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

The table shows the total square footage (in billions) of
retailing space at shopping centers and their sales (in billions
of dollars) for 10 years. The equation of the regression line
is
ModifyingAbove y with caret equals 605.666 x minus
2189.023y=605.666x−2189.023.
Complete parts a and b.
Total Square Footage, x
5.15.1
5.25.2
5.15.1
5.45.4
5.55.5
5.75.7
5.75.7
5.95.9
5.95.9
6.16.1
Sales, y
881.6881.6
940.1940.1
981.4981.4
1050.21050.2
1121.81121.8
1200.71200.7
1294.31294.3
1339.11339.1
1438.91438.9
1536.71536.7
(a) Find the coefficient of determination and interpret...

The table shows the total square footage (in billions) of
retailing space at shopping centers and their sales (in billions
of dollars) for 10 years. The equation of the regression line
is
ModifyingAbove y with caret equals 550.067 x minus
1890.986y=550.067x−1890.986.
Complete parts a and b.
Total Square Footage, x
4.94.9
5.25.2
5.35.3
5.45.4
5.55.5
5.75.7
5.75.7
5.85.8
6.16.1
6.26.2
Sales, y
870.4870.4
938.4938.4
976.8976.8
1056.91056.9
1119.21119.2
1200.11200.1
1299.81299.8
1330.51330.5
1449.71449.7
1542.11542.1
(a) Find the coefficient of determination and interpret...

The table shows the total square footage? (in billions) of
retailing space at shopping centers and their sales? (in billions
of? dollars) for 10 years. Construct a? 90% prediction interval for
sales when the total square footage is 5.5 billion. The equation of
the regression line is Modifying above y with caret= 608.356x-
2207.079
Total Square?Footage, x
5.1
5.2
5.3
5.2
5.5
5.6
5.8
5.9
5.9
6.1
?Sales, y
878.7
925.4
980.8
1064.3
1112.8
1206.3
1281.2
1340.4
1429.6
1534.3

The table shows the total square footage (in billions) of
retailing space at shopping centers and their sales (in billions
of dollars) for 10 years. Construct a 90% prediction interval for
sales when the total square footage is
5.65.6
billion. The equation of the regression line is
ModifyingAbove y with caret equals 626.092 x minus
2290.110y=626.092x−2290.110.
Total SquareFootage, x
5.15.1
5.25.2
5.35.3
5.25.2
5.45.4
5.65.6
5.85.8
5.85.8
5.95.9
6.16.1
Sales, y
867.3867.3
943.5943.5
995.9995.9
1055.91055.9
1111.71111.7
1209.11209.1
1286.61286.6
1341.41341.4
1429.81429.8...

3.
The accountant
at Walmart wants to determine the relationship between customer
purchases at the store, Y ($), and the customer monthly salary, X
($). A sample of 15 customers is randomly selected and the results
are summarized in the ANOVA table below:
df
SS
Regression
1
186952
Residual
13
99236
Total
14
286188
Coefficients
Standard
Error
t
Stat
p-value
Intercept
78.58
7.540
1.202
0.035
Salary
0.066
0.013
4.948
0.003
a.
What is the
estimated regression equation that relates the...

Barclay's manager of Financial Service wants to find out
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The results from the Regression are presented below:
y^=1.4606x-6.5321;R2=0.735
What are the Independent and Dependent Variables?
Independent variable:
Dependent variable:
What is the value of the correlation coefficient?
Interpret it.
What % of the variation in the amount of sales...

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Seeds Produced
62
41
55
50
47
54
41
63
46
Sprout Percent
54
67.5
63.5
67
59.5
58
65.5
50.5
54
Find the correlation coefficient:
r=r= Round to 2 decimal places.
The null and alternative hypotheses for correlation are:
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H1:H1: ? ρ μ r ≠≠ 0...

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Movies
5
8
8
8
1
5
5
9
4
Books
6
0
0
0
7
6
3
0
3
Find the correlation coefficient:
r=r= Round to 2 decimal places.
The null and alternative hypotheses for correlation are:
H0:H0: ? r μ ρ ==...

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Vacation Days
0
1
4
9
13
13
15
1
6
9
Sick Days
9
12
10
5
5
1
0
6
4
6
Find the correlation coefficient: r=r= Round
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The null and alternative hypotheses for correlation are:
H0:? r μ...

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Time
9
3
13
5
15
8
5
16
Score
80
75
91
75
93
78
82
91
Find the correlation coefficient:
r=r= Round to 2 decimal places.
The null and alternative hypotheses for correlation are:
H0:H0: ? μ r ρ == 0
H1:H1: ? r ρ μ ≠≠ 0
The p-value is: (Round to four...

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