Prob 13.5

# Where y is the mean weekly gross revenue expected for

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where Y is the mean weekly gross revenue expected for a weekly newspaper advertising budget of x2 (both in \$K); R^2 = 0.0004 (from the graph). Neither simple linear regression by itself results in a good predictive tool. So use both independent variable together in a multiple regression. The Excel output regression report is contained in the Excel workbook “ASW Prob 13.5.xls” and is shown below. (This is asked for part b of the problem.) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 A B C D E F G SUMMARY OUTPUT Regression Statistics Multiple R 0.958663444 R Square 0.9190356 Adjusted R Square 0.88664984 Standard Error 0.642587303 Observations 8 ANOVA df SS MS F Significance F Regression 2 23.43540779 11.7177039 28.37776839 0.001865242 Residual 5 2.064592208 0.412918442 Total 7 25.5 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 83.23009169 1.573868952 52.88247894 4.57175E-08 79.18433275 87.27585063 X Variable 1 2.290183621 0.304064556 7.531899313 0.000653232 1.508560797 3.071806445 X Variable 2 1.300989098 0.320701597 4.056696662 0.009760798 0.476599399 2.125378798 The multiple regression coefficients are listed in column B under the heading “Coefficients” starting in row 17. Specifically, b0 = 83.2301 (cell B17) b1 = 2.2902 (cell B18) b2 = 1.3010 (cell B19) (All reported to four decimal places.) The regression coefficients mean the following: Holding the newspaper advertising budget fixed, every additional \$1K (=\$1000) weekly spent in TV advertising is expected to increase weekly gross revenue by \$2.2902K (= \$2,290.20). Holding the TV advertising budget fixed, every additional \$1K (=\$1000) weekly spent in newspaper advertising is expected to increase weekly gross revenue by \$1.3010K (= \$2,290.20). ASW 5e Prob 13.5 (p. 541) 2 © 2008 Harvey Singer

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(This is essentially asked for part c of the problem.) (Note: If an additional \$1000 is available for advertising, it should be spent on TV ads, because that will lead to the highest increase in weekly gross revenue.) Putting this together, the equation of the multiple regression is Y = 83.2301 + 2.2902x1 + 1.3010x2.
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