Question

The accompanying table shows raw data of fifteen adult sample. where income is in dollars. enter the data into Excel and solve the problems using the multiple regression procedures .

	annual income	age	years of education	years of work
ID	Y(1000s)	X1	X2	X3
1	21	24	12	3
2	28	33	14	5
3	34	40	14	7
4	46	47	18	15
5	33	39	10	12
6	49	38	16	10
7	19	20	11	2
8	40	36	16	10
9	35	40	16	11
10	29	36	11	4
11	20	25	10	2
12	38	39	14	7
13	49	44	18	10
14	33	50	9	18
15	41	39	14	5

1. What is the p-value of the F test to determine the overall significance of the regression model? Use 3 decimal points.

2. What is the p-value of the t test to examine an impact of age on annual income using the regression analysis output? Use 3 decimal points.

3. What is the p-value of the t test to examine an impact of years of education on annual income using the regression analysis output? Use 3 decimal points.

4. What would be the estimated annual income for an adult with 34 years old, 12 years of education, and 9 vears of work ? Use two decimal points

5. Interpret the impact of years of education on annual income. Use alpha=0.01

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.917202298
R Square	0.841260056
Adjusted R Square	0.797967344
Standard Error	4.409448715
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	3	1133.458	377.819	19.432	0.000
Residual	11	213.876	19.443
Total	14	1347.333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	-15.135	7.788	-1.943	0.078	-32.277
X1	0.674	0.289	2.332	0.040	0.038
X2	1.854	0.439	4.225	0.001	0.888
X3	-0.043	0.482	-0.089	0.931	-1.105

=================================================================

1. p-value = 0.000  

==============================================================

2. p-value = 0.040, As age increases income also increases

=============================================================

3. p-value = 0.001

===========================================================

  

==========================================================

5. p-value is less than 0.01 , so it is statistically significant.

So, more the year of education will be , more will be the yearly Income.