Medicorp Company sells medical supplies to hospitals, clinics and doctor's offices. The management of the company is interested in modeling the total sales of their company in each of the regional sales territories. To model the total sales (in $1000's), the following variables were considered important: Adv: The total amount spent on advertising in each sales territory (in $100's) Bonus: total amount of bonuses paid in each territory (in $100's) Mktshr: the marketshare percentage currently held by Medicorp in each territory Compet: the largest competitor's sales (in $1000's) in each territory The data are in the file MEDIC. The regression output follows below. a) Fit the multiple regression model and confirm that there does not seem to be any need for transformations (i.e. evidence of non-constant variance or curvilinear relationships) through the standardized residual plot. Are there any outliers? What is the equation of the fitted model? b) Is there evidence that at least one X variable is related to the Y variable? c) Which of the explanatory variables in the model are important on an individual basis, after accounting for the other variables? d) (Answer this sub-question using the full model, even though it is obvious from (c) that at least one variable may be excluded from the model). The regional manager of one territory (not included in the sample) calls up the main office, claiming that his territory has posted exceptional sales. You find out the following information about his sales territory: Sales=1550 (in $1000's) adv=610 (in $100's) Bonus=260 (in $100's) mktshr=30% compet=325 (in $1000's) Based on the model you have fitted above, would you believe the regional sales manager? Justify your answer. 2) In this problem, we will build a multiple regression model to predict the price of a refrigerator based on some of its characteristics. The data consists of a sample of 37 different brands of fridges available in the U.S. and is stored in the file FREEZE The variables are: Price: Price of the refrigerator in $ E_cost: the average amount of money spent per year to operate the fridge (i.e. the energy cost) R_cu_ft: size of the fridge in cubic feet F_cu_ft: size of the freezer compartment in cubic feet Shelves: number of shelves in the fridge and freezer doors Features: number of features a) Fit a multiple regression model to the data. What is the equation of the fitted model? b) What proportion of variability in the price is explained by the predictor variables? c) Is there evidence that the model is useful? d) Which of the explanatory variables are important on an individual basis, after accounting for the remaining variables in the model? e) Interpret the coefficient associated with the variable e_cost in the fitted regression model. Does the sign of this coefficient support your economic intuition? f) Make a scatter plot of rice versus e_cost. The scatter plot reveals a positive relationship between price and e_cost in apparent contradiction to what you obtained in (e) above. Why might this occur? g) Based on your fitted model, obtain a 90% PI for the price of a refrigerator which has 3 features, 2 shelves, f_cu_ft = 5, r_cu_ft = 13.3 and an energy cost of $69.

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