A real estate agent wanted to develop a model to predict the selling price of a house. The agent believed that the most important variables in determining the price (Y) of a house are its size (X1) and the number of bedrooms (X2). The agent randomly selected 100 homes that were recently sold and recorded the selling price, the size (in squares) and the number of bedrooms. The agent, 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 55.97% of the variation in Y is due to the variations in X1 and X2, regression (ii) results show that 55.91% of the variation in Y is due to the variation in X1, and regression (iii) results show that 41.66% 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)