QUESTION 1 : Please look at the following output from the regression.
What does the value of R-square tell us about our model?
Note: It is not sufficient to just provide some general answers. Use the numbers from the output, and write your answers specific to our regression model.
|
Model Summary
|
|
Model
|
R
|
R Square
|
Adjusted R Square
|
Std. Error of the Estimate
|
|
1
|
.771a
|
.594
|
.580
|
21.741
|
|
a. Predictors: (Constant), DENSITY
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QUESTION 2 : Please look at the following output from the regression.
What do the value of F-test and its P-value tell us about our model?
Note: It is not sufficient to just provide some general answers. Use the numbers from the output, and write your answers specific to our regression model.
|
ANOVAa
|
|
Model
|
Sum of Squares
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df
|
Mean Square
|
F
|
Sig.
|
|
1
|
Regression
|
20747.246
|
1
|
20747.246
|
43.895
|
.000b
|
|
Residual
|
14179.629
|
30
|
472.654
|
|
|
|
Total
|
34926.875
|
31
|
|
|
|
|
a. Dependent Variable: SALES
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|
b. Predictors: (Constant), DENSITY
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QUESTION 3 : The regression coefficient output is shown below.
Does Density matter in terms of explaining sales? Can you provide an explanation of the coefficient estimate for Density? (Note: the unit of Density is number of homes per acre, and the unit of Sales is dollars per thousand homes ).
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Coefficientsa
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|
Model
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Unstandardized Coefficients
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Standardized Coefficients
|
t
|
Sig.
|
|
B
|
Std. Error
|
Beta
|
|
1
|
(Constant)
|
141.525
|
9.109
|
|
15.538
|
.000
|
|
DENSITY
|
-12.893
|
1.946
|
-.771
|
-6.625
|
.000
|
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a. Dependent Variable: SALES
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QUESTION 4 : Managers suspect that the effect of Density on Sales can be nonlinear; in other words, as density increases, there will a decreasing marginal effect on density. To test this idea, they ran an additional regression, with Density and Density_Squared (i.e. Density*Density) as the independent variables (again, Sales as the dependant variable), and the output of the new regression shows below.
Can you explain what the R_square and F-test tell us about the new model? Is the new model better than the model with only Density as the independent variable?
|
Model Summary
|
|
Model
|
R
|
R Square
|
Adjusted R Square
|
Std. Error of the Estimate
|
|
1
|
.910a
|
.829
|
.817
|
14.354
|
|
a. Predictors: (Constant), Density2, DENSITY
|
|
ANOVAa
|
|
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
|
1
|
Regression
|
28951.384
|
2
|
14475.692
|
70.253
|
.000b
|
|
Residual
|
5975.491
|
29
|
206.051
|
|
|
|
Total
|
34926.875
|
31
|
|
|
|
|
a. Dependent Variable: SALES
|
|
b. Predictors: (Constant), Density2, DENSITY
|
|
Coefficientsa
|
|
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
t
|
Sig.
|
|
B
|
Std. Error
|
Beta
|
|
1
|
(Constant)
|
212.595
|
12.768
|
|
16.650
|
.000
|
|
DENSITY
|
-47.293
|
5.601
|
-2.827
|
-8.444
|
.000
|
|
Density2
|
3.419
|
.542
|
2.113
|
6.310
|
.000
|
|
a. Dependent Variable: SALES
|
QUESTION 5 : Continuing from Question 4, can you explain the meaning of the coefficient estimate of Density_Squared (i.e. Density*Density)? (Hint: the effect of Density on Sales is negative, while the effect of Density_Squared on Sales is positive).
Attachment:- data.rar