The manager of a chain of video rental stores plans to use a regression model to help select a location for a new store. She decides to use annual gross revenue as a measure of success, which is the dependent variable (Y). The manager believes that the two most determinants of success are: mean income of households within 1 km of the store (X1); and number of people living within 1 km of the store (X2). The manager randomly selects 50 video stores and records the values of each of the variables mentioned. The manager, before making her final decison, wants to determine which independent variable to include in the model, and thus she runs three different linear regression models:

(i) a regression of Y on X1 and X2;

(ii) a regression of Y on X1; and

(iii) a regression of Y on X2.

Regression (i) results show that 53.28% of the variation in Y is due to the variations in X1 and X2, regression (ii) results show that 51.55% of the variation in Y is due to the variation in X1, and regression (iii) results show that 3.03% of the variation in Y is due to the variation in X2.

Based on this information, answer the following questions showing all the necessary steps.

(a) At the 5% significance level, does each independent variable makes a significant contribution to the regression model? (8 marks)

(b) On the basis of your results in (a), which regression model is the most appropriate? (2 marks)