Question 3 (Marks distribution: 4+3+4+3+0+0+4+4+3= 25/90)

The human resources manager of DataCom, Inc. is curious to find out if employee characteristics and DataCom’s task requirements can help explain the salary structure of its employees. He considers the following regression model.

Salaryi=β0+β1 Yearpriori+β2 Yearwithi+β3 Edui+β4 Genderi+β5 Depti+εi, (1) where variables used in this equation are defined as,

Salaryi= Salary of employee i,

Yearpriori= the number of years of prior relevant work experience,

Yearwithi= the number of years of employment at DataCom,

Edui= the number of years of education or training beyond year 10 of high school,

Genderi= 1 when it is a male employee and 0 when it is a female,

Depti= the employee’s department, there being four departments (1 = Sales, 2 = Purchasing, 3 = Advertising & 4 = Engineering)

The data on various variables have been collected for a sample of employees and are given in the file

• (a)  Obtain matrix of inter-correlation coefficients for variables Salary, Yearprior, Yearafter and Edu using Excel. Comment on the strength of the linear relationship between Salary and each of the predictor variables.
• (b)  Explain, how are the predictor variables Gender and Department different from the other predictors as given in data?
• (c)  Suppose the interest is to a fit model specifying Salary as a linear function of predictors Yearprior, Yearwith, Edu, Gender and Dept.
• Will the fitting of model (1) capture the effect of the employee’s department on his/her salary? If yes, explain your reasoning; if not then what would be needed to improve the model so that it can capture the effect of the employee’s department on his/her salary? Assume we wish to compare salaries across departments using Sales-department’s salary as the base level.
• (d)  Fit the regression model considered suitable in part (c) using Excel and report the model.
• (g) Should all predictor variables be kept in the model? Explain your reasoning. If not which predictor variable should be considered first for dropping from the model.
• (h)  Refit the model by dropping the predictor variable, not seemed reasonable in part (g), from the model. Is there any other variable that can be dropped from the model? Provide summary of your fitted models in a tabular form as displayed below. Compare the performance of your
• fitted models. Which is the best performing model? Give reason for your choice of the best performing model.

• (i) Using Excel and your best fitting regression model, obtain a 95% prediction interval estimate of the annual salary of a male employee who has acquired a 3-year university business degree following school year 12 level, has been in the purchasing department since joining the company 5 years ago. 

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