10 Use the Excel Regression tool to run a regression analysi

10. Use the Excel Regression tool to run a regression analysis using salary as the dependent variable and age as the independent variable. Interpret each of the following regression statistics: multiple R, R Square and standard error. State the hypotheses for the F-test. Explain how the

Solution

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.875719

R Square

0.766883

Adjusted R Square

0.762485

Standard Error

5995.166

Observations

55

ANOVA

df

SS

MS

F

Significance F

Regression

1

6.27E+09

6.27E+09

174.3536

2.16E-18

Residual

53

1.9E+09

35942013

Total

54

8.17E+09

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

8133.265

2895.786

2.808655

0.006951

2325.053

13941.48

2325.053

13941.48

Age

895.5297

67.82105

13.2043

2.16E-18

759.4979

1031.561

759.4979

1031.561

10. Use the Excel Regression tool to run a regression analysis using salary as the dependent variable and age as the independent variable.

The regression line salary = 8133.265+895.5297* age

Interpret each of the following regression statistics:

When age increases by one year, the salary increases by $895.5297.

Intercept is 8133.265. when age is 0, the salary is 8133.265. This is no meaning in this case.

multiple R = 0.8757, R Square = 0.7669 and standard error= 5995.166

76.69% of variance in salary is explained by age.

State the hypotheses for the F-test.

Null hypothesis: the regression model is not significant.

Alternate hypothesis: the regression model is significant.

Explain how the

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.875719
R Square	0.766883
Adjusted R Square	0.762485
Standard Error	5995.166
Observations	55
ANOVA
	df	SS	MS	F	Significance F
Regression	1	6.27E+09	6.27E+09	174.3536	2.16E-18
Residual	53	1.9E+09	35942013
Total	54	8.17E+09
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	8133.265	2895.786	2.808655	0.006951	2325.053	13941.48	2325.053	13941.48
Age	895.5297	67.82105	13.2043	2.16E-18	759.4979	1031.561	759.4979	1031.561