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

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Num shopping centers (X) :

630

370

616

700

430

558

1200

2976

Sales (Y) :

15.5

7.5

13.9

18.7

8.2

13.2

23.0

87.3

The regression equation obtained using the online regression calculator is :

y = 0.03025X - 4.87014

2.) The slope value, for every unit change in number of shopping centers, the number of sales increases by 0.03025

3.)

The Coefficient of determination (R²) as obtained by the R² value calculator is : 0.9823

4.)

About 98%  of variation in number of sales is explained by the regression line

5.)

Correlation Coefficient = 0.9911

H0 : p ≥ 0.99

H1 : p < 0.99