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Doctor of Education in Educational Leadership with a Specialization in Educational Technology Phoniex University Oct-1999 - Nov-2005
HR Executive a21, Inc. Nov-1998 - Dec-2005
Please look at the following output from the regression.Â
What does the value of R-square tell us about our model?Â
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
12.5 points  Â
What do the value of F-test and its P-value tell us about our model?Â
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.
Â
ANOVAa
Sum of Squares
df
Mean Square
F
Sig.
Regression
20747.246
43.895
.000b
Residual
14179.629
30
472.654
Total
34926.875
31
a. Dependent Variable: SALES
b. Predictors: (Constant), DENSITY
The regression coefficient output is shown below.Â
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 ).Â
Coefficientsa
Unstandardized Coefficients
Standardized Coefficients
t
B
Std. Error
Beta
(Constant)
141.525
9.109
15.538
.000
DENSITY
-12.893
1.946
-.771
-6.625
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?
.910a
.829
.817
14.354
a. Predictors: (Constant), Density2, DENSITY
28951.384
2
14475.692
70.253
5975.491
29
206.051
b. Predictors: (Constant), Density2, DENSITY
212.595
12.768
16.650
-47.293
5.601
-2.827
-8.444
Density2
3.419
.542
2.113
6.310
(This is a Bonus Question)
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).Â
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