A corporation owns several companies. The strategic planner for the corporations believes dollars spend on advertising can to some extend be a predictor of total sales dollars. As an aid in long-term planning, she gathers the following sales and advertising information from several of the companies for 2017 ($ millions). Advertising Sales 12.5 148 3.7 55 21.6 338 60.0 994 37.6 541 6.1 89 16.8 126 41.2 379 i. Based on the output given, develop the equation of the simple linear regression line to predict sales from advertising expenditures using this data. ii. Explain the values of r and r 2 . iii. Predict the sales if the advertising expenditures is 50 ($ millions). iv. Do the data support the existence of a linear relationship between advertising expenditures and sales? Test using α = 0.05. Output Model Summary MODEL R R Square Adjusted R Square Std. Error of the Estimate 1 .351a .123 -.169 3.94292 ANOVAa MODEL SUM OF SQUARES DF MEAN SQUARE F SIG 1Regression Residual 6.560 46.640 1 3 6.560 15.547 .422 .562b a. Dependent Variable: y b. Predictors: (Constant), x Coefficientsa Model Unstandardized Coefficients B Unstandardized Coefficients Std. Error Standardized Coefficients t sig. 1(Constant) X 16.510 .162 4.786 .250 .351 3.449 .650 .041 .562 a. Dependent Variable: y
A corporation owns several companies. The strategic planner for the corporations believes dollars spend on advertising can to some extend be a predictor of total sales dollars. As an aid in long-term planning, she gathers the following sales and advertising information from several of the companies for 2017 ($ millions).
Advertising Sales
12.5 148
3.7 55
21.6 338
60.0 994
37.6 541
6.1 89
16.8 126
41.2 379
i. Based on the output given, develop the equation of the simple linear regression line to predict sales from advertising expenditures using this data.
ii. Explain the values of r and r 2 .
iii. Predict the sales if the advertising expenditures is 50 ($ millions).
iv. Do the data support the existence of a linear relationship between advertising expenditures and sales? Test using α = 0.05.
Output
Model Summary
| MODEL | R | R Square | Adjusted R Square |
Std. Error of the Estimate |
| 1 | .351a | .123 | -.169 | 3.94292 |
ANOVAa
| MODEL | SUM OF SQUARES | DF | MEAN SQUARE | F | SIG |
|
1Regression
Residual |
6.560
46.640 |
1
3 |
6.560
15.547 |
.422
|
.562b
|
a. Dependent Variable: y
b. Predictors: (Constant), x
Coefficientsa
| Model |
Unstandardized Coefficients B |
Unstandardized Coefficients Std. Error |
Standardized Coefficients |
t | sig. |
|
1(Constant) X |
16.510 .162 |
4.786 .250 |
.351 |
3.449 .650 |
.041 .562 |
a. Dependent Variable: y
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