An appraiser collected the data found in the file Appraiser.xlsx describing the auction selling price, diameter (in inches), and item type of several pieces of early 20th century metal tableware manufactured by a famous artisan. The item type variable is coded as follows: B = bowl, C = casserole pan, D = dish, T = tray, and P = plate. The appraiser wants to build a multiple regression model for this data to predict average selling prices of similar items. a. Construct a multiple regression model for this problem. (Hint: Create binary independent variables to represent the item type data.) What is the estimated regression function? If required, round your answers to one decimal place. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) Price = -403.7+ 181.9 B + 436.2 C + 311.8 D + 139.5 T + 73.5 Diameter b. Interpret the value of the R2 statistic for this model. Round your percentage value to one decimal place. Approximately 76.9 % of the predicted variation in price for a given metal tableware can be accounted by this model. c. Construct an approximate 95% prediction interval for the expected selling price of an 18 inch diameter casserole pan. Interpret this interval. Round your prediction interval limits to a whole dollar amount. We are 95% confident that the |price of 18 inch diameter casserole pans will be within between $ and $ d. What other variables not included in the model might help explain the remaining variation in auction selling prices for these items? The input in the box below will not be graded, but may be reviewed and considered by your instructor. The quality of the indicator variables such as caserole pan might affect the remaining variation in the auction selling prices