"""The sum of the squares of the lengths of the four sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals"" is known as what?"
Parallelogram law Parallelogram law In mathematics, the simplest form of the parallelogram law (also called the parallelogram identity) belongs to elementary geometry. It states that the sum of the squares of the lengths of the four sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals. Using the notation in the diagram on the right, the sides are ("AB"), ("BC"), ("CD"), ("DA"). But since in Euclidean geometry a parallelogram necessarily has opposite sides equal, or ("AB") = ("CD") and ("BC") = ("DA"), the law can be stated as, If the parallelogram is a rectangle, the
Explained sum of squares greater the ESS, the better the estimated model performs. If formula_1 and formula_2 are the estimated coefficients, then is the "i" predicted value of the response variable. The ESS is the sum of the squares of the differences of the predicted values and the mean value of the response variable: In some cases (see below): total sum of squares = explained sum of squares + residual sum of squares. The following equality, stating that the total sum of squares equals the residual sum of squares plus the explained sum of squares, is generally true in simple linear regression: Square both