Question

a) Write the linear model equation for the regression line identified by this Regression Report.

Part III: A leading consumer packaged goods company is analyzing the impact of various advertising media on its sales. It has been keeping meticulous data on weekly sales and weekly advertising spending on television, radio, and Google Ads. It knows from a prior study that, in its business, weekly advertising has a direct impact on same-week sales. It randomly selected 30 weeks of data correlating same-week sales with same-week advertising in the three media. That data appears here below. The Chief Marketing Officer of the company ran a Regression Report on the data, which appears to the right of the database. On the next page answer the five questions pertaining to this problem. Week Sales 1 $ 2 $ 3 $ 4 $ 5 $ 6 $ 7 $ 8 $ 9 $ 10 $ 16 $ 17 $ 18 $ 19 $ 20 $ 21 $ 22 $ 23 $ 24 $ P-value Television Radio 300,000 $ 50,000 $ 491,345 $ 26,248 $ 402,752 $ 14,697 $ 337,697 $ 19.170 $ 446,203 $ 11,055 $ 231,789 $ 17,972 $ 203,876 $ 8,568 $ 324,798 $ 16,972 $ 625,479 $ 67,863 $ 236,919 $ 31,864 $ 423,096 $ 21,459 $ 235,678 $ 32,469 $ 522,450 $ 67,453 $ 383,011 $ 16,155 $ 510,188 $ 72,807 $ 485,000 $ 64,815 $ 515,363 $ 98,645 $ 353,958 $ 57,451 $ 459,718 $ 4,309 $ 549,903 $ 15,454 512,375 $ 86,938 420,988 $ 14,609 372,803 $ 95,768 446,110 $ 89,503 375,045 $ 46,107 $ Google 35,000 $ 18,302 $ 16,914 $ 58,591 $ 56,893 $ 60,548 $ 64,776 $ 85,073 $ 89,679 $ 6,844 $ 19,745 $ 34,855 $ 1,647 $ 33,931 $ 102 $ 51,909 $ 49,130 $ 18,119 $ 49,814 $ 79,294 $ 53,799 $ 90,304 $ 30,480 $ 34,066 $ 81,446 $ 20,000 95,091 SUMMARY OUTPUT: Sales vs. Ad Spending Mix 81,208 40,751 Regression Statistics 74,813 Multiple R 1.00 24,060 R Square 0.99 16,514 Adjusted R Square 0.99 25,934 Standard Error 10065.95 63,409 Observations 30.00 31,910 79,808 22,195 Coefficients 79,199 Intercept -9003.79 66,671 Television 72,891 Radio 1.97 51,778 Google 4.08 30,292 36,342 86,791 86,238 32,434 49,138 6,135 27,367 18,458 3.08 0.219 0.000 0.000 0.000 Lower 95% -23712.694 2.938 1.825 3.927 Upper 95% 5705.117 3.220 2.124 4.238 25 $ 26 $ 27 $ 28 $ 29 $

b) Do all three advertising types (Television, Radio or Google) have a positive impact on sales? Which has the greatest impact? Explain your answer.

c) What is the confidence interval and p value for the independent variable “Radio”? Does radio have a significant linear relationship with Sales?

d) What is the net effect on Same-Week Sales of spending $1,000 in a week of television advertising? Show your work.

e) What would Same-Week Sales be if the company spent $10,000 on television ads, $8,000 on radio ads, and $4,000 on Google Ads? Show your work.

Answer 1

a) Regression equation is: sales= -9003.79 + 3.08 * television + 1.97 * radio + 4.08 * google

b) Yes, all three advertising types ( televison, radio, google) have a positive impact on sales, since, the slope of all the three advertising types are positive i.e slope of televison, radio, google are 3.08, 1.97, 4.08 respectively.

c) confidence interval for radio is (1.825, 2.124) and p value is zero. Yes, radio have a significant linear relationship with sales as the p value is zero and smaller the p-value higher is significance.

d) Since the slope of television is 3.08. Thus, unit increase in television ads result in additional $3.08. So, keeping the radio and google ads constant, and spending $1,000 in a week will result in net increase of $3080(3.08*1000) in sales.

e) sales = -9003.79 + 3.08 * (10,000) + 1.97 * (8,000) + 4.08 * (4000) = -9003.79+3080+15760+16320= 26156.21