Question

1. Predict the annual income for a female aged 45 with 10 years of education. How much would the predicted income have changed for a male? [3.5 points]

Plot the standardized residuals against predicted income,  from regression in part (a). Check for outliers and explain whether the residual plot supports the assumptions about Ɛ. What is your conclusion? Submit the graph to earn full points.

EDUCATION	AGE	GENDER	INCOME (in $1000)
12	60	female	6.5
16	39	male	120
16	33	female	21.75
12	51	male	82.5
16	42	female	55
14	20	male	7.5
14	57	male	37.5
13	61	female	5.5
16	31	male	9
12	30	male	37.5
14	68	female	13.75
16	50	male	32.5
12	27	male	0.5
16	30	male	55
18	65	female	55
19	36	male	67.5
12	22	male	21.75
6	35	male	21.75
12	67	female	9
12	48	male	23.75
12	48	female	45
15	42	male	120
14	61	female	37.5
13	34	male	82.5
17	53	male	82.5
12	39	male	67.5
16	61	male	175
18	34	male	100
12	39	female	45
14	32	male	37.5
16	54	female	45
14	55	female	13.75
14	62	male	32.5
6	39	male	16.25
12	30	female	32.5
12	35	female	16.25
16	55	male	175
17	43	male	175
16	71	male	100
16	55	male	100
14	68	female	45
11	47	male	82.5
16	30	male	55
16	38	female	100
16	41	female	45
20	62	female	120
20	49	male	67.5
16	52	female	100
16	52	male	82.5
14	33	male	82.5

Answer 1

Answer:

1. Predict the annual income for a female aged 45 with 10 years of education. How much would the predicted income have changed for a male? [3.5 points]

MINITAB used.

The variable gender is coded as female = 1 and male =0.

Regression Equation

INCOME (in $1000)

=

-61.9 + 0.691 AGE - 34.2 Gender + 7.13 EDUCATION

When age =0, female and 10 years education,

predicted income (in 1000) = -61.9+0.691*45-34.2*1+7.13*10 =6.295

or $6295

When age =0, male and 10 years education,

predicted income (in 1000) = -61.9+0.691*45-34.2*0+7.13*10 =40.495

or $40495.

For male predicted value increases by $34200.

Regression Analysis: INCOME (in $1000) versus AGE, ... r, EDUCATION

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Regression	3	35265	11755	8.58	0.000
AGE	1	3544	3544	2.59	0.115
Gender	1	12136	12136	8.85	0.005
EDUCATION	1	19171	19171	13.99	0.001
Error	46	63046	1371
Lack-of-Fit	43	59746	1389	1.26	0.495
Pure Error	3	3301	1100
Total	49	98312

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
37.0213	35.87%	31.69%	25.70%

Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	-61.9	30.5	-2.03	0.048
AGE	0.691	0.430	1.61	0.115	1.18
Gender	-34.2	11.5	-2.98	0.005	1.14
EDUCATION	7.13	1.91	3.74	0.001	1.04

Regression Equation

INCOME (in $1000)

=

-61.9 + 0.691 AGE - 34.2 Gender + 7.13 EDUCATION

Fits and Diagnostics for Unusual Observations

Obs	INCOME (in $1000)	Fit	Resid	Std Resid
27	175.0	94.4	80.6	2.27	R
37	175.0	90.2	84.8	2.36	R
38	175.0	89.0	86.0	2.38	R

R Large residual

Plot the standardized residuals against predicted income,  from regression in part (a). Check for outliers and explain whether the residual plot supports the assumptions about Ɛ. What is your conclusion? Submit the graph to earn full points.

The residuals fan out from left to right rather than exhibiting a consistent spread around the residual = 0 line. The standardized residual vs. fits plot suggests that the error variances are not equal.

Scatterplot of SRES vs FITS SRES o 20 40 60 FITS 80 100 120