. These reparations could take the form of direct cash transfers. However, reparations do not only have to mean sending checks. In fact, many argue that reparations in the form of a one time payment, will not address the systemic barriers that continue to impact people of color. Reparations could also involve any or all of the following:
- Full and free access to college education
- Guaranteed minimum livable income
- Community development funds
- Land grants
- Construction of monuments and museums honoring the history of communities of color
- Legislation mandating ethnic studies curriculum
- Legislation that requires the government to acknowledge racial injustice and execute a plan to address its impact
According to The Movement for Black Lives , "The government, responsible corporations and other institutions that have profited off of the harm they have inflicted on Black people — from colonialism to slavery through food and housing redlining, mass incarceration, and surveillance — must repair the harm done" (2021). The harm inflicted on Black Americans ranges from the TransAtlantic Slave Trade to chattel slavery (intergenerational slavery for life) to Jim Crow to the War on Drugs to police terror/violence to redlining to poverty to health inequities to unemployment to incarceration (The Movement for Black Lives, 2021).
In The Case for Reparations , TaNehisi Coates writes,
What I’m talking about is more than recompense for past injustices—more than a handout, a payoff, hush money, or a reluctant bribe. What I’m talking about is a national reckoning that would lead to spiritual renewal. Reparations would mean the end of scarfing hot dogs on the Fourth of July while denying the facts of our heritage. Reparations would mean the end of yelling “patriotism” while waving a Confederate flag. Reparations would mean a revolution of the American consciousness, a reconciling of our self-image as the great democratizer with the facts of our history...But I believe that wrestling publicly with these questions matters as much as—if not more than—the specific answers that might be produced. An America that asks what it owes its most vulnerable citizens is improved and humane. An America that looks away is ignoring not just the sins of the past but the sins of the present and the certain sins of the future. More important than any single check cut to any African American, the payment of reparations would represent America’s maturation out of the childhood myth of its innocence into a wisdom worthy of its founders.
In this expose, Coates reminds the reader that Representative John Conyers introduced (for 25 years straight) a bill, now called House Resolution 40 or the Commission to Study Reparation Proposals for African Americans Act, to study slavery and its lingering effects was never even voted on in Congress. Sponsored most recently in 2019 by Representative Shelia Jackson Lee, this bill has never received a vote. Coates has questioned why. Why couldn't a bill simply to study reparations ever get to a vote, let alone be passed?
Perhaps the racial reckoning appeals from the summer 2020 multiracial protests throughout the U.S. (and the world) against the police killing of George Floyd may usher into the U.S. a similar kind of response that Germany provided post WWII. Despite initial resistance to provide reparations for the inhumane harm inflicted upon Jewish people by Nazi Germany, Germany ultimately provided billions of dollars of reparation payments to Israel in the two decades following the end of the Nazi occupation (Coates, 2014). Though such reparations could never make up for the atrocious murder of more than 6 million people, Coates offers, "They did launch Germany's reckoning with itself, and perhaps provided a road map for how a great civilization might make itself worthy of the name."
Contributors and Attributions
- Rodriguez, Lisette. (Long Beach City College)
- Tsuhako, Joy. (Cerritos College)
Works Cited
- Coates, T. (2014, June). The case for reparations. The Atlantic.
- The Movement for Black Lives. (2021). Policy Platforms: Reparations. The Movement for Black Lives.
- Yamamoto, E. (2009). Interracial Justice: Conflict and Reconciliation in Post Civil Rights America . New York: New York University Press.


2 .
In a scenario where a laboring person has a contracted pelvis (passage), how might this impact the powers (contractions) and the overall birthing process? What actions would you take as a nurse?
3 .
During the late active phase of the first stage, a laboring person expresses feeling overwhelmed and anxious. How would you adapt your communication and support strategies to address their emotional needs?
4 .
A laboring person exhibits prolonged bleeding during the third stage of labor. How would you differentiate between normal uterine contractions and potential postpartum hemorrhage? What immediate actions would you take?
5 .
A laboring person in the active phase of the first stage appears fatigued and anxious. As an attending nurse, how would you explain the physiologic changes contributing to their fatigue, and what nursing interventions might address both physical and emotional aspects?
6 .
A postpartum person complains of chills and diaphoresis within the first hour after birth. How would you explain the physiologic changes contributing to these symptoms, and what nursing interventions might provide comfort?
7 .
A laboring person in the active phase of the first stage becomes increasingly anxious and requests pain medication despite initially planning for a natural birth. As a nursing student, how would you explain the psychologic changes contributing to this shift, and what nursing interventions might address the patient’s evolving emotional state?


13.3: Hermeneutic Analysis
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Hermeneutic analysis is a special type of content analysis where the researcher tries to ‘interpret’ the subjective meaning of a given text within its sociohistoric context. Unlike grounded theory or content analysis—which ignores the context and meaning of text documents during the coding process—hermeneutic analysis is a truly interpretive technique for analysing qualitative data. This method assumes that written texts narrate an author’s experience within a sociohistoric context, and should be interpreted as such within that context. Therefore, the researcher continually iterates between singular interpretation of the text (the part) and a holistic understanding of the context (the whole) to develop a fuller understanding of the phenomenon in its situated context, which German philosopher Martin Heidegger called the hermeneutic circle . The word hermeneutic (singular) refers to one particular method or strand of interpretation.
More generally, hermeneutics is the study of interpretation and the theory and practice of interpretation. Derived from religious studies and linguistics, traditional hermeneutics—such as biblical hermeneutics —refers to the interpretation of written texts, especially in the areas of literature, religion and law—such as the Bible. In the twentieth century, Heidegger suggested that a more direct, non-mediated, and authentic way of understanding social reality is to experience it, rather than simply observe it, and proposed philosophical hermeneutics , where the focus shifted from interpretation to existential understanding. Heidegger argued that texts are the means by which readers can not only read about an author’s experience, but also relive the author’s experiences. Contemporary or modern hermeneutics, developed by Heidegger’s students such as Hans-Georg Gadamer, further examined the limits of written texts for communicating social experiences, and went on to propose a framework of the interpretive process, encompassing all forms of communication, including written, verbal, and non-verbal, and exploring issues that restrict the communicative ability of written texts, such as presuppositions, language structures (e.g., grammar, syntax, etc.), and semiotics—the study of written signs such as symbolism, metaphor, analogy, and sarcasm. The term hermeneutics is sometimes used interchangeably and inaccurately with exegesis , which refers to the interpretation or critical explanation of written text only, and especially religious texts.
Finally, standard software programs, such as ATLAS.ti.5, NVivo, and QDA Miner, can be used to automate coding processes in qualitative research methods. These programs can quickly and efficiently organise, search, sort, and process large volumes of text data using user-defined rules. To guide such automated analysis, a coding schema should be created, specifying the keywords or codes to search for in the text, based on an initial manual examination of sample text data. The schema can be arranged in a hierarchical manner to organise codes into higher-order codes or constructs. The coding schema should be validated using a different sample of texts for accuracy and adequacy. However, if the coding schema is biased or incorrect, the resulting analysis of the entire population of texts may be flawed and non-interpretable. However, software programs cannot decipher the meaning behind certain words or phrases or the context within which these words or phrases are used—such sarcasm or metaphors—which may lead to significant misinterpretation in large scale qualitative analysis.