In: Statistics and Probability
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 |
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. Predict Sales if Advertising is $4000, Price is $2995.00, and Time is 22 hours.
b. State the null and alternative hypothesis for the overall test of significance.
c. What is the result of the overall test at the ,05 level of significance. How do you know?
d. Which independent variables are significant at the .05 level of significance? How do you know?
e. Provide the 95% confidence interval for the independent variable price.