Sales/Advertising The vice-president of marketing for a large firm is concerned about the effect of advertising on sales of the firm?s major product. To investigate the relationship between advertising and sales, data on the two variables were gathered from a random sample of 20 sales districts. These data are available in a file named SALESAD3. (Sales and advertising are both expressed in hundreds of dollars. For example, 4250 represents $425,000). The scatterplot is in Figure 3.21. The results for the regress ion of sales (SALES) on advertising (ADV) are shown in Figure 3.22. Using the information given, answer the following questions:

a. Is there a linear relationship between sales and advertising? Use ? = 0.05. State the hypotheses to be tested, the decision rule, the test statistic, and your decision.

b. What implications does this test result have for the firm?

c. What is the sample regression equation relating sales to advertising?

d. If ADV increases by $1000, what would be the resulting change in our prediction of SALES?

e. Construct a 90% confidence interval estimate of ?0.

f. Construct a 95% confidence interval estimate of ?1.

g. Test the hypotheses

H0: ?1 = 20

Ha: ?1 ? 20

using a 5% level of significance. State the decision rule, the test statistic, and your decision.

h. What conclusion can be drawn from the result of the test in part g?

Figure 3.21:?Scatterplot for Sales and Advertising Exercise.

Figure 3.22:?Regression Results for Sales and Advertising Exercise.

Step-by-st

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SALES 8000 7000 6000 5000 4000 3000 2000 150 200 Scatterplot of SALES vs ADV 250 300 ADV 350 400 450 Variable Intercept ADV Coefficient -57.281 17.570 Regression Error Total DF 1 Std Dev 509.750 1.642 Standard Error = 594.808 R-Sq = 86.4% R-Sq(adj) = 85.7 Analysis of Variance Source 18 19 Sum of Squares T Stat 40523671 6368342 46892014 -0.11 10.70 Mean Square F Stat 40523671 353797 114.54 P Value 0.912 0.000 P Value 0.000 SALES 8000 7000 6000 5000 4000 3000 2000 150 200 Scatterplot of SALES vs ADV 250 300 ADV 350 400 450 Variable Intercept ADV Coefficient -57.281 17.570 Regression Error Total DF 1 Std Dev 509.750 1.642 Standard Error = 594.808 R-Sq = 86.4% R-Sq(adj) = 85.7 Analysis of Variance Source 18 19 Sum of Squares T Stat 40523671 6368342 46892014 -0.11 10.70 Mean Square F Stat 40523671 353797 114.54 P Value 0.912 0.000 P Value 0.000

Answer rating: 100% (QA)

aSetting of hypothesis Null hypothesis H 0 ie There is no significant impacting Correlation between sales and advertising Alternative hypothesis H1 0 ... View the full answer