Question

A researcher wants to know if there is a relationship between the number of shopping centers in a state and the retail sales (in billions $) of that state. A random sample of 8 states is listed below. After determining, via a scatter-plot, that the data followed a linear pattern, the regression line was found. Using the given data and the given regression output answer the following questions. State Num Sales

1 630 15.5

2 370 7.5

3 616 13.9

4 700 18.7

5 430 8.2

6 558 13.2

7 1200 23.0

8 2976 87.3

1.What is the equation of the regression line?

2.Interpret the slope in the context of the problem.

3.Find the coefficient of determination.

4.Interpret the meaning of R2 in the context of the problem.

5.State the hypotheses to test for the significance of the regression equation.

6.Is there a significant relationship between dependent and independent variables at alpha=0.05? Why?

7.Use a 95% prediction interval to predict the sales for a state with 100 shopping centers

Paste the table with the results of regression analysis.

Answer 1

data

shopping center	sales
630	15.5
370	7.5
616	13.9
700	18.7
430	8.2
558	13.2
1200	23
2976	87.3

result

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9911
R Square	0.9823
Adjusted R Square	0.9793
Standard Error	3.7849
Observations	8.0000
ANOVA
	df	SS	MS	F	Significance F
Regression	1.0000	4760.0537	4760.0537	332.2703	0.0000
Residual	6.0000	85.9551	14.3258
Total	7.0000	4846.0088
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-4.8701	2.0489	-2.3769	0.0550	-9.8837	0.1434	-9.8837	0.1434
shopping center	0.0302	0.0017	18.2283	0.0000	0.0262	0.0343	0.0262	0.0343

1) sales^ = -4.8701 + 0.0302* shopping center

2) slope = 0.0302

when number of shopping center increase by 1, sales increase by 0.0302 units

3)

this is given by R^2 = 0.9823

4) that means 98.23% of variation of sales is explained by this model