The following data show the dollar value of sales with corresponding advertising

Question

The following data show the dollar value of sales with corresponding advertising levels for a small retail chain in PhIladelphia.

a. Plot these data in the form of scatter diagram. Does the linear model appear to be appropriate for estimating sales as a funciton of dollars spent on advertising?

b. Based on regression analysis, what is the estimated increase in the amount of sales per every extra dollar in advertising?

c. What would be the value of estimated sales if advertising expenditures were $622? (To the nearest $100).

d. What is an estimate of the standard deviation of error term in the regression model? (To the nearest $100).

e. Test whether a linear relationship exists between adveritsing and sales.

f. Find the appropriate p-value for the test statistics.

g. Find the upper bound of a 95% confidence interval for the increase in the amount of sales per extra dollar in advertising (To the nearest $).

h, Find the percentage of variation of amount of sales that can be explained by changes in advertising.

i. Find the estimated correlation coefficient.

Advertising Sales $584 $6445 $386 $4015 $452 $4822 $635 $7017 $242 $2848 $328 $3888 $517 $5554

Explanation / Answer

11.91894

a) Yes, linear model seems to be appropriate for estimating sales as a funciton of dollars spent on advertising because R is very close to 1

b) Estimated increase in the amount of sales per every extra dollar in advertising is $10.51

c) Estimated sales

Sales = 221.8119+10.50773*622

= $6758

d) tandard deviation of error term in the regression model = 189.3102

SUMMARY OUTPUT Regression Statistics Multiple R 0.993245 R Square 0.986536 Adjusted R Square 0.983843 Standard Error 189.3102 Observations 7 ANOVA df SS MS F Significance F Regression 1 13129464 13129464 366.3522 7.18E-06 Residual 5 179191.8 35838.36 Total 6 13308655 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 221.8119 256.7443 0.863941 0.427113 -438.17 881.7941 -438.17 881.7941 X Variable 1 10.50773 0.548984 19.14033 7.18E-06 9.096526 11.91894 9.096526

11.91894

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