Examples

Example of Stepwise Multiple Regression Analysis

*Research Question* : What are the factors that influence the economic performance of a company. The

economic performance is measured by the return of capital employed.

*Methodology* : Stepwise Multiple Regression Analysis

*Dataset* :
FINANCE.DAT
FINANCE.DIC

SYNTAX

$RUN REGRESSN

$FILES

PRINT = FINANCE.LST

DICTIN = FINANCE.DIC

DATAIN = FINANCE.DAT

$SETUP

MULTIPLE REGRESSION ANALYSIS

BADDATA=MD1 -

MDHANDLING=20 -

PRINT=(DICT,MATRIX)

METHOD=STEP -

DEPVAR=V2 -

VARS=(V3-V14) -

FINRATIO=4.0 -

FOUTRATIO=3.9 -

PRINT=STEP

EXTRACT FROM COMPUTER PRINTOUT

Ê 0After filtering 40 cases read from the input data file

1

0 Number of variables = 13

0

Number of cases = 40

0 General statistics

0 Variable Standard Range

Number Sum Average Deviation Max Min Variable name

3 6.51000 .16275 .29387 .6300 -1.2800 wcftcl

4 5.50000 .13750 .26862 .6000 -1.2800 wcftdt

5 186.62000 4.66550 .56091 5.7600 3.8500 logsale

6 178.48000 4.46200 .54956 5.7800 3.5400 logasst

7 12.18000 .30450 .29506 1.7800 .0000 gearrat

8 72.61000 1.81525 .96339 5.4400 .3600 capint

9 12.48000 .31200 .16801 .7200 .0400 nfatast

10 18.64000 .46600 .24250 1.1600 .0700 fattot

11 10.31000 .25775 .12751 .5000 .0000 invtast

12 20.99000 .52475 .67732 4.2100 .0000 payout

13 32.78000 .81950 .43338 2.6300 .2400 quikrat

14 56.81000 1.42025 .57876 3.9800 .5400 currat

2 5.89000 .14725 .13832 .3800 -.5000 retcap

0

0

Total correlation matrix,R(i,j)

Variable 3 4 5 6 7 8 9 10 11 12

3 1.00000

4 .97571 1.00000

5 .14950 .10485 1.00000

6 .28584 .23865 .92288 1.00000

7 -.80590 -.85831 -.23171 -.26941 1.00000

8 -.27071 -.25965 .32128 -.02663 .04959 1.00000

9 .23904 .28834 -.15964 -.02112 .01890 -.28992 1.00000

10 .22706 .25003 -.17268 -.06891 .06415 -.27656 .89277 1.00000

11 -.29647 -.29789 .21327 .00413 .08117 .47623 -.51601 -.45605 1.00000

12 .06847 .06442 -.10710 -.14761 -.20794 .04481 -.04754 .02995 .00440 1.00000

13 .36545 .27387 -.11104 .03927 -.24832 -.35899 -.17360 -.13197 -.23884 .15625 1.00000

14 .26125 .17287 .06019 .13924 -.22736 -.18670 -.28630 -.25807 .20761 .13312 .85640 1.00000

2 .83467 .84840 .18609 .22485 -.79247 -.04618 -.00229 -.03428 -.15417 -.02805 .14635 .07227 1.00000

Ë Step No. 0

Dependent variable is V 2 retcap

F-level to enter= 4.000

Standard error of Y = .1383

F-level to remove = 3.900

0 Variable numbers

3 4 5 6 7 8 9 10 11 12 13 14 2

0**************** Listing of marginal R-squares for all potential predictors ***

0 Step no. Var. no. Variable name Marg rsqd Categorical variables (all codes) Previously in (*)

Marg RSQD T-ratio

0 3 WCFTCL .6967

0 4 WCFTDT .7198

0 5 LOGSALE .0346

0 6 LOGASST .0506

0 7 GEARRAT .6280

0 8 CAPINT .0021

0 9 NFATAST .0000

0 10 FATTOT .0012

0 11 INVTAST .0238

0 12 PAYOUT] .0008

0 13 QUIKRAT .0214

0 14 CURRAT .0052

Ì
**Step No 1**

Variable entered 4 WCFTDT

F-level 97.610

T-level 9.880

0 Standard error of estimate .7418E-01

0 F ratio for the regression 97.610

0 Multiple correlation coefficient .84840 adjusted .84404

0 Fraction of explained variance (RSQD) .71979 adjusted .71241

0 Determinant of the correlation matrix 1.0000

0 Residual degrees of freedom (N-K-1) 38

0 Constant term .87180E-01

0 Partial

Var. no. B Sigma(B) Beta Sigma(Beta) RSQD Marg RSQD T-ratio Cov. ratio Variable name

4 .4369 .0442 .8484 .0859 .7198 .7198 9.8798 .0000 wcftdt

0**************** Listing of marginal R-squares for all potential predictors ***

0 Step no. Var. no. Variable name Marg rsqd Categorical variables (all codes) Previously in (*)

Marg RSQD T-ratio

1 3 WCFTCL .0010

1 4 WCFTDT .7198 *

1 5 LOGSALE .0095

1 6 LOGASST .0005

1 7 GEARRAT .0157

1 8 CAPINT .0325

1 9 NFATAST .0665

1 10 FATTOT .0648

1 11 INVTAST .0107

1 12 PAYOUT] .0069

1 13 QUIKRAT .0080

1 14 CURRAT .0057

Í
**Step No 2**

Variable entered 9 NFATAST

F-level 11.513

T-level 3.393

0 Standard error of estimate .6565E-01

0 F ratio for the regression 68.063

0 Multiple correlation coefficient .88673 adjusted .88019

0 Fraction of explained variance (RSQD) .78628 adjusted .77473

0 Determinant of the correlation matrix .91686

0 Residual degrees of freedom (N-K-1) 37

0 Constant term +.15086

0 Partial

Var. no. B Sigma(B) Beta Sigma(Beta) RSQD Marg RSQD T-ratio Cov. ratio Variable name

4 .4769 .0409 .9261 .0794 .7863 .7863 11.6673 .0831 WCFTDT

9 -.2217 .0653 -.2693 .0794 .2373 .0665 3.3930 .0831 NFATAST

0**************** Listing of marginal R-squares for all potential predictors ***

0 Step no. Var. no. Variable name Marg rsqd Categorical variables (all codes) Previously in (*)

Marg RSQD T-ratio

2 3 WCFTCL .0004

2 4 WCFTDT .7863 *

2 5 LOGSALE .0022

2 6 LOGASST .0000

2 7 GEARRAT .0003

2 8 CAPINT .0153

2 9 NFATAST .0665 *

2 10 FATTOT .0032

2 11 INVTAST .0004

2 12 PAYOUT] .0102

2 13 QUIKRAT .0277

2 14 CURRAT .0321

Î Step no 3

Variable entered 14 CURRAT

F-level 6.367

T-level 2.523

0 Standard error of estimate .6135E-01

0 F ratio for the regression 54.080

0 Multiple correlation coefficient .90465 adjusted .89625

0 Fraction of explained variance (RSQD) .81840 adjusted .80327

0 Determinant of the correlation matrix .77647

0 Residual degrees of freedom (N-K-1)36

0 Constant term .23146

0 Partial

Var. no. B Sigma(B) Beta Sigma(Beta) RSQD Marg RSQD T-ratio Cov. ratio Variable name

4 .5048 .0398 .9803 .0772 .8174 .8128 12.6937 .1542 wcftdt

9 -.2805 .0654 -.3407 .0794 .3385 .0929 4.2917 .1996 nfatast

14 -.0465 .0184 -.1947 .0772 .1503 .0321 2.5233 .1531 currat

0**************** Listing of marginal R-squares for all potential predictors ***

0 Step no. Var. no. Variable name Marg rsqd Categorical variables (all codes) Previously in (*)

Marg RSQD T-ratio

3 3 WCFTCL .0028

3 4 WCFTDT .8128 *

3 5 LOGSALE .0017

3 6 LOGASST .0001

3 7 GEARRAT .0007

3 8 CAPINT .0065

3 9 NFATAST .0929 *

3 10 FATTOT .0032

3 11 INVTAST .0000

3 12 PAYOUT] .0068

3 13 QUIKRAT .0008

3 14 CURRAT .0321 *

0 Completed 3 steps of regression

**INTERPRETATION**

- IDAMS reports that 40 cases were read from the input data file and used in the analysis.

- General Statistics

Descriptive statistics of all predictor variables

- Correlation matrix of predictor + dependent variables

- Step No. 0

No variables in the model. Correlation matrix shows that V_{4 }(WCFTDT) has the highest correlation with the dependent variable (0.8480), marginal RSQD (0.7198)

Hence V_{4} is entered at Step 1.

Ì Step No. 1

Variable V_{4} is entered at this step with F ratio = 97.610>>FIN RATIO

With V_{4} is the equation V_{9} (NFATST) is now the best candidate, since it has the highest value of RSQD.

Í
**Step No. 2**

Variable V_{9} is entered in the model, with F ratio = 11.513

With V_{4} and V_{9} in the equation, the best candidate is now V_{14} (CURRAT) since it has the

highest value of Marginal RSQD after V_{4} and V_{9}.

Î
**Step No. 3**

V4 is entered into the equation of this step. With V4 and V9 already in the equation, V14

enters with F ratio = 6.367

After this step no other variable qualifies for entering into the regression equation.

The regression model is:

RETCAP = .23146+.5048 WCFTDT-.2805 NFATAST-.0465 CURRAT

Adequacy of the fitted model

F ratio = 54.080 df (3,36) p < .000 highly significant

Standard error of the estimate of the dependent variable = .06135 which is quite low Þ high reliability of

estimation.

Determinant of the correlation matrix = .77647,

Value close to 0 Þ Multicolinearity

1 Þ No multicolliearity

Recall that for the full scale model the determinants of the correlation matrix was which is close to 0 Þ

high multicollinearity.

The standard error of the estimate is now much less than that for the full scale model:

Full Scale Model: 7.371

Reduced Model : 0.06135