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8. [l4pts] Suppose the manager of a company wants to evaluate the performance of team's salesperson. Each salesperson is responsible for one sales region individually, and the manager decides to measure the performance of a salesperson (Y) by using the annual sales in units of the company's product in his sales region. The manager decides to use the ve predictors for the performance: X1 = number of months the salesperson has been worked for the company; X2 = sales of the company's product in the sales region ($1000); X3 = dollar advertising expenditure in the sales region ($); X4 = weighted average of the company's market share in the sales region for the last 5 years; X5 = change in the company's market share in the sales region over the last 5 years. Dene the following to be Model.1: Y = b0 + b1X1 + b2X2 + b3X3 + b4X4 + bsXs Some regression analysis results are given below: Regression Analysis: y versus x1, x2, x3, x4, x5 (Modell) Analysis of Variance Source DF SS MS FValue PValue Regression 5 37862659 7572532 40.91 0.000 Error 19 3516890 185099 Total 24 41379549 Model Summary S Rsq 430.232 91.50% Coefficients Term Coef SE Coef TValue PValue VIF Constant 1114 420 2.65 0.016 X1 3.61 1.18 .06 .006 .36 X2 0.04209 0.00673 .25 .000 .45 X3 0.1289 0.0370 .48 .003 .29 X4 257.0 39.1 .57 .000 .20 X5 325 157 .06 .053 .24 Prediction for Y Regression Equation Y = 1114 + 3.61 X1 + 0.04209 X2 + 0.1289 X3 + 257.0 X4 + 325 X5 Variable Setting X1 150 X2 65000 X3 5550 X4 8 X5 0.11 Fit SE Fit 95% CI 95% PI 4970.25 182.917 (4587.40, 5353.10) {3991.76, 5948.75} 9".\" F\" Is the model useful? If yes, how useful is the model? If no, why? Which predictors are useful to predict the performance of a salesperson (Y) at 5% signicant level. What is the change of the mean performance if the dollar amount of advertising expenditure is decreased by $100 in Model.1 (Assume the values of the other predictors remain the same)? Explain the effect of sales of the company's product (X2) on Y. Under Model. 1 , predict the performance of an individual salesperson with the following attributes (X1=150, X2=65000, X3=5550, X4=8, X5=0.11) using point estimate and 95% interval estimate? Interpret the interval estimate. Compute the Rid)- in Model.l. Is there multicollinearity problem? Why or why not