The marketing manager of a large supermarket chain would like to determine the effect of shelf space (in feet) on the weekly sales of international food (in hundreds of dollars). A random sample of 12 equal-sized stores is selected, with the following results: Store Shelf Space X Weekly Sales Y 1 10 2 2 10 2.6 3 10 1.8 4 15 2.3 5 15 2.8 6 15 3 7 20 2.7 8 20 3.1 9 20 3.2 10 25 3 11 25 3.3 12 25 3.5 Copy the above sample data to Excel, use Excel to run a regression analysis on this data set, and answer the following questions accordingly. You don't need to include the entire tables of the regression results in your answer. (1) What are the least squares regression coefficients of the Y-intercept (a) and slope (b)? (2) Predict the average weekly sales (in hundreds of dollars) of international food for stores with 12 feet of shelf space for international food. (3) Is it appropriate to predict the average weekly sales (in hundreds of dollars) of international food for stores with 28 feet of shelf space for international food? And why? (4) Identify the coefficient of determination (R square), and interpret its meaning. (5) What can you comment on the assumption of constant variance as interpreted using the residual plot generated by Excel? (2 points)