Need help with question 6 that builds off questions 1 and 5 below. 1.Build a lin

Question

Need help with question 6 that builds off questions 1 and 5 below.

1.Build a linear regression using percent market as the predictor and percent sales as the outcome. Please record the slope (round to two significant digits after the decimal) of the relationship between percent market (predictor) and percent sales (outcome) and the p value of the slope estimate (5@ 2point = 10 points).

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.677472

R Square

0.458969

Adjusted R Square

0.45625

Standard Error

6.01437

Observations

201

ANOVA

df

SS

MS

F

Significance F

Regression

1

6106.523

6106.523

168.8161

2.37E-28

Residual

199

7198.356

36.17264

Total

200

13304.88

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

13.04276

0.846245

15.41251

8.62E-36

11.374

14.71152

11.374

14.71152

percent_market

0.951013

0.073195

12.99292

2.37E-28

0.806676

1.09535

0.806676

1.09535

Slope = 0.95 and p value =2.37 x 10-28

5. Fit a second, third, and fourth degree polynomial using percent market as the predictor and percent sales as the outcome. What are the parameter estimates and their pvalues for these models (20points)?

Model

Percent

Market

pvalue

Percent

Market^2

pvalue

Percent Market^3

pvalue

Percent

Market^4

pvalue

Second Degree

3.17

3.48E-28

-0.11

1.83E-17

Third Degree

1.309953

0.029824

0.120768

0.08346

-0.00769

0.000875

Fourth Degree

1.883479

0.121805

-0.00741

0.975941

0.002231

0.903419

-0.00025

0.586711

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.790471

R Square

0.624844

Adjusted R Square

0.621055

Standard Error

5.020867

Observations

201

ANOVA

df

SS

MS

F

Significance F

Regression

2

8313.475

4156.737

164.8903

7.03E-43

Residual

198

4991.404

25.20911

Total

200

13304.88

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

5.66717

1.058518

5.35387

2.37E-07

3.579754

7.754587

3.579754

7.754587

percent_market^2

-0.11059

0.011819

-9.35659

1.83E-17

-0.1339

-0.08728

-0.1339

-0.08728

percent_market

3.165944

0.244483

12.94954

3.48E-28

2.683819

3.648069

2.683819

3.648069

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.803371

R Square

0.645405

Adjusted R Square

0.640005

Standard Error

4.893715

Observations

201

ANOVA

df

SS

MS

F

Significance F

Regression

3

8587.035

2862.345

119.5211

4.03E-44

Residual

197

4717.843

23.94844

Total

200

13304.88

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

8.767608

1.380565

6.35074

1.45E-09

6.045025

11.49019

6.045025

11.49019

percent_market^2

0.120768

0.069416

1.739776

0.08346

-0.01613

0.257662

-0.01613

0.257662

percent_market

1.309953

0.598618

2.188294

0.029824

0.12943

2.490476

0.12943

2.490476

percent_market^3

-0.00769

0.002276

-3.37978

0.000875

-0.01218

-0.0032

-0.01218

-0.0032

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.803704

R Square

0.645941

Adjusted R Square

0.638715

Standard Error

4.902476

Observations

201

ANOVA

df

SS

MS

F

Significance F

Regression

4

8594.161

2148.54

89.39486

4.15E-43

Residual

196

4710.717

24.03427

Total

200

13304.88

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

8.186393

1.747044

4.685853

5.21E-06

4.740975

11.63181

4.740975

11.63181

percent_market^3

0.002231

0.018364

0.121501

0.903419

-0.03399

0.038448

-0.03399

0.038448

percent_market

1.883479

1.212045

1.553968

0.121805

-0.50684

4.273803

-0.50684

4.273803

percent_market^4

-0.00025

0.000454

-0.54451

0.586711

-0.00114

0.000648

-0.00114

0.000648

percent_market^2

-0.00741

0.245463

-0.0302

0.975941

-0.4915

0.476675

-0.4915

0.476675

6. What are the r squares of the models from question 5 when a 3rd degree polynomial is fit to the data and how does it compare to the r square of the fitted line from question 1 (10 points)?

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.677472

R Square

0.458969

Adjusted R Square

0.45625

Standard Error

6.01437

Observations

201

ANOVA

df

SS

MS

F

Significance F

Regression

1

6106.523

6106.523

168.8161

2.37E-28

Residual

199

7198.356

36.17264

Total

200

13304.88

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

13.04276

0.846245

15.41251

8.62E-36

11.374

14.71152

11.374

14.71152

percent_market

0.951013

0.073195

12.99292

2.37E-28

0.806676

1.09535

0.806676

1.09535

Slope = 0.95 and p value =2.37 x 10-28

Explanation / Answer

Answer to the question is as follows. Wtite back to me in case you have further doubts:

To find out Rsquare find out the SS regression.

This is the %age of variation explained by model as against total variation.

Basically with the 3degree polynomial equation, get the SSregression/SStotal

= 8587.04/13304.88

=64.56%

For 1st case the same is 6106.523/13304.88 = .4590 or 45.9%.

Since the no. this is not a high degree polynomial equation the rsquare value is not high

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