Regression and Forecasting



Regression and Forecasting

Question 15:

Solution

Model Summaryb

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.921a

.847

.826

4.66508

a. Predictors: (Constant), 1st test grade

b. Dependent Variable: final average

The value of R square is 0.847 which is close to 1 so it can be said that a strong relationship exists among the dependent variable and predictors.

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

845.659

1

845.659

38.858

.000a

Residual

152.341

7

21.763

Total

998.000

8

a. Predictors: (Constant), 1st test grade

b. Dependent Variable: final average

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

18.989

9.752

1.947

.093

1st test grade

.740

.119

.921

6.234

.000

a. Dependent Variable: final average

Final Average = 18.989 + 0.740*1st test grade

Question 30:

Solution

The ANOVA table for the given data set shows that the model is good fitted; the magnitude of significance F shows that there is association between the variables which means that the higher the Median SAT score charge more in tuition and fees.

ANOVA

 

df

SS

MS

F

Significance F

Regression

1

133481.474

133481.5

4.53856

0.049004837

Residual

16

470568.526

29410.53

Total

17

604050

 

 

 

The analysis of regression shows that the coefficient of median SAT score is significant at 95% confidence interval, a unit increase in the score will increase the total cost of tuition and fees by 0.01 dollars. The regression equation for the given data set could be given as:

Total Cost ($) = 1491.133 + 0.0102 (Median SAT)

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

1491.133317

134.75769

11.06529

6.6E-09

1205.459777

1776.807

1205.46

1776.807

Total Cost($)

0.010221025

0.00479773

2.13039

0.049005

5.03013E-05

0.020392

5.03E-05

0.020392

Question 31a:

Solution

From the above chart it can be observed that increasing trend is presents so it decompose this trend difference of order 1 has been applied.

Question 31b:

Solution

After applying the difference of 1

Question 31c:

Solution

Autocorrelations

Series:taxes

Lag

Autocorrelation

Std. Errora

Box-Ljung Statistic

Value

df

Sig.b

1

.000

.228

.000

1

1.000

2

.185

.220

.706

2

.702

3

-.171

.212

1.357

3

.716

4

.608

.204

10.229

4

.037

5

-.128

.195

10.660

5

.059

6

-.007

.186

10.662

6

.099

7

-.274

.177

13.071

7

.070

8

.304

.167

16.397

8

.037

9

-.182

.156

17.757

9

.038

10

-.115

.144

18.395

10

.049

11

-.303

.132

23.669

11

.014

12

.104

.118

24.443

12

.018

13

-.165

.102

27.050

13

.012

14

-.141

.083

29.930

14

.008

a. The underlying process assumed is independence (white noise).

b. Based on the asymptotic chi-square approximation.

Partial Autocorrelations

Series:taxes

Lag

Partial Autocorrelation

Std. Error

1

.000

.250

2

.185

.250

3

-.177

.250

4

.619

.250

5

-.289

.250

6

-.240

.250

7

.073

.250

8

-.119

.250

9

-.066

.250

10

-.059

.250

11

-.092

.250

12

-.112

.250

13

-.014

.250

14

-.082

.250

After analyzing the Autocorrelations and Partial Autocorrelations it can be said that there is a increasing trend is presents revenue in state sales tax on certain types of goods and services.

Question 31d:

Solution

Seasonal Decomposition

Series Name:taxes

DATE_

Original Series

Moving Average Series

Ratio of Original Series to Moving Average Series (%)

Seasonal Factor (%)

Seasonally Adjusted Series

Smoothed Trend-Cycle Series

Irregular (Error) Component

Q1 2000

218.000

.

.

88.5

246.212

247.870

.993

Q2 2000

247.000

.

.

98.6

250.409

248.801

1.006

Q3 2000

243.000

250.0000

97.2

97.3

249.782

250.663

.996

Q4 2000

292.000

251.7500

116.0

115.5

252.737

252.658

1.000

Q1 2001

225.000

253.5000

88.8

88.5

254.118

254.971

.997

Q2 2001

254.000

256.5000

99.0

98.6

257.506

257.391

1.000

Q3 2001

255.000

258.2500

98.7

97.3

262.117

259.706

1.009

Q4 2001

299.000

260.5000

114.8

115.5

258.796

261.706

.989

Q1 2002

234.000

263.2500

88.9

88.5

264.282

264.582

.999

Q2 2002

265.000

265.5000

99.8

98.6

268.658

268.789

1.000

Q3 2002

264.000

272.5000

96.9

97.3

271.368

273.791

.991

Q4 2002

327.000

276.5000

118.3

115.5

283.031

279.122

1.014

Q1 2003

250.000

281.0000

89.0

88.5

282.353

283.930

.994

Q2 2003

283.000

287.2500

98.5

98.6

286.906

290.080

.989

Q3 2003

289.000

294.5000

98.1

97.3

297.066

297.368

.999

Q4 2003

356.000

.

.

115.5

308.132

301.012

1.024

Question 32:

Solution

Model Summaryb

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.810a

.657

.632

.700

a. Predictors: (Constant), taxes

b. Dependent Variable: period 4

The value of R square is 0.657 which is close to 1 so it can be said that a strong relationship exists among the dependent variable and predictors.

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

13.137

1

13.137

26.797

.000a

Residual

6.863

14

.490

Total

20.000

15

a. Predictors: (Constant), taxes

b. Dependent Variable:period 4

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

-4.271

1.320

-3.237

.006

taxes

.025

.005

.810

5.177

.000

a. Dependent Variable:period 4

Residuals Statisticsa

Minimum

Maximum

Mean

Std. Deviation

N

Predicted Value

1.22

4.70

2.50

.936

16

Residual

-1.026

1.150

.000

.676

16

Std. Predicted Value

-1.368

2.347

.000

1.000

16

Std. Residual

-1.466

1.643

.000

.966

16

a. Dependent Variable: QUARTER, period 4

Predicted taxes

1.220019382

1.950537225

1.849776144

3.084099397

1.396351275

2.126869119

2.152059389

3.26043129

1.623063709

2.403962094

2.378771823

3.965758863

2.026108037

2.857386962

3.008528585

4.696276707

Question 37:

Solution

The above trend lines indicate that a increasing trend is present in the data set.

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

499.993

1

499.993

54.542

.000a

Residual

165.007

18

9.167

Total

665.000

19

a. Predictors: (Constant), DJIA index

b. Dependent Variable: YEAR, ...