Kindly Make the Answer Typed A researcher wants to know if there is a relationsh
ID: 3150491 • Letter: K
Question
Kindly Make the Answer Typed
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
568
13.2
7
1200
23.0
8
2976
87.3
a. What is the equation of the regression line?
b. Interpret the slope in the words of the problem.
c. Find r2 and interpret its meaning in the words of the problem.
d. Find the error for predicting the sales of a state with 1200 stores.
e. Use the regression line to predict the sales for a state with 100 stores
State
Num
Sales
1
630
15.5
2
370
7.5
3
616
13.9
4
700
18.7
5
430
8.2
6
568
13.2
7
1200
23.0
8
2976
87.3
Explanation / Answer
sol) From Excel
a) The Regression equation is y=a+bx
from Excel
y=-4.93 + 0.03 X
b) Slope=0.03 and Intercept= -4.93
C) R2 =0.98
Hence 98% variation in dependent variable is due to independent variable
d)
The fitted regression is
y= -4.93 + 0.03 X
Now x=1200
y=-4.93 + 0.03*1200 = 31.07
e)
The fitted regression is
y= -4.93 + 0.03 X
Now x=100
y=-4.93 + 0.03*100 = 1.93
SUMMARY OUTPUT Regression Statistics Multiple R 0.991159 R Square 0.982396 Adjusted R Square 0.979461 Standard Error 3.770754 Observations 8 ANOVA df SS MS F Significance F Regression 1 4760.697 4760.697 334.8222 1.72E-06 Residual 6 85.3115 14.21858 Total 7 4846.009 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -4.93018 2.043656 -2.41243 0.0524 -9.93082 0.070468 Num 0.030273 0.001654 18.29815 1.72E-06 0.026224 0.034321Related Questions
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