Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.
Regression Analysis
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
-- Font family --Andale MonoArialArial BlackBook AntiquaComic Sans MSCourier NewGeorgiaHelveticaImpactSymbolTahomaTerminalTimes New RomanTrebuchet MSVerdanaWebdingsWingdings -- Font size --1 (8pt)2 (10pt)3 (12pt)4 (14pt)5 (18pt)6 (24pt)7 (36pt) -- Format --HeadingSub Heading 1Sub Heading 2ParagraphFormatted Code -- Font family -- -- Font size --
Path: p
Words:0
12.5 points
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
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
b. Predictors: (Constant), DENSITY
-- Font family --Andale MonoArialArial BlackBook AntiquaComic Sans MSCourier NewGeorgiaHelveticaImpactSymbolTahomaTerminalTimes New RomanTrebuchet MSVerdanaWebdingsWingdings -- Font size --1 (8pt)2 (10pt)3 (12pt)4 (14pt)5 (18pt)6 (24pt)7 (36pt) -- Format --HeadingSub Heading 1Sub Heading 2ParagraphFormatted Code -- Font family -- -- Font size -- Path: p
Words:0
12.5 points
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 ).
Coefficientsa
Model
Unstandardized Coefficients
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
a. Dependent Variable: SALES
For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). -- Font family --Andale MonoArialArial BlackBook AntiquaComic Sans MSCourier NewGeorgiaHelveticaImpactSymbolTahomaTerminalTimes New RomanTrebuchet MSVerdanaWebdingsWingdings -- Font size --1 (8pt)2 (10pt)3 (12pt)4 (14pt)5 (18pt)6 (24pt)7 (36pt) -- Format --HeadingSub Heading 1Sub Heading 2ParagraphFormatted Code -- Font family -- -- Font size -- 5
Path: p
Words:28
12.5 points
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
-- Font family --Andale MonoArialArial BlackBook AntiquaComic Sans MSCourier NewGeorgiaHelveticaImpactSymbolTahomaTerminalTimes New RomanTrebuchet MSVerdanaWebdingsWingdings -- Font size --1 (8pt)2 (10pt)3 (12pt)4 (14pt)5 (18pt)6 (24pt)7 (36pt) -- Format --HeadingSub Heading 1Sub Heading 2ParagraphFormatted Code -- Font family -- -- Font size -- Path: p
Words:0
12.5 points
QUESTION 5
(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).
