The following printout shows the results of a simple linear regression model that predicts monthly sales (in thousands of dollars) based on how much money was spent on advertising (in thousands of dollars) during a particular month for 15 stores of a retail chain. a) Is there a statistically significant relationship between money spent on advertising and sales? Test at the 5% level of significance and explain your approach (including hypotheses). b) Somebody claims that every additional $1,000 in advertising will increase sales by more than $2,000 in the population. Can you find support for this claim given the results of your analysis? Test at the 5% level of significance and explain your approach (including hypotheses). How is this test different from the one in part a)? c) Find a 95% confidence interval for the change in sales given a $1,000 increase in the amount of money spent on advertising. How does this confidence interval relate to your answer to part a)?

The following printout shows the results of a simple linear regression model that predicts monthly sales (in thousands of dollars) based on how much money was spent on advertising (in thousands of dollars) during a particular month for 15 stores of a retail chain. a) Is there a statistically significant relationship between money spent on advertising and sales? Test at the 5% level of significance and explain your approach (including hypotheses). b) Somebody claims that every additional $1,000 in advertising will increase sales by more than $2,000 in the population. Can you find support for this claim given the results of your analysis? Test at the 5% level of significance and explain your approach (including hypotheses). How is this test different from the one in part a)? c) Find a 95% confidence interval for the change in sales given a $1,000 increase in the amount of money spent on advertising. How does this confidence interval relate to your answer to part a)?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 12DE

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Problem 2

a) Is there a statistically significant relationship between money spent on advertising and sales? Test at the 5% level of significance and explain your approach (including hypotheses).

b) Somebody claims that every additional $1,000 in advertising will increase sales by more than $2,000 in the population. Can you find support for this claim given the results of your analysis? Test at the 5% level of significance and explain your approach (including hypotheses). How is this test different from the one in part a)?

c) Find a 95% confidence interval for the change in sales given a $1,000 increase in the amount of money spent on advertising. How does this confidence interval relate to your answer to part a)?

SUMMARY OUTPUT
Regression Statistics
Multiple R
0.880726335
R Square
0.775678876
Adjusted R Square 0.758423405
Standard Error
13.04990405
Observations
15
ANOVA
df
S
MS
Significance F
Regression
1
7655.43339
7655.43339 44.95263409
1.46013E-05
Residual
13
2213.899944 170.2999957
Total
14
9869.333333
Coefficients Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Interce pt
162.4290612
8.901071145 18.24826008 1.20354E-10
143.1994661 181.6586563
Advertising
3.778221987
0.563520732 6.704672556 1.46013E-05
2.56080946 4.995634514

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