Bob is a statistics textbook author and aspiring photographer who sells his 13 * 19 prints on consignment at Island Art in Stone Harbor, New Jersey (stop in if you are in the area and ask for Spencer). To improve his inventory management, Bob would like to develop a model to predict the number of prints he will sell in a week. The Excel file Island Art 2. xlsx provides the following data from a random selection of summer weeks over the past few years: the number of prints sold per week, the price of the prints during the week, the number of prints in inventory at the start of the week, and the season (in season or off season).
a. Construct a regression model to predict the average demand for prints during the week using all three independent variables.
b. Interpret the meaning of the regression coefficients from part a.
c. Test the significance of the overall regression model from part a using α = 0.05.
d. Show the calculation for the adjusted multiple coefficient of determination for part a.
e. Using p values, identify which independent variables are significant from the model in part a with α = 0.05.
f. Using PHStat, check for the presence of multicollinearity for all three independent variables. If it is present, take the necessary steps to eliminate it.
g. Construct a regression model using a general stepwise regression using the independent variables from part
f. Use α = 0.05 for the p value to enter and remove independent variables.
h. Predict the average demand for an in season week in which Bob has 65 prints in inventory priced at $ 59 per print using the model developed in part g.
i. Construct a 95% confidence interval for the regression coefficients for the Price variable from part g. Be sure to interpret the meaning of this confidence interval.
j. Perform a residual analysis to verify that the conditions for the regression model are met for the model developed in part g.