Fortune magazine publishes an annual list of the 100 best companies to work for.
ID: 3320405 • Letter: F
Question
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 coefficients.
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
5. Do a global overall test.
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 55.85709042Explanation / Answer
Regression Equation: -
Average Annual Salary=26.97+1.22*Hourly-3.21*Size-Midsize+34.4*Size-Small
1)
Intercept: 26.97: This means that Average Annual Salary would remain constant at 26.97 even if there are no other factors affecting Average Annual Salary.
Hourly: This means that Average Annual Salary would go up by 1.22 for every increase of 1 in Hourly, keeping all other factors constant.
Size-Midsize: This means that Average Annual Salary would go down by 3.21 if the company is a midsize company, keeping all other factors constant.
Size-Small: This means that Average Annual Salary would go up by 34.4 if the company is a smallsize company, keeping all other factors constant.
2)
r^2=0.5749. This means that 57.49% of the variation in dependent variable is accounted for by the variation in the independent variables.
3)
r=0.7582. This indicates a positive correlation between the variables. This means that if one of the variable goes up, the other goes up as well and vice versa.
4)
tSTAT have already been reported above. tCRIT would be +/-2.05 for n-2=28 DF. Hence, reject the null hypothesis for
Hourly ($1000s) and Size-small. These two variables are thus significant in explaining variation in the dependent variable.
5)
Since F>Fcrit, reject the null hypothesis. Thus, we conclude that atleast one of the independent variables affects the dependent variable.
Hourly ($1000s) and Size-small. These two variables are thus significant in explaining variation in the dependent variable.
5)
Since F>Fcrit, reject the null hypothesis. Thus, we conclude that atleast one of the independent variables affects the dependent variable.