Question

In order to be able to predict salaries of middle managers of a large bank, 90 individuals were randomly selected, and data for the following variables were collected:

Salary = the monthly salary,

Educ = the number of years of education,

Exper = the number of months of experience,

Gender = the gender of an individual; 1 for males, and 0 for females.

Excel results of a regression analysis are shown below:

	Regression Statistics
	Multiple R			0.8186
	R2			0.6700
	Adjusted R2			0.6585
	Standard Error			400.4350
	Observations			90
		df	SS		MS	F		Significance F
Regression		3	28,029,969.88		9,343,323.29	58.21		0.000
Residual		86	13,803,720.12		162,508.37
Total		89	41,833,690.00
		Coefficients	Standard Error		t-stat	p-value
Intercept		4,713.26	327.1967		14.40	1.21E-24
Educ		139.54	19.7253		7.07	3.78E-10
Exper		3.35	0.4649		7.20	2.10E-10
Gender		609.25	94.9920		6.41	7.39E-09

f. Provide an interpretation of (state the meaning of) the intercept.

g. Provide an interpretation of (state the meaning of) the slope for the variable Educ.

h. Provide an interpretation of (state the meaning of) the slope for the variable Gender.

i. Provide an interpretation of (state the meaning of) the standard error of estimate.

j. Provide an interpretation of (state the meaning of) the coefficient of determination.

k. Use the information to make a prediction for the salary of a female manager with 16 years of education and 105 months of experience.

Answer 1

Answer f. The average expected monthly salary for a female with zero years of education and 0 months isof experience is 4713.26

Answer g. With every one year increase in education the average expected salary is expected to increase by 139.54 keeping all other variables constant.

Answer h. the average expected salary for males is 609.25 higher than the average expected salary of females depend on other variables constant.

Answer i. The standard distance between the observations and the regression line is 400.4350

Answer j. Coefficient of determination equals 67% which means that 67% of the total variation in the salaries of middle managers of a large bank is explained by the regression line

Answer k.

The fitted Regression Equation is:

Y' = 4713.26 + 139.54*Educ + 3.35*Exper + 609.25*Gender

So, for X1 = 16, X2 = 105 and X3 =0

Y' = 4713.26 + 139.54*16 + 3.35*105 + 609.25*0 = 7297.65