In determining the best companies to work for, a number of variables are conside
ID: 3312546 • Letter: I
Question
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) Predict the turnover rate for a company with a trust index score of 70 and an average annual bonus of $6500. If the company observe a turnover rate of 2.15%, what is the value of the residual for this company? What does the value of the residual tell you about the prediction?
b) Comment on whether the conditions for multiple regression are satisfied based on the plots shown below.
Dependent Variable is Turnover Rate Predictor Constant Trust Index Average Bo SE Coef 0.7826 15.46 0.000 0.01966 -3.64 0.001 nus -0.0007216 0.0001481 -4.87 0.000 12.1005 0.07149 S= 1.49746 R-Sg 79.6% R-Sg (adj ) =78.3% = AnalysiS OI Variance Source Regression Residual Error Total MS 2 262.73 131.36 2.24 DF 30 67.27 32 330.00Explanation / Answer
a) Predict the turnover rate for a company with a trust index score of 70 and an average annual bonus of $6500. If the company observe a turnover rate of 2.15%, what is the value of the residual for this company? What does the value of the residual tell you about the prediction?
Answer : The linear regression model:
TurnOver rate= 12.1005 - 0.07149 * Trust Index - 0.0007216 * Average Bonus
TurnOver rate= 12.1005 - 0.07149 * 70 - 0.0007216 * 6500 = 2.4058 %
Observed turnover rate = 2.15
Residual = 2.15 - 2.4058 = -0.2558 %
Here the predicted value entails higher turnover rate then the actual that's why it is negative here.
b) Comment on whether the conditions for multiple regression are satisfied based on the plots shown below.
Answer :
Assumption 1 : Equal variance or homoscedasticity. Here in plot 1 we can see that the data is homogeneously scattered around the mean line. That equal variance can be assumed and validate here.
Assumption 2 : Normality of residuals. Here also we can see that the mode of residuals is at 0 and it is symmetric around mean so we can also assume that residuals are normally distributed.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.