Fortune magazine publishes an annual list of the 100
best companies to work for. The data in the file named FortuneBest
shows a portion of the data for a random sample of 30 of the
companies that made the top 100 list for 2012 (Fortune,
February 6, 2012). The column labeled Rank shows the rank of the
company in the Fortune 100 list; the column labeled Size indicates
whether the company is a small, midsize, or large company; the
column labeled Salaried ($1000s) shows the average annual salary
for salaried employees rounded to the nearest$1000 ; and the column
labeled Hourly ($1000s) shows the average annual salary for hourly
employees rounded to the nearest $1000 . Fortune defines
large companies as having more than 10,000employees, midsize
companies as having between 2500 and 10,000 employees, and small
companies as having fewer than 2500
To incorporate the effect of size, a categorical variable with
three levels, we used two dummy variables: Size-Midsize and
Size-Small. The value of size-Midsize =1 if the company
is a midsize company and 0 otherwise. And, the value of size-small
=1 if the company is a small company and 0 otherwise. Develop an
estimated regression equation that could be used to predict the
average annual salary for salaried employees given the average
annual salary for hourly employees and the size of the company.
1. Interpret the regression constant and regression
coefficient.
2. Interpret the coefficient of determination
3. Interpret the Multiple Correlation Coefficient
4. For the estimated regression equation developed above, use
the t test to determine the significance of the independent
variables. Use Alpha =0.05
The Summary Output of the data file is as follows.
| SUMMARY OUTPUT | ||||||||
| Regression Statistics |
||||||||
| Multiple R | 0.758226532 | |||||||
| R Square | 0.574907473 | |||||||
| Adjusted R Square | 0.525858336 | |||||||
| Standard Error | 25.47515084 | |||||||
| Observations | 30 | |||||||
| ANOVA | ||||||||
| df | SS | MS | F | Significance F | ||||
| Regression | 3 | 22820.30059 | 7606.766865 | 11.72105159 | 4.81713E-05 | |||
| Residual | 26 | 16873.56607 | 648.9833105 | |||||
| Total | 29 | 39693.86667 | ||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | 26.96589812 | 14.00431214 | 1.925542494 | 0.065164701 | -1.820377748 | 55.75217398 | -1.820377748 | 55.75217398 |
| Hourly ($1000s) | 1.224044868 | 0.258106065 | 4.742410332 | 6.63374E-05 | 0.693500254 | 1.754589482 | 0.693500254 | 1.754589482 |
| Size-Midsize | -3.208216286 | 12.63462389 | -0.253922579 | 0.801552712 | -29.17905763 | 22.76262506 | -29.17905763 | 22.76262506 |
| Size-Small | 34.40215452 | 10.437669 | 3.295961437 | 0.0028371 | 12.94721862 | 55.85709042 | 12.94721862 | 55.85709042 |
