Question

Data on monthly spending of 50 individuals on fruits (in dollars) has been collected and researchers want to know the relationship with one’s annual income of each individual (in thousands of dollars), whether they are male (male =1 if yes, 0 otherwise) and whether they are college graduates (COLLEGE=1 if yes, 0 otherwise). The analysis of data is presented below:

Regression Statistics
Multiple R	0.745
R Square	0.569
Adjusted R Square	0.546
Standard Error	17.126
Observations	50

ANOVA
	df	SS	MS	F	Significant F
Regression	3	16826.69404	5608.89801	19.1235213	3.4028E-08
Resigual	46	13491.72596	293.29839	No data	No data
Total	49	30318.42	No data	No data	No data

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	45.209	6.3782	7.0882	6.72E-09	32.3708799	58.0480507
Income	0.263	0.0907	2.8958	0.0058	0.08007318	0.44517957
Male	-30.452	6.6464	-5.1835	4.74E-06	-47.830171	-21.073211
College Grad	4.820	6.9444	0.6941	0.4911	-9.1581414	18.7986359

a)Based on this analysis, what percentage of variations in monthly spending on fruits can be explained by the model?

b)If you were to use this given anlaysis, what would be the point prediction for the mean value of monthly spending on fruits for men who are college graduates with an annual income of $60,000?

c) Based on this result, on average _______________ spend more on fruits than ______________ per month?

*Men, Women

*Women, Men

d)At a 5% level of significance, is (are) there any variable(s) which should be removed from the model? (Select all that apply.)

Income

Male

College

Grad

None of the above

Answer 1

a). 56.9% of variations in monthly spending on fruits can be explained by the model.

b). Let Y be the monthly spending.

Let X1 be the individual’s annual income.

Let X2 be the male (male =1 if yes, 0 otherwise).

Let X3 be the college graduates (COLLEGE=1 if yes, 0 otherwise).

On the basis of given analysis, the estimated regression equation is,

The point prediction for the mean value of monthly spending on fruits for men who are college graduates with an annual income of $60,000 is given by,

Therefore, the point prediction for the mean value of monthly spending on fruits for men who are college graduates with an annual income of $60,000 is $15799.577.

c). The variable college graduate must be removed from the model because its p-value (0.4911) is greater than the significance level 0.05 which signifies that the variable college graduate does not give significant results.