5. Develop a multiple-regression model for auto sales as a function of population and household income from the following data for 10 metropolitan areas:Estimate values for b0, b1, and b2 for the following model:b. Are the signs you ﬁnd for the coefﬁcients consistent with your expectations? Explain.c. Are the coefﬁcients for the two explanatory variables signiﬁcantly different from zero? Explain.d. What percentage of the variation in AS is explained by this model?e. What point estimate of AS would you make for a city where INC $23,175 and POP 128.07? What would the approximate 95 percent conﬁdence interval be?8. Consider now that you have been asked to prepare a forecast of wholesale furniture sales for the entire United States. You have been given the monthly time-series data inthe accompanying table:WFS is wholesale furniture sales in millions of dollars. It is not seasonally adjusted.PHS measures new private housing starts in thousands. UR is the unemployment rateas a percent. You believe that furniture sales are quite probably related to the generalstate of the economy and decide to test whether the unemployment rate affects furniture sales. You expect that as the unemployment rate rises (and the economy thus shows some sign of difﬁculty), furniture sales will decline.a. Summarize the results of your bivariate regression by completing the followingtable:b. After discussing the results at a staff meeting, someone suggests that you ﬁt amultiple-regression model of the following form:where:M1 A dummy variable for JanuaryM2 A dummy variable for FebruaryM4 A dummy variable for AprilM9 A dummy variable for SeptemberM10 A dummy variable for OctoberSummarize the results in the following table:• Do the signs of the coefﬁcients make sense?• Are the coefﬁcients statistically signiﬁcant at a 95 percent conﬁdence level(one-tailed test)?• What percentage of the variation in WFS is explained by the model?11. The data presented below are for retail sales in the United States quarterly from theperiod 1992Q1 through 2003Q4. Also included is disposable personal income percapita (DPIPC) (to use as a measure of the well-being of the economy).a. Develop a regression model of retail sales as a function of the S&P 500. Commenton the relevant summary statistics.b. Estimate a new multiple-regression model using seasonal dummy variables forquarters 2, 3, and 4. Additionally, add a time index to account for trend. Commenton the relevant statistics of this model. Is this model an improvement on the modelabove? What evidence is there that this second model provides an improvement (noimprovement)?c. Square the time index variable and add it to the multiple-regression model above.Does the resulting model perform better than either previous model? Explain yourreasoning.13. This is a problem in model selection. A “big box” home improvement store hascollected data on its sales and demographic variables relating to its various stores. Thecross-sectional data set for these variables is below:where:Sales average monthly store sales (in thousands of dollars)X1 Households in a 5-mile ring that are do-it-youselfers (in thousands)X2 Average monthly advertising expenditures (in dollars)X3 Square footage of competitor stores in a 5-mile ring (in thousands)X4 Households in a 5-mile ring that are below the poverty level (in hundreds)X5 Weighted average daily trafﬁc count at store intersectiona. Begin by estimating a model with independent variables X1, X2, and X3. Comment on the appropriateness of this model and its accuracy.b. Now add X4 to the model above and again comment on the appropriateness of the model. Has the accuracy improved?c. Finally, add X5 to the model and again comment on the accuracy of the model. Use the appropriate summary statistics of the three models to suggest which of the ﬁve independent variables should be in the model. Advise the “big box” retailer on which characteristics are important when choosing new store locations.