Question

a. Develop a scatter plot with income as the dependent variable and age as the independent variable. Include the estimated regression equation and the coefficient of determination on your scatter plot. Briefly comment on the relationship between the two variables, and fully interpret the coefficient of determination. b. 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 (?_1level of education attained in number of years), age (?_2 ?? ?????), and gender (?_3 dummy variable, 1= female, 0 = male). Develop the dummy variable for the gender variable first. c. Test whether the coefficients obtained in part (b) are significant at 5%. What is your conclusion? [5 points] d. Fully interpret the meaning of the coefficient on gender, ?_3. e. 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? f. Plot the standardized residuals against predicted income, ? ̂ from regression in part (b). 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.

ATTENTION - COULD ONLY FIT HALF OF DATA. OTHER HALF IS POSTED BY ME AS ANOTHER QUESTION

GENDER	EDUCATION	X3 DUMMY	AGE	Income ($1000)
male	12	0	42	120
female	17	1	28	32.5
female	16	1	36	6.5
male	4	0	52	16.25
female	13	1	35	55
male	12	0	36	55
female	13	1	47	45
male	12	0	55	67.5
male	14	0	54	67.5
female	16	1	45	100
male	15	0	22	18.75
female	13	1	44	9
female	14	1	63	55
male	16	0	40	67.5
female	14	1	42	45
male	18	0	62	67.5
male	11	0	52	67.5
female	12	1	49	45
female	17	1	27	32.5
female	14	1	30	45
female	18	1	29	100
female	18	1	51	175
female	16	1	57	175
male	16	0	44	175
male	16	0	68	175

Answer 1

a) scatter plot is under

The relationship between the variables seems not to be linear as R square = 18.1% only. The amount of the variation which is explained by the model or regression equation is R-square.

b) The regression equation is
Income ($1000) Y = - 131.77 + 8.85 EDUCATION X1 - 19.21 DUMMY X3 + 2.00 AGE X2

The excel output is given below

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.639925889
R Square	0.409505143
Adjusted R Square	0.325148735
Standard Error	43.567122
Observations	25
ANOVA
	df	SS	MS	F	p.value
Regression	3	27642.68849	9214.229498	4.854463961	0.010164928
Residual	21	39859.97651	1898.094119
Total	24	67502.665
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-131.7712464	59.02824031	-2.232342446	0.036613045	-254.5271917	-9.015301033	-254.5271917	-9.015301033
EDUCATION (X1)	8.848443265	3.115728165	2.839927875	0.009809024	2.368931861	15.32795467	2.368931861	15.32795467
DUMMY (X3 )	-19.21093781	18.90789047	-1.01602756	0.321180021	-58.53204845	20.11017283	-58.53204845	20.11017283
AGE (X2)	2.002108147	0.761463744	2.629288868	0.015675596	0.418557607	3.585658686	0.418557607	3.585658686

c) Since P.value obtained in F.test is 0.01016 is less then 0.05 hence we conclude that the model or regression coefficients are significant.

d) The coefficient on gender, ?_3 = -19.21, which means a unit change in gender will results -19.21 units change in the response variable Y.

e) The regression equation is
Income ($1000) Y = - 131.77 + 8.85 EDUCATION X1 - 19.21 DUMMY X3 + 2.00 AGE X2

Income ($1000) Y = - 131.77 + 8.85 *10 - 19.21*0 + 2.00 * 45 = 46.73

f)

Residual plot does not supports the assumptions about error term as the error terms are not randomly distributed in the above graph and are concentrated in the center of the residual plot. Further test of homoscedasticity is also not met.

No outlier has been detected from the data as given below through qq plot