Question

In order to improve the linear model to predict an employee’s salary (in thousands), the researcher decided to also include in the model the previous work experience (in years) and education of each employee (in years). The multiple regression linear model is as follows:

Salaryi=β0+β1Employmenti+β2Experience+β3Education+εi

The following information was obtained from the statistical software:

Source                   df                  SS            MS                    F           P-value

Model                      3      29231989 9743996                   ?                 .006  

Error                      4      1739708    434927

Total                        7      30971697      

Variable                Parameter Est.     Std. Err. Of Parameter Est.           T      

Constant                  49764.00                        1981.00                        25.12

Employment               364.41                             48.32                           7.54

Experience                  227.60                          123.80                           1.838

Education                    266.90                           147.40                          1.81

1. Test the hypothesis   H₀: β1=β2=β3=0 H_a: at least one of the βj's is not 0

1. Find the test statistic and P-value.                                                                                                                                              
2. Make a decision to reject or not reject the null hypothesis.                                                                    
3. Summarize the results in the context of the problem.

Answer 1

Given the ANOVA table we can easily calculate the value of the F-statistic:

F = MSM/MSE

F = 9743996/434927 = 22.40375

The corresponding p-value of the F-statistic with 3,4 degrees of freedon is 0.006

Since, the p-value is less than 0.05 we reject the null hypothesis at 5% level of significance and conclude that atleast one of the betas is not equal to zero.

This means that the decision of the researcher to include more than one variable such as previous work experience and education to the linear model to create a multiple regression linear model is valid.

In order to obtain the individual significance of the regression coeffcients we will calculate calculate the critical value of t for 3 degrees of freedom which is 4.177

Comparing the critical value with the indicidual values of the t-statistic we get that the regression coefficient of the intercept and employment are significant while the regression coefficients of experience and education may not be significant at 5% level of significance. So we may reject the claims of the researcher at 5% level of significance.