Reference no: EM131503208
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.
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Model Summary
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Model
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R
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R Square
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Adjusted R Square
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Std. Error of the Estimate
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1
|
.771a
|
.594
|
.580
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21.741
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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.
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ANOVAa
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Model
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Sum of Squares
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df
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Mean Square
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F
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Sig.
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1
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Regression
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20747.246
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1
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20747.246
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43.895
|
.000b
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Residual
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14179.629
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30
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472.654
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|
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Total
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34926.875
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31
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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
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t
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Sig.
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B
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Std. Error
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Beta
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1
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(Constant)
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141.525
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9.109
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15.538
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.000
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DENSITY
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-12.893
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1.946
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-.771
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-6.625
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.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?
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Model Summary
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|
Model
|
R
|
R Square
|
Adjusted R Square
|
Std. Error of the Estimate
|
|
1
|
.910a
|
.829
|
.817
|
14.354
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a. Predictors: (Constant), Density2, DENSITY
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ANOVAa
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Model
|
Sum of Squares
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df
|
Mean Square
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F
|
Sig.
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|
1
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Regression
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28951.384
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2
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14475.692
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70.253
|
.000b
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Residual
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5975.491
|
29
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206.051
|
|
|
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Total
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34926.875
|
31
|
|
|
|
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a. Dependent Variable: SALES
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b. Predictors: (Constant), Density2, DENSITY
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Coefficientsa
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|
Model
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Unstandardized Coefficients
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Standardized Coefficients
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t
|
Sig.
|
|
B
|
Std. Error
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Beta
|
|
1
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(Constant)
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212.595
|
12.768
|
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16.650
|
.000
|
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DENSITY
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-47.293
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5.601
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-2.827
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-8.444
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.000
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Density2
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3.419
|
.542
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2.113
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6.310
|
.000
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a. Dependent Variable: SALES
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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