Question

The following data shows the yearly income (in $1,000) and age of a sample of seven individuals.

Income (in $1,000) (Y)	Age (X)
20	18
24	20
24	23
25	34
26	24
27	27
34	27

SUMMARY OUTPUT
Regression Statistics
Multiple R	$0.48
R Square	$0.23
Adjusted R Square	$0.07
Standard Error	$4.11
Observations	7
ANOVA
	df	SS	MS	F	Significance F
Regression	1	24.79	24.79	1.46	0.28
Residual	5	84.64	16.93
Total	6	109.43
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	16.20	8.01	2.02	0.10	-4.39	36.80	-4.39	36.80
Age (X)	0.38	0.32	1.21	0.28	-0.43	1.20	-0.43	1.20

a.Using the Excell output, develop the least squares estimated regression equation.

b.At 95% confidence, using the p-value approach, determine whether or not the slope is significantly different from zero. Write out the decision rule.

c.Estimate the yearly income of a 30-year-old individual. (show your work)

Answer 1

a. Using the Excel output, develop the least squares estimated regression equation.

From given excel output, the least squares regression equation is given as below:

Y = 16.20 + 0.38*X

Income (in $1000) = 16.20 + 0.38*Age

Income (in $1000) is the dependent variable and Age (in years) is the independent variable of this regression model.

Y-intercept for this regression model is given as 16.20 and slope for this regression model is given as 0.38.

b. At 95% confidence, using the p-value approach, determines whether or not the slope is significantly different from zero. Write out the decision rule.

We are given

c = 95% = 0.95

So, ? = 1 – c = 1 – 0.95 = 0.05

For the t test for significance of slope, p-value is given as 0.28.

P-value = 0.28

Decision rule: Reject null hypothesis H₀ if P-value < ?

P-value > ? = 0.05

So, we do not reject the null hypothesis that slope for regression equation is not statistically significant.

There is insufficient evidence to conclude that slope is significantly different from zero.

c. Estimate the yearly income of a 30-year-old individual. (Show your work)

We have regression equation given as below:

Income (in $1000) = 16.20 + 0.38*Age

Age = 30

Income (in $1000) = 16.20 + 0.38*30

Income (in $1000) = 27.6

Income = $27600

Required answer = $27600