Derive the normal equations (Equations 5.7) for the least-squares coefficients of the general multiple-regression model with k explanatory variables. [Hint: Differentiate the sum-of-squares function...

Derive the normal equations (Equations 5.7) for the least-squares coefficients of the general multiple-regression model with k explanatory variables. [Hint: Differentiate the sum-of-squares function S(A; B₁; ... ; B_k
) with respect to the regression coefficients, and set the partial derivatives to 0.]

Show that in simple-regression analysis, the standardized slope coefficient B' is equal to the correlation coefficient r. (In general, however, standardized slope coefficients are not correlations and can be outside of the range [0, 1].)