Refer to the previous exercise.

(a) Find the partial correlation between y and x1, controlling for x2. Interpret the partial correlation and its square.

(b) Find the estimate of the conditional standard deviation, and interpret.

(c) Show how to find the estimated standardized regression coefficient for x1 using the unstandardized estimate and the standard deviations, and interpret its value.

(d) Write the prediction equation using standardized variables.

Interpret.

(e) Find the predicted z-score for a country that is one standard deviation above the mean on both explanatory variables. Interpret.