A regression analysis relating a company’s sales, their advertising expenditure, price (per unit), and time (taken per unit production) resulted in the following output.
Regression Statistics
Multiple R0.9895
R Square0.9791
Adjusted R Square0.9762
Standard Error232.29
Observations25
ANOVA ?
df
SS
MS
F
Significance F
Regression3
53184931.86
17728310.62
328.56
0.0000
Residual21
1133108.30
53957.54
Total24
54318040.16
?
?
?
?
Coefficients
Standard Error
t Stat
P-value
Intercept927.23
1229.86
0.75
0.4593
Advertising (x1)1.02
3.09
0.33
0.7450
Price (x2)15.61
5.62
2.78
0.0112
Time (x3)170.53
28.18
6.05
0.0000
?
a.Using ? = .01, determine whether or not the regression model is significant. Fully explain how you arrived at your conclusion (give numerical reasoning) and what your answer indicates.b.At ? = .01, determine which variables are significant and which are not. Explain how you arrived at your conclusion (give numerical reasoning).c.Fully explain the meaning of R Square, which is given in the above regression results. Be very specific and give numerical explanation.
What will be an ideal response?
| a. | Significance F = .0000 < ? = .01; the model is significant. It indicates that this regression model is adequate for predicting the company's sales. |
| b. | The p-values for Time is less than ?= .01 and therefore this is a significant variable.The p-value for Advertising and Price is greater than ? = .01, and so, there is no evidence that these variables are significant. |
| c. | R2 = .9791, indicating 97.91% of the variation in Sales is explained by the variation in Price, Time, and Advertising. There is 2.09% unexplained variation. |
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