Question

A survey conducted by a research team was to investigate how the education level, tenure in current employment, and age are related to annual income. A sample of 20 employees is selected and the data are given below.

Education (No. of years)	Length of tenure in current employment (No. of years)	Age (No. of years)	Annual income ($)
17	8	40	124,000
12	12	41	30,000
20	9	44	193,000
14	4	42	88,000
12	1	19	27,000
14	9	28	43,000
12	8	43	96,000
18	10	37	110,000
16	12	36	88,000
11	7	39	36,000
16	14	36	81,000
12	4	22	38,000
16	17	45	140,000
13	7	42	11,000
11	6	18	21,000
20	4	40	151,000
19	7	35	124,000
16	12	38	48,000
12	2	19	26,000
10	6	44	124,000

Estimate a linear regression model (equation) that can be used to predict annual income from the other 3 variables. How much variation in annual income is explained by the model (i.e., by the 3 independent variables)? Enter your answer as a percentage to 2 decimal places, but do not include the % sign in the box below.

A survey conducted by a research team was to investigate how the education level, tenure in current employment, and age are related to annual income. A sample of 20 employees was selected and the same data as in the previous problem were collected. In addition a multiple linear regression analysis was performed to predict annual income from the other 3 variables. A portion of the output from the analysis is shown below.

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-143481.19	39925.60	-3.59	0.00	-228119.67	-58842.71
Education	10011.92	2570.58	3.89	0.00	4562.52	15461.32
Length of tenure	-2193.88	2158.83	-1.02	0.32	-6770.40	2382.63
Age	2689.24	986.35	2.73	0.01	598.26	4780.22

a. All other things being equal, if an employee's education increased by one year, how much would we predict their annual income would change? Enter your answer as an integer. If you predict that annual income will decrease, enter a negative sign before your number. Do not enter a dollar sign in the box.  

b. All other things being equal, if an employee's age increased by one year, how much would we predict their annual income would change? Enter your answer as an integer. If you predict that annual income will decrease, enter a negative sign before your number. Do not enter a dollar sign in the box.

c. What do you predict annual income would be for a 32-year old employee with 16 years of education and 6 years of tenure in their current employment? Enter your answer as an integer. Do not enter a dollar sign in the box.  

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.8186
R Square	0.6701
Adjusted R Square	0.6083
Standard Error	32446.8745
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	3	34218155395	11406051798	10.83402	0.000393507
Residual	16	16844794605	1052799663
Total	19	51062950000
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-143481.19	39925.60	-3.59	0.00	-228119.67	-58842.71
Education	10011.92	2570.58	3.89	0.00	4562.52	15461.32
Length of tenure	-2193.88	2158.83	-1.02	0.32	-6770.40	2382.63
Age	2689.24	986.35	2.73	0.01	598.26	4780.22

The regression equation that can be used to predict annual income from the other 3 variables

Income=- 143481.19 + 10011.92 (Education) - 2193.88 (Length of tenure) + 2689.24 Age

The 67.01 percentage variations in annual income are explained by the model (i.e., by the 3 independent variables).

a. All other things being equal if an employee's education increased by one year, the mean of the annual income will be increased by $10011.92.

b. All other things being equal, if an employee's age increased by one year, the mean of the annual income will be increased by $2689.24.

c. The predicted annual income for a 32-year old employee with 16 years of education and 6 years of tenure in their current employment would be

  Income=- 143481.19 + 10011.92 *16 - 2193.88 *6+ 2689.24*32 = $ 89602