Question

2 Use technology to find the equation of the regression line in which the explanatory variable (or x variable) is the cost of a student population (in thousands) at the university and the response variable (or y variable) is the quarterly sales of a restaurant on campus (in thousands). Restaurant 1 2 3 4 5 6 7 8 9 10 Student population (X) 2 6 8 8 12 16 20 20 22 26 Quarterly Sales (Y) 58 105 88 118 117 137 157 169 149 202

A) Simple linear regression analysis relating to x = Student population to y = Restaurant sales. The linear regression equation we would use to predict the quarterly sales given the student population? y ˆ =

B) Estimate the restaurant sales when the population is 12 (thousand) using the regression equation.

C) What is the null and alternative hypothesis that you would use to determine if the student population and the restaurants income were related to each other?

D) What is the p-value for this test?

E) Assume that the significance level is .05. State your conclusion in F in the context of this problem. Be sure to supply the reason.

F) What is the R value from the test that you ran?

G) Interpret the R value in context of this problem.

Answer 1

using excel>data>data analysis >regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.950123
R Square	0.902734
Adjusted R Square	0.890575
Standard Error	13.82932
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	14200	14200	74.24837	2.55E-05
Residual	8	1530	191.25
Total	9	15730
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	60	9.226035	6.503336	0.000187	38.72473	81.27527
student population (x)	5	0.580265	8.616749	2.55E-05	3.661906	6.338094

A) the regression equation is

y ˆ = 60+5 x

B)the restaurant sales when the population is 12 is 60+5*12 = 120

C) the null and alternative hypothesis that we would use to determine if the student population and the restaurant's income were related to each other

Ho:the student population and the restaurant's income were not related to each other

ha: the student population and the restaurant's income were related to each other

D) the p-value for this test is 0.0000

E) Assume that the significance level is .05. since p value is less than 0.05 so we reject Ho and conclude that the student population and the restaurant's income were related to each other

F) What is the R-value 0.950

G) there is strong positive lineare relationship between student population and the restaurant's income