John, an assistant. in the district sales ofce of a national cosmetics rm, obtained the following data in 14 districts: District D M P 5' District D M P S l 4.2 4.0 3.0 32.6 3 4.3 4.0 5.0 107.7 2 6.5 6.5 5.0 147.0 0 2.6 2.5 5.0 75.6 3 3.0 3.5 4.0 97.3 10 3.1 3.0 4.0 39.0 4 2.1 2.0 3.0 56.2 11 6.2 6.0 4.5 125.1 5 2.9 3.0 4.0 73.4 12 5.5 5.5 5.0 104.6 6 7.2 7.0 3.0 121.8 13 2.2 2.0 4.0 71.5 7 4.8 5.0 4.5 35.6 14 3.0 2.8 3.0 67.4 where D (in $1000 per month) is the expenditure on displays in beauty salons and department. stores, M {in $1000 per month) is the expenditure on local media, P {in percentage) is the prorated share of national media advertising, and S (in $1000 per month} is the amount of sales. Johnis aim is to be able to obtain a linear model to forecast. the amount. of sales in a district. a. Clearly state the model with all the neenssary assumptions. b. Obtain the scatter-plots of the response variable and each of the explanatory variables and comments on each of the plot. 0. Interpret the coefcients of the model stated in part (a). What are the sign of the each of the coefcient in the model do you expect to have? W'hy'? d. Report the predicted model and does the sign of the estimated coefcients agree to your answer in part. {c}? e. At 5% level of signicance, is the model a signicant model? f. At 5% level of signicance, test Ho : ii.- = 0 versus Hn : .13.- ;E 0 for all i in the model. g. Use variance ination to determine if multicollinearity is a problem. 11. Repeat part. (g) but use the condition indicts method. i. At 5% level of signicance, if you need to drop on explanatory variable from the model, which one will you drop? Why? j. 1Without. using any software, obtain the estimated standardized model