$1.$ Bob is a statistics textbook author and aspiring photographer who sells his $\backslash (13^\{\backslash$prime $\backslash$prime$\}\backslash$times $19^\{\backslash$prime $\backslash$prime$\}\backslash )$ 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 $\backslash (\backslash$alpha$=0\mathrm{.}05\backslash ).$

d$.$ Show the calculation for the adjusted multiple coefficient of determination for part a$.$

e$.$ Using $\backslash ($ p $\backslash )-$values, identify which independent variables are significant from the model in part a with $\backslash (\backslash$alpha$=0\mathrm{.}05\backslash ).$