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A manager at a roadside cafe is concerned that the weak economic environment has caused a decline in sales. To offset the decline in sales, the manager has pursued a strong advertising campaign (billboards up and down the road). She believes advertising expenditures have a positive influence on sales. To support her claim, the manager estimates the following linear regression model: Sales = β0 + β1Unemployment + β2Advertising + ε. A portion of the regression results is shown in the accompanying table.
ANOVA |
df |
SS |
MS |
F |
Significance F |
Regression |
2 |
72.6374 |
36.3187 |
8.760 |
0.003 |
Residual |
14 |
58.0438 |
4.1460 |
|
|
Total |
16 |
130.681 |
|
|
|
|
Coefficients |
Standard |
t Stat |
p-Value |
Intercept |
17.5060 |
3.9817 |
4.397 |
0.007 |
Unemployment |
–0.6879 |
0.2997 |
–2.296 |
0.038 |
Advertising |
0.0266 |
0.0068 |
3.932 |
0.002 |
- What is the value of the test statistic regarding whether the predictor variables jointly influence sales (round to 3 decimal places)?
- At the 5% significance level, do the predictor variables jointly influence sales? (Y/N)
- Is Advertising negatively related with sales? (Y/N)
- Are both Unemployment and Advertising statistically significant in this model? (Y/N)
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