Question

# A researcher wants to know if there is a relationship between the number of shopping centers...

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.

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

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