2. In determining the best companies to work for, a number of variables are cons
ID: 3152700 • Letter: 2
Question
2. In determining the best companies to work for, a number of variables are considered, including size, average annual pay, and turnover rate, etc. Moreover, employee surveys are conducted in order to assess aspects of the organization’s culture, such as trust and openness to change. In an attempt to determine what affects turnover rate, a sample of 33 companies was randomly selected and data collected on the average annual bonus and turnover rate (%). In addition, a questionnaire was administered to the employees of each company to arrive at a trust index (measured on a scale of 0 – 100). Below are the multiple regression results.
a. Write out the estimated regression equation.
b. Is the regression equation significant overall? Explain.
c. How much of the variability in Turnover Rate is explained by the regression
equation?
d. State the hypotheses for testing the regression coefficient of Trust Index. Based on
the results, what do you conclude?
e. State the hypotheses for testing the regression coefficient of Average Annual Bonus.
Based on the results, what do you conclude?
f. Predict the turnover rate for a company with a trust index score of 70 and an average
annual bonus of $6500.
g. Comment on whether the conditions for multiple regression are satisfied based on the
plots shown below.
Explanation / Answer
2. In determining the best companies to work for, a number of variables are considered, including size, average annual pay, and turnover rate, etc. Moreover, employee surveys are conducted in order to assess aspects of the organization’s culture, such as trust and openness to change. In an attempt to determine what affects turnover rate, a sample of 33 companies was randomly selected and data collected on the average annual bonus and turnover rate (%). In addition, a questionnaire was administered to the employees of each company to arrive at a trust index (measured on a scale of 0 – 100). Below are the multiple regression results.
a. Write out the estimated regression equation.
The estimated regression equation is given as below:
Turnover rate = 12.1005 – 0.0715*Trust index – 0.0007*average bonus
b. Is the regression equation significant overall? Explain.
The regression equation is significant because we get the p-value less than the given level of significance or alpha value 0.05 or 5% so we reject the null hypothesis that the given regression model is not significant.
c. How much of the variability in Turnover Rate is explained by the regression equation?
The value for the multiple correlation or the coefficient of determination R-square is not given so we can find the explained variation in the turnover rate due to the independent variables.
d. State the hypotheses for testing the regression coefficient of Trust Index. Based on the results, what do you conclude?
The null and alternative hypothesis for testing the regression coefficient of trust index is given as below:
Null hypothesis: H0: The slope of the trust index is not significant.
Alternative hypothesis: Ha: The slope of the trust index is significant.
The p-value for this test is given as 0.001 so we reject the null hypothesis that the slope of the trust index is not significant.
e. State the hypotheses for testing the regression coefficient of Average Annual Bonus.
The null and alternative hypothesis for testing the regression coefficient of average annual bonus is given as below:
Null hypothesis: H0: The slope of the average annual bonus is not significant.
Alternative hypothesis: Ha: The slope of the average annual bonus is significant.
Based on the results, what do you conclude?
The p-value for this test is given as 0.0001481 which is less than the given level of significance so we reject the null hypothesis that the slope of the average annual bonus is not significant.
f. Predict the turnover rate for a company with a trust index score of 70 and an average annual bonus of $6500.
The regression equation is given as below:
Turnover rate = 12.1005 – 0.0715*Trust index – 0.0007*average bonus
Turnover rate = 12.1005 – 0.0715*70 – 0.0007*6500
Turnover rate = 2.5455
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