You are given the following matrix of simple (product moment) correlations among a dependent variable Y (first variable) and three independent variables. (a) From inspection of the correlation matrix,...

You are given the following matrix of simple (product moment) correlations among a dependent variable Y (first variable) and three independent variables.

(a) From inspection of the correlation matrix, which independent variable would account for the greatest variability in Y? What proportion of the corrected sum of squares in Y would be accounted for by this variable? If Y were regressed on all three independent variables (plus an intercept), would the coefficient of determination for the multiple regression be smaller or larger than this proportion?

(b) Inspection of the three pairwise correlations among the X variables suggests that at least one of the independent variables will not be useful for the regression of Y on the Xs. Explain exactly the basis for this statement and why it has this implication.