EMP. When both CO 2 and TSI are included, the model accounts for R 2 = 0.764 of the variability in GISTEMP. The slope for CO 2 is 1.15°C per 100 ppm of CO2, given that TSI is already in the model. This slope estimate means that over the time period of the data, the average increase in GISTEMP has been 1.15°C for each 100 ppm of CO 2 added to the atmosphere. The p-value shows that the relationship between C O 2 and GISTEMP is strong and not likely due to chance. The slope for TSI versus GISTEMP is positive 8.05 x 1/100°C per W/m2, given that CO 2 is in the model. This agrees with the physical science expectation that increasing TSI should increase GISTEMP. As the two-sided p-value of 0.104 is not small, these data provide insufficient evidence to exclude random variation as the source of the observed positive value for the slope. Still, this example illustrates the important insight that unless the carbon dioxide variable is present in the model, the positive effect of increasing temperature for increasing solar irradiance cannot even be detected. Accordingly, this example serves to illustrate the meaning of the slope coefficients in a multiple regression.  Table 2 and can be used as appropriate regression diagnostics for an introductory class in statistics. Figure 13 is a simple histogram showing the distribution of the residuals for the multiple regression model displayed in Table 2. As in all ordinary least squares regressions, the mean of the residuals is zero. The residual standard error from Table 2 is 9.204. From the five-number summary below Figure 13, the residual IQR = 12.74. The residual distribution in Figure 13 has an IQR = 12.74/9.2 = 1.385 standard deviations. For comparison, the IQR of the normal distribution is 1.35 standard deviations and the IQR of the continuous uniform is 1.73 standard deviations.
(Note that for the uniform, standard deviation = range/√12 and IQR = range/2.) Although the residual distribution in Figure 13 shows some asymmetry, half of the residuals are below zero, half above zero. The upper and lower quartiles are approximately equidistant from the zero mean as are the minimum and maximum. There is almost no skew visible in the Figure 13 histogram. No residual is greater than 2 standard deviations from the mean. Based on these observations from Figure 13, the distribution of residuals appears to be roughly normal. Figure 14 is a time series plot of the residuals. It does not show any obvious serial dependence over time. If the assumption of independent residuals is more fully addressed in an introductory statistics course, the Durbin-Watson statistic D can be used in time series examples such as this one. For the residuals from the model in Table 2, D= 1.94, near the expected value of E(D) = 2 when the underlying distribution is independent. This supports the visual finding from Figure 14 of no serial dependence. Figure 15 is a graph of the residuals as a function of predicted GISTEMP. It is intended to address possible violation of the assumption of constant variance across predictors in a multiple regression model. It reveals no obvious pattern to the variance of the residuals such as a trumpet or reverse trumpet. Although not included in this paper, the two scatterplots of the residuals vs. each independent variable, CO2 and TSI, showed no pattern indicating that the constant variance assumption has been violated.
From Figure 12, the correlation between the two independent variables TSI and CO 2 is -0.543. This correlation can be used to determine the effect of collinearity on the precision of the slope estimates. According to Stine and Foster (2011, p. 612), an introductory statistics text with an insightful treatment of regression, "The variance inflation factor (VIF) quantifies the amount of unique variation in each explanatory variable and uses this to summarize the effect of collinearity." In this regression model with only two independent variables, the effect of collinearity can easily be summarized by calculating VIF from the correlation between TSI and CO 2 : VIF = 1/(1 -r 2 ) = 1.42 where r = -0.543 is the correlation. The square root of the VIF is 1.19 meaning that the standard error of the coefficients for TSI and CO 2 are increased by a factor of 1.19 from the value they would have had if TSI and CO 2 were uncorrelated. Stine and Foster (2011, p. 613) recommend "Generally, finding VIF > 5 or 10 suggests our variables are highly redundant and that the partial slopes will be difficult to interpret." With a VIF of 1.42, potential concerns about collinearity in this model give no reason to exclude one of the two variables.     In addition to data, some research papers in climate science geared to a wider audience are almost ready-made for use in introductory statistics. For instance, see the recent publication Hansen, Sato, and Ruedy (2012) at NASA. Hansen and his colleagues use graphs to show how the distribution of temperature extremes around the world has evolved over the last few decades. With graphs and summary statistics, they carefully explain that both the average and the variability of global temperature have increased. Here is a quote from the Author Summary of Hansen, Sato and Ruedy (2012). "We illustrate variability of seasonal temperature in units of standard deviation (σ), including comparison with the normal distribution ("bell curve") that the lay public may appreciate. The probability distribution (frequency of occurrence) of local summer-mean temperature anomalies was close to the normal distribution in the 1950s, 1960s, and 1970s in both hemispheres. However, in each subsequent decade the distribution shifted toward more positive anomalies, with the positive tail (hot outliers) of the distribution shifting the most." This paper illustrates well how teachers of introductory statistics can choose from many interesting examples as climate scientists strive to make their work more accessible.

Conclusion
Weather is the temperature, precipitation, atmospheric pressure and wind speed at one location on the earth at one point in time. Climate is the distribution of these variables for an entire region across time. While students can understand weather with no knowledge of statistics, climate is inherently a statistical concept. Because climate change is a topic of interest for many students today, teachers of introductory statistics can use the wealth of available climate data to motivate students to see that statistics can help them better understand their world.
This paper presents two examples of data sets from climate science that can be understood by students in an introductory statistics course. The first shows how the trend in Arctic sea ice data can be well-represented with a quadratic regression. This example has been used successfully by the author in introductory statistics for undergraduate business majors and MBAs for the past three years. The second example shows that solar irradiance alone does not explain global surface temperature change over the last three decades but the increasing atmospheric concentration of CO 2 does explain three-fourths of the variability in temperature. The second example also shows that the sign of slope of temperature versus solar irradiance agrees with the known physical relationship between the two variables only when atmospheric CO 2 concentration is also included in the model. This example is a little more advanced but has been well-received in MBA level statistics classes. For undergraduates, it can be used omitting the multiple regression with both explanatory variables. Of course this paper only brushes the surface using a few climate data sets. Other climate data sources were listed so that statistics teachers can construct other such examples.

Sea Ice
Since 1979, satellites have continuously measured the extent of sea ice in the Arctic Ocean. Daily numbers are averaged to get the monthly sea ice extent for each month.
This Sea Ice Data includes 34 observations with 2 variables.NEVER before since the launch of the Newspaper Awards back in 1997 have we had such a magnificent early response following the announcement of the call for entries.
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