Examples
Example of Stepwise Multiple Regression Analysis
Research Question
: What are the factors that influence the economic performance of a company. Theeconomic 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 file1
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
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
1.0000014 .26125 .17287 .06019 .13924 -.22736 -.18670 -.28630 -.25807 .20761 .13312
.85640 1.000002 .83467 .84840 .18609 .22485 -.79247 -.04618 -.00229 -.03428 -.15417 -.02805
.14635 .07227 1.00000
Ë
Step No. 0Dependent 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 .05060 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 1Variable 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 2Variable 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 3Variable 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 wcftdt9 -.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
Descriptive statistics of all predictor variables
No variables in the model. Correlation matrix shows that V4 (WCFTDT) has the highest correlation with the dependent variable (0.8480), marginal RSQD (0.7198)
Hence V4 is entered at Step 1.
Ì Step No. 1
Variable V4 is entered at this step with F ratio = 97.610>>FIN RATIO
With V4 is the equation V9 (NFATST) is now the best candidate, since it has the highest value of RSQD.
Í Step No. 2
Variable V9 is entered in the model, with F ratio = 11.513
With V4 and V9 in the equation, the best candidate is now V14 (CURRAT) since it has the
highest value of Marginal RSQD after V4 and V9.
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