Question

Question 8. Results of a multiple linear regression on these four variables are depicted in the table below.

Multiple Linear Regression: Summary Output
	Coefficients
Intercept	-35.2
Training	2.5
Performance Score	8.2
Years of Service	1.1

a) Use this information to develop and interpret a Regression Equation.

b) Estimate the value of the dependent variable when an employee has attended 5 hours of training, receives a performance evaluation score of 3.6, and has been working for the company for 9 years.

Answer 1

a)

Regression equation

y = -35.2 + x1*R_{traininghours} + x2*R_{Perfromance score} +x3*R_{Years of service}

y = -35.2 + x1*2.5 + x2*8.2 +x3*1.1

Interpretation

Multiple regression indicates effect of multiple factors on dependent variable

R_training, R_{Perfromance score},R_{Years of service} are partial regression coefficients
x1,x2,x3 are independent variables

In multiple regression, regression coefficients are interpreted as change in dependent variable with 1 unit change of the independent variable considering all other variables constant

So, Change in dependent variable is 2.5 when training hours is changed by 1
Change in dependent variable is 8.2 when Performance score is changed by 1
Change in dependent variable is 1.1 when Years of service is changed by 1

b)

Value of dependent variable = -35.2 + 2.5*5 + 8.2*3.6 +1.1*9 = 16.72