Question

Individual	Bettendorf	Experience (X1)	Education (X2)	Sex (X3)
1	53600	5.5	4	F
2	52500	9	4	M
3	58900	4	5	F
4	59000	8	4	M
5	57500	9.5	5	M
6	55500	3	4	F
7	56000	7	3	F
8	52700	1.5	4.5	F
9	65000	8.5	5	M
10	60000	7.5	6	F
11	56000	9.5	2	M
12	54900	6	2	F
13	55000	2.5	4	M
14	60500	1.5	4.5	M

1. At the 5% level of significance, is there a relationship in the population between the three predictors taken as a group and the annual salary for teachers?

Select one:

a. Yes

b.Cannot be determined from the data

c.No

d.50/50 chance that there is.

Which predictor(s), if any, would you remove because it does not contribute to the regression models, using the 90% confidence level, α = .10?

Select one:

a.Sex and Experience

b. None

c. Education

d. Experience

Answer 1

Using Excel, input data in the following manner:

Bettendorf	Experience (X1)	Education (X2)	Sex (X3)
53600	5.5	4	1
52500	9	4	0
58900	4	5	1
59000	8	4	0
57500	9.5	5	0
55500	3	4	1
56000	7	3	1
52700	1.5	4.5	1
65000	8.5	5	0
60000	7.5	6	1
56000	9.5	2	0
54900	6	2	1
55000	2.5	4	0
60500	1.5	4.5	0

Go to Data, select Data Analysis, choose Regression. Put Experience, Education and Sex in X input range and Bettendorf in Y input range.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.569
R Square	0.323
Adjusted R Square	0.120
Standard Error	3249.019
Observations	14
ANOVA
	df	SS	MS	F	Significance F
Regression	3	50450913.071	16816971.024	1.593	0.252
Residual	10	105561229.786	10556122.979
Total	13	156012142.857
	Coefficients	Standard Error	t Stat	P-value
Intercept	50546.956	4427.058	11.418	0.000
Experience (X1)	195.327	329.659	0.593	0.567
Education (X2)	1480.630	808.958	1.830	0.097
Sex (X3)	-1595.060	1857.615	-0.859	0.411

1. H₀: β₁ = β₂ = β₃ = 0, There is no relationship in the population between the three predictors taken as a group and the annual salary for teachers

H₁: At least one β_i is not 0, There is a relationship in the population between the three predictors taken as a group and the annual salary for teachers

p-value (Significance F) = 0.252

Level of significance = 0.05

Since p-value is more than 0.05, we do not reject the null hypothesis.

So, there is no relationship in the population between the three predictors taken as a group and the annual salary for teachers. (Option C)

2. Since p-values for Education (0.097) is less than 0.1, and p-values for other two variables is more than 0.1, we can say that only Education is a significant variable. So, we can remove experience and sex (Option A)