Question

a. Using the Excel’s Regression Tool, develop the estimated regression equation to show how income (y annual income in $1000s) is related to the independent variables education(level of education attained in number of years), age ( Develop the dummy variable for the gender variable first. [ 6 points]

2. Use the t test to test whether each of the coefficients obtained in part (a) are significant at .05 level of significance. What are your conclusions? [3 points]

3. Use the F test to test for overall significance of the relationship. What is your conclusion?

[ 2 points]

4. Fully interpret the meaning of the coefficient on gender,. [ 2 points]

5. 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]

6. 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. [3.5 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

you can use =IF(C2="male",1,0) to code male as 1 , female as 0  

Note that C2 is cell value of gender

Using Excel

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.5989
R Square	0.3587
Adjusted R Square	0.3169
Standard Error	37.0213
Observations	50
ANOVA
	df	SS	MS	F	Significance F
Regression	3	35265.1280	11755.0427	8.5767	0.0001
Residual	46	63046.4920	1370.5759
Total	49	98311.6200
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-96.1315	32.9981	-2.9132	0.0055	-162.5532	-29.7097
EDUCATION	7.1314	1.9068	3.7400	0.0005	3.2933	10.9695
AGE	0.6914	0.4299	1.6081	0.1147	-0.1740	1.5568
gender	34.2128	11.4976	2.9756	0.0046	11.0693	57.3563

a)
y^ = -96.1315 + 7.1314 Educ + 0.6914 Age + 34.2128 Gender

b)
if p-value < alpha, we reject the null hypothesis
if p-value > alpha, we fail to reject the null hypothesis

here Education and Gender are significant
Age is not significant

c)
p-value = 0.0001 < alpha
hence overall model is significant

d)
coefficent of Gender = 34.2128
It means on average Male earn 34.2128 thousand more than female

Please rate if helpful

By HOMEWORKLIB RULES, we have to answer only first 4 sub-parts in multiple sub-parts

Please post rest questions again