Module 04 Session Long Project

The data taken for analysis for this module is from “From Business Week’s analysis of the S&P 500 for 2004”. The Industry Ranking S&P 500 is based on three factors Market Value (MarketValue, MvOneYearTotalReturn, and MvThreeYearTotalReturn), Sales (Sales, SalesChangeFrom2002, and Sales3YrAverageChange) and Profitability (Profitability, ProfitChangeFrom2002, and Profit3YrAverageChange).

Descriptive Statistics and Frequency Tabulations

Table 1 shows the descriptive statistics of all variables. From table 1, it can be seen that all the variables are highly positively skewed (i.e. skewed to left) as the value of skewness coefficient is greater than zero for all variables. The positive skewness is also confirmed from the mean, median and mode values. The mean value for all the variables is greater than median values and median values for all the variables are greater than mode values. The Histograms for all the variables confirms positive skewness as the right tail for all the variables are longer.

Table 1: Descriptive Statistics

OverallSP500Rank_04

MarketValue

MvOneYearTotalReturn

MvThreeYearTotalReturn

Sales

SalesChangeFrom2002

Sales3YrAverageChange

Profitability

ProfitChangeFrom2002

Profit3YrAverageChange

N

Valid

483

488

479

312

486

408

312

428

264

251

Missing

236

231

240

407

233

311

407

291

455

468

Mean

245.56

21321.459

57.267

51.984

13277.491

14.85

10.833

1115.366

93.09

25.960

Median

243.00

9251.550

45.400

36.350

6316.000

11.00

7.200

478.000

27.00

15.700

Mode

28

4021.5a

25.1a

8.0a

679.6a

11

3.3

109.8a

9a

10.4

Std. Deviation

143.509

39064.4620

50.4681

51.6895

23919.9416

22.125

11.2732

2108.2942

288.293

35.9557

Skewness

.021

4.663

5.107

2.403

5.793

9.586

2.236

5.148

7.530

4.457

Std. Error of Skewness

.111

.111

.112

.138

.111

.121

.138

.118

.150

.154

Range

493

325661.2

682.8

395.4

258577.1

352

70.3

20957.1

2834

302.4

Minimum

1

867.6

.3

.1

103.9

0

.0

2.9

0

.2

Maximum

494

326528.8

683.1

395.5

258681.0

352

70.3

20960.0

2834

302.6

a. Multiple modes exist. The smallest value is shown

Histograms

Scatterplots

The Scatter plots for MarketValue, MvOneYearTotalReturn, MvThreeYearTotalReturn, Sales and Profitability are drawn against OverallSP500Rank_04. Except for MvOneYearTotalReturn, all other variables show a decreasing linear trend against OverallSP500Rank_04.

Correlation matrix

Table 2 shows the Correlation matrix of all variables. The strongest correlation is between variables MarketValue and Profitability. The weakest correlation is between variables ProfitChangeFrom2002 and Profitability. OverallSP500Rank_04 has strongest correlation is with MvThreeYearTotalReturn and weakest correlation with ProfitChangeFrom2002. Most of the correlations for the variables OverallSP500Rank_04 with other variables are significant at 95% significance level (p-value less than 0.05), except two that are ProfitChangeFrom2002 and Profit3YrAverageChange (p-value greater than 0.05).

Table 2: Correlations

OverallSP500Rank_04

MarketValue

MvOneYearTotalReturn

MvThreeYearTotalReturn

Sales

SalesChangeFrom2002

Sales3YrAverageChange

Profitability

ProfitChangeFrom2002

Profit3YrAverageChange

OverallSP500Rank_04

Pearson Correlation

1.000

-.296**

.125**

-.329**

-.235**

-.183**

-.305**

-.292**

-.029

.095

Sig. (2-tailed)

.000

.006

.000

.000

.000

.000

.000

.636

.137

N

483.000

483

475

309

483

405

312

427

262

249

MarketValue

Pearson Correlation

-.296**

1.000

-.129**

-.101

.664**

.000

-.014

.873**

.047

-.026

Sig. (2-tailed)

.000

.005

.074

.000

.993

.800

.000

.446

.677

N

483

488.000

479

312

486

408

312

428

264

251

MvOneYearTotalReturn

Pearson Correlation

.125**

-.129**

1.000

.171**

-.103*

.108*

.087

-.107*

.049

-.031

Sig. (2-tailed)

.006

.005

.003

.025

.030

.126

.028

.431

.626

N

475

479

479.000

308

478

401

307

421

257

245

MvThreeYearTotalReturn

Pearson Correlation

-.329**

-.101

.171**

1.000

-.120*

.126*

.172*

-.109

.022

-.132

Sig. (2-tailed)

.000

.074

.003

.035

.038

.011

.060

.773

.097

N

309

312

308

312.000

311

273

220

301

171

160

Sales

Pearson Correlation

-.235**

.664**

-.103*

-.120*

1.000

-.010

.010

.709**

.063

-.009

Sig. (2-tailed)

.000

.000

.025

.035

.846

.854

.000

.305

.888

N

483

486

478

311

486.000

408

312

428

264

251

SalesChangeFrom2002

Pearson Correlation

-.183**

.000

.108*

.126*

-.010

1.000

.314**

-.037

-.008

-.016

Sig. (2-tailed)

.000

.993

.030

.038

.846

.000

.480

.910

.816

N

405

408

401

273

408

408.000

300

372

223

210

Sales3YrAverageChange

Pearson Correlation

-.305**

-.014

.087

.172*

.010

.314**

1.000

-.044

-.016

.022

Sig. (2-tailed)

.000

.800

.126

.011

.854

.000

.450

.843

.788

N

312

312

307

220

312

300

312.000

295

166

158

Profitability

Pearson Correlation

-.292**

.873**

-.107*

-.109

.709**

-.037

-.044

1.000

-.002

.015

Sig. (2-tailed)

.000

.000

.028

.060

.000

.480

.450

.974

.821

N

427

428

421

301

428

372

295

428.000

230

221

ProfitChangeFrom2002

Pearson Correlation

-.029

.047

.049

.022

.063

-.008

-.016

-.002

1.000

.031

Sig. (2-tailed)

.636

.446

.431

.773

.305

.910

.843

.974

.669

N

262

264

257

171

264

223

166

230

264.000

198

Profit3YrAverageChange

Pearson Correlation

.095

-.026

-.031

-.132

-.009

-.016

.022

.015

.031

1.000

Sig. (2-tailed)

.137

.677

.626

.097

.888

.816

.788

.821

.669

N

249

251

245

160

251

210

158

221

198

251.000

**. Correlation is significant at the 0.01 level (2-tailed).

*. Correlation is significant at the 0.05 level (2-tailed).

Regression Analysis

The variables MvThreeYearTotalReturn, Sales3YrAverageChange, MarketValue, and Profitability have the highest correlations with OverallSP500Rank_04.

The regression analysis gives a model for predicting dependent variables based on independent variables. The regression analysis gives three types of statistics in SPSS:

· The coefficient of determination, designated as R Square ( R2) that tells the proportion of variance in the dependent variable that can be accounted for by the independent variable.

· An ANOVA table for the regression equation for testing null hypothesis that R2 in the population equals zero, and allows us to decide whether or not the linear model significantly fits the data at the p<.05 level.

· The output (coefficients for intercepts and slope) that provides the information needed to construct the regression (prediction) equation.

1. Regression: OverallSP500Rank_04 (DV) and MvThreeYearTotalReturn (IV)

The regression analysis for OverallSP500Rank_04 (DV) and MvThreeYearTotalReturn (IV) is significant as the sig value in ANOVA table is less than 0.05. The value of the coefficient of determination 0.108 implies that the MvThreeYearTotalReturn (IV) can account for 10.8% of variance in the OverallSP500Rank_04 (DV).

The linear regression equation will be:

‘OverallSP500Rank_04 = 240.811 – 0.816(MvThreeYearTotalReturn)

Variables Entered/Removedb

Model

Variables Entered

Variables Removed

Method

1

MvThreeYearTotalReturna

.

Enter

a. All requested variables entered.

b. Dependent Variable: OverallSP500Rank_04

Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.329a

.108

.105

120.307

a. Predictors: (Constant), MvThreeYearTotalReturn

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

539735.167

1

539735.167

37.291

.000a

Residual

4443418.587

307

14473.676

Total

4983153.754

308

a. Predictors: (Constant), MvThreeYearTotalReturn

b. Dependent Variable: OverallSP500Rank_04

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

240.811

9.731

24.747

.000

MvThreeYearTotalReturn

-.816

.134

-.329

-6.107

.000

a. Dependent Variable: OverallSP500Rank_04

2. Regression: OverallSP500Rank_04 (DV) and Sales3YrAverageChange (IV)

The regression analysis for OverallSP500Rank_04 (DV) and Sales3YrAverageChange (IV) is significant as the sig value in ANOVA table is less than 0.05. The value of the coefficient of determination 0.093 implies that the Sales3YrAverageChange (IV) can account for 9.3% of variance in the OverallSP500Rank_04 (DV).

The linear regression equation will be:

‘OverallSP500Rank_04 = 231.106 – 3.527(Sales3YrAverageChange)

Variables Entered/Removedb

Model

Variables Entered

Variables Removed

Method

1

Sales3YrAverageChangea

.

Enter

a. All requested variables entered.

b. Dependent Variable: OverallSP500Rank_04

Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.305a

.093

.090

124.383

a. Predictors: (Constant), Sales3YrAverageChange

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

491538.189

1

491538.189

31.772

.000a

Residual

4796012.927

310

15471.009

Total

5287551.115

311

a. Predictors: (Constant), Sales3YrAverageChange

b. Dependent Variable: OverallSP500Rank_04

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

231.106

9.773

23.646

.000

Sales3YrAverageChange

-3.527

.626

-.305

-5.637

.000

a. Dependent Variable: OverallSP500Rank_04

3. Regression: OverallSP500Rank_04 (DV) and MarketValue (IV)

The regression analysis for OverallSP500Rank_04 (DV) and MarketValue is significant as the sig value in ANOVA table is less than 0.05. The value of the coefficient of determination 0.088 implies that the MarketValue can account for 8.8% of variance in the OverallSP500Rank_04 (DV).

The linear regression equation will be:

‘OverallSP500Rank_04 = 268.786 – 0.001(MarketValue)

Variables Entered/Removedb

Model

Variables Entered

Variables Removed

Method

1

MarketValuea

.

Enter

a. All requested variables entered.

b. Dependent Variable: OverallSP500Rank_04

Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.296a

.088

.086

137.216

a. Predictors: (Constant), MarketValue

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

870326.947

1

870326.947

46.224

.000a

Residual

9056401.877

481

18828.278

Total

9926728.824

482

a. Predictors: (Constant), MarketValue

b. Dependent Variable: OverallSP500Rank_04

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

268.786

7.117

37.768

.000

MarketValue

-.001

.000

-.296

-6.799

.000

a. Dependent Variable: OverallSP500Rank_04

4. Regression: OverallSP500Rank_04 (DV) and Profitability (IV)

The regression analysis for OverallSP500Rank_04 (DV) and Profitability is significant as the sig value in ANOVA table is less than 0.05. The value of the coefficient of determination 0.085 implies that the Profitability can account for 8.5% of variance in the OverallSP500Rank_04 (DV).

The linear regression equation will be:

‘OverallSP500Rank_04 = 239.049 – 0.018(Profitability)

Variables Entered/Removedb

Model

Variables Entered

Variables Removed

Method

1

Profitabilitya

.

Enter

a. All requested variables entered.

b. Dependent Variable: OverallSP500Rank_04

Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.292a

.085

.083

124.606

a. Predictors: (Constant), Profitability

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

612846.265

1

612846.265

39.470

.000a

Residual

6598854.601

425

15526.717

Total

7211700.867

426

a. Predictors: (Constant), Profitability

b. Dependent Variable: OverallSP500Rank_04

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

239.049

6.819

35.058

.000

Profitability

-.018

.003

-.292

-6.283

.000

a. Dependent Variable: OverallSP500Rank_04

Multiple Regression: (Taking four Independent Variables that have highest Correlation with OverallSP500Rank_04)

The regression analysis for OverallSP500Rank_04 (DV) and MvThreeYearTotalReturn, Sales3YrAverageChange, MarketValue, and Profitability (IVs) is significant as the sig value in ANOVA table is less than 0.05. The value of the coefficient of determination 0.330 implies that the MvThreeYearTotalReturn, Sales3YrAverageChange, MarketValue, and Profitability (IVs) can account for 33% of variance in the OverallSP500Rank_04 (DV).

The linear regression equation will be:

‘OverallSP500Rank_04 = 247.781 – 0.591(MvThreeYearTotalReturn) – 3.329(Sales3YrAverageChange) – 0.013(Profitability)

Variables Entered/Removedb

Model

Variables Entered

Variables Removed

Method

1

Profitability, Sales3YrAverageChange, MvThreeYearTotalReturn, MarketValuea

.

Enter

a. All requested variables entered.

b. Dependent Variable: OverallSP500Rank_04

Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.574a

.330

.317

93.252

a. Predictors: (Constant), Profitability, Sales3YrAverageChange, MvThreeYearTotalReturn, MarketValue

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

894689.681

4

223672.420

25.722

.000a

Residual

1817443.777

209

8695.903

Total

2712133.458

213

a. Predictors: (Constant), Profitability, Sales3YrAverageChange, MvThreeYearTotalReturn, MarketValue

b. Dependent Variable: OverallSP500Rank_04

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

247.781

11.181

22.161

.000

MvThreeYearTotalReturn

-.591

.117

-.294

-5.037

.000

Sales3YrAverageChange

-3.329

.542

-.353

-6.137

.000

MarketValue

.000

.000

-.116

-.838

.403

Profitability

-.013

.008

-.217

-1.563

.119

a. Dependent Variable: OverallSP500Rank_04

We can leave variable MarketValue, as for four variable regression analysis, MarketValue has not significant effect on linear regression equation.

Multiple Regression (Taking all Independent Variables)

The regression analysis for OverallSP500Rank_04 (DV) and Profit3YrAverageChange, SalesChangeFrom2002, Profitability, MvThreeYearTotalReturn, ProfitChangeFrom2002, Sales3YrAverageChange, MvOneYearTotalReturn, Sales, and MarketValue (IVs) is significant as the sig value in ANOVA table is less than 0.05. The value of the coefficient of determination 0.502 implies all the independent variables can account for 50.2% of variance in the OverallSP500Rank_04 (DV).

Variables Entered/Removedb

Model

Variables Entered

Variables Removed

Method

1

Profit3YrAverageChange, SalesChangeFrom2002, Profitability, MvThreeYearTotalReturn, ProfitChangeFrom2002, Sales3YrAverageChange, MvOneYearTotalReturn, Sales, MarketValuea

.

Enter

a. All requested variables entered.

b. Dependent Variable: OverallSP500Rank_04

Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.708a

.502

.440

84.217

a. Predictors: (Constant), Profit3YrAverageChange, SalesChangeFrom2002, Profitability, MvThreeYearTotalReturn, ProfitChangeFrom2002, Sales3YrAverageChange, MvOneYearTotalReturn, Sales, MarketValue

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

520912.573

9

57879.175

8.161

.000a

Residual

517747.981

73

7092.438

Total

1038660.554

82

a. Predictors: (Constant), Profit3YrAverageChange, SalesChangeFrom2002, Profitability, MvThreeYearTotalReturn, ProfitChangeFrom2002, Sales3YrAverageChange, MvOneYearTotalReturn, Sales, MarketValue

b. Dependent Variable: OverallSP500Rank_04

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

331.979

28.440

11.673

.000

MarketValue

.003

.002

.324

1.600

.114

MvOneYearTotalReturn

-.955

.402

-.228

-2.373

.020

MvThreeYearTotalReturn

-.500

.170

-.285

-2.951

.004

Sales

.001

.001

.259

2.244

.028

SalesChangeFrom2002

-.714

.756

-.090

-.944

.348

Sales3YrAverageChange

-4.377

1.124

-.377

-3.896

.000

Profitability

-.135

.036

-.773

-3.703

.000

ProfitChangeFrom2002

-.051

.040

-.141

-1.283

.203

Profit3YrAverageChange

.158

.270

.051

.585

.561

a. Dependent Variable: OverallSP500Rank_04

We can leave variable MarketValue, SalesChangeFrom2002, ProfitChangeFrom2002, and Profit3YrAverageChange as these variables has not significant effect on linear regression equation.