Question

3. The accountant at Walmart wants to determine the relationship between customer purchases at the store, Y ($), and the customer monthly salary, X ($). A sample of 15 customers is randomly selected and the results are summarized in the ANOVA table below:

	df	SS
Regression	1	186952
Residual	13	99236
Total	14	286188
	Coefficients	Standard Error	t Stat	p-value
Intercept	78.58	7.540	1.202	0.035
Salary	0.066	0.013	4.948	0.003

a. What is the estimated regression equation that relates the amount of customer’s purchase (Y) to the customer’s monthly salary (X)?

b. Is the regression relationship significant? Use the p-value approach and 1% level of significance.

c. Compute the coefficient of determination between the amount purchase and the customer’s monthly salary. Interpret the result in the context of the problem.

d. Calculate the correlation coefficient and comment on the goodness of fit in this linear relationship

Answer 1

SOLUTION A: THE ESTIMATED REGRESSION EQUATION IS

SOLUTION B: NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

LEVEL OF SIGNIFICANCE =0.01

TEST STATISTIC t= 4.948

P value= 0.003

Since P value SMALLER than the level of significance therefore SIGNIFICANT

Decision: REJECT NULL HYPOTHESIS H0.

Conclusion: THERE IS SIGNIFICANT RELATIONSHIP BETWEEN CUSTOMER'S PURCHASE AND CUUSTOMER'S SALARY.

SOLUTION C: COEFFICIENT OF DETERMINATION R squared= SS regression/SS Total

R squared= 18692/286188

R squared= 0.065

Interpretation: 0.065  indicates that the model explains 6.5% of the variability of the response data around its mean.

SOLUTION D: Correlation r= sqrt( COEFFICIENT OF DETERMINATION)= r= sqrt(0.065)

r= 0.2550

Since r=0.2550 it means it is  positively correlated but value is less than 0.5 so the correlation between X and Y is weak.