Question

The Conference Board produces a Consumer Confidence Index (CCI) that reflects people’s feelings about general business conditions, employment opportunities, and their own income prospects. Some researchers may feel that consumer confidence is a function of the median household income. Shown here are the CCIs for nine years and the median household incomes for the same nine years published by the U.S. Census Bureau. Determine the equation of the regression line to predict the CCI from the median household income. Compute the standard error of the estimate for this model. Compute the value of r². Does median household income appear to be a good predictor of the CCI? Why or why not? Conduct the five step hypothesis test for both the model and regressor, using .05 level of significance.

Please provide the 5 steps for both the model and the regressor test, the Minitab output for each hypothesis test, and state the business implication based upon your analysis. You must use Minitab and the 5 step hypothesis testing process.

CCI            Median Household Income ($1,000)

116.8        37.415

91.5          36.770

68.5          35.501

61.6          35.047

65.9          34.700

90.6          34.942

100.0        35.887

104.6        36.306

125.4        37.005

Please provide the 5 steps and Minitab output, and make a decision about the data. You must use Minitab and the 5 step hypothesis testing process.

Answer 1

Result:

The Conference Board produces a Consumer Confidence Index (CCI) that reflects people’s feelings about general business conditions, employment opportunities, and their own income prospects. Some researchers may feel that consumer confidence is a function of the median household income. Shown here are the CCIs for nine years and the median household incomes for the same nine years published by the U.S. Census Bureau. Determine the equation of the regression line to predict the CCI from the median household income.

Regression Equation

CCI

=

-599 + 19.22 Median Household Income

Compute the standard error of the estimate for this model.

standard error of the estimate =13.5389

Compute the value of r2.

R square = 0.6880   (68.80%)

Does median household income appear to be a good predictor of the CCI? Why or why not? Conduct the five step hypothesis test for both the model and regressor, using .05 level of significance.

To test median household income appear to be a good predictor of the CCI,

 H0: β = 0   H1: β ≠ 0

 Level of significance =0.05

Rejection rule: if obtained p value < 0.05, reject Ho.   

 Calculated t=3.93, P=0.006 ( from the output)

Obtained p value 0.006 is < 0.05 level of significance.

Ho is rejected.

We conclude that median household income appear to be a good predictor of the CCI.

To test significance of the model

H0: the regression model is not significant, H1: the regression model is  significant, 

 Level of significance =0.05

Rejection rule: if obtained p value < 0.05, reject Ho.   

 Calculated F=15.43, P=0.006 ( from the output)

Obtained p value 0.006 is < 0.05 level of significance.

Ho is rejected.

We conclude that  the regression model is  significant.

MINITAB output:

Regression Analysis: CCI versus Median Household Income

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Regression	1	2829	2829.0	15.43	0.006
Median Household Income	1	2829	2829.0	15.43	0.006
Error	7	1283	183.3
Total	8	4112

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
13.5389	68.80%	64.34%	50.08%

Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	-599	176	-3.41	0.011
Median Household Income	19.22	4.89	3.93	0.006	1.00

Regression Equation

CCI

=

-599 + 19.22 Median Household Income