4. A regression analysis relating a company’s sales, their advertising expenditu
ID: 3264999 • Letter: 4
Question
4. 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 R
0.9895
R Square
0.9791
Adjusted R Square
0.9762
Standard Error
232.29
Observations
25
ANOVA
df
SS
MS
F
Significance F
Regression
3
53184931.86
17728310.62
328.56
0.0000
Residual
21
1133108.30
53957.54
Total
24
54318040.16
Coefficients
Standard Error
t Stat
P-value
Intercept
927.23
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 = .05, 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 = .05, 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 Squared, which is given in the above regression results. Be very specific and give numerical explanation.
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4. 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 R
0.9895
R Square
0.9791
Adjusted R Square
0.9762
Standard Error
232.29
Observations
25
ANOVA
df
SS
MS
F
Significance F
Regression
3
53184931.86
17728310.62
328.56
0.0000
Residual
21
1133108.30
53957.54
Total
24
54318040.16
Coefficients
Standard Error
t Stat
P-value
Intercept
927.23
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 = .05, 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 = .05, 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 Squared, which is given in the above regression results. Be very specific and give numerical explanation.
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Explanation / Answer
a. Note that the F-test of the overall significance is a specific form of the F-test. It compares a model with no predictors to the model that you specify. A regression model that contains no predictors is also known as an intercept-only model.
The hypotheses for the F-test of the overall significance are as follows:
Null hypothesis: The fit of the intercept-only model and your model are equal.
Alternative hypothesis: The fit of the intercept-only model is significantly reduced compared to your model.
If the P value for the F-test of overall significance test is less than your significance level, you can reject the null-hypothesis and conclude that your model provides a better fit than the intercept-only model.
Here, = .05 and P value=0.0000 , we reject the null-hypothesis at 5% level of significance and conclude that your model provides a better fit than the intercept-only model.
b. Note that individual coefficients test is used to determine sigificance of each variable.
The hypotheses for this test are as follows:
Null hypothesis: Variable is insignificant.
Alternative hypothesis: Variable is significant.
If the P value for this is less than your significance level, you can reject the null-hypothesis and conclude that
corresponding variable is significant.
Here, P value corresponding to a variable Advertising (x1) is 0.7450 which is greater than 0.05 , we fail to reject null hypothesis and conclude that Advertising (x1) is insignificant at 5% level of sigificance.
P value corresponding to a variable Price (x2) is 0.0112 which is less than 0.05 , we reject null hypothesis and conclude that Price (x2 is significant at 5% level of sigificance.
P value corresponding to a variable Time (x3) is 0.0000 which is less than 0.05 , we reject null hypothesis and conclude that Time (x3) is in significant at 5% level of sigificance.
c.Note that R Square denotes proportion of variation in dependent variable explained by all of your independent variables in the model.
Here,R Square=0.9791 which denotes 97.91% variation in dependent variable explained by all of your independent variables namely Advertising (x1) , Price (x2) & Time (x3) .
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