Question 1
The regression equation is y=10004.9665+0.4349service cost+178.0989cost increase+141.4783payment.
| Service cost | 30,000 |
| Cost increase | 70 |
| Payment | 60 |
| Predicted annual | =10004.9665+0.4349*30,000+178.0989*70+141.4783*60=$44,007.59 |
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The predicted annual earnings for the firm are $44,007.59 when the average cost increase is $30,000 with a contract completion of seventy percent, with sixty percent of the clients paying for services upfront.
Question 2
The test to ascertain whether the predictor variables are jointly significant in describing the earnings is the F-test for the overall significance.
| ANOVA | df | SS | MS | F | Significance F |
| Regression | 1 | 44182633.37 | 44182633.37 | 57.737 | |
| Residual | 18 | 13774291.07 | 765238.393 | ||
| Total | 19 | 57956924.44 |
Based on the results shown above, the F-value is 57.737. The p-value for the f-test of the overall significance test is 0. The null hypothesis is that the model without the predictor variables fits the data and the model. On the contrary, the alternative hypothesis indicates that the model fits the data better than the model with the intercept only. The significance level, which is the alpha, is 0.05. The p-value of the overall F-test is compared to the chosen significance level. Based on the comparison, the p-value of the overall F-test, which is 0.00, is lower than the selected significance level. In this regard, the null hypothesis is rejected, and it is concluded that the model offers a better fit than the specific model with the intercept only. Each predictor is not sufficiently predictive on its own to exhibit statistical significance. The overall F-test lacks significance and, as a result, there is a high likelihood that the predictor variables are not significant either. The predictor variables in the specific model are not jointly significant in describing the earnings at an alpha level of 0.05.
