Title 'Multiple Regression Example'.
Data list fixed records=1
/1 gpa 1-3 greq 5-7 grev 9-11 mat 13-14 ar 16-18.
begin data
3.2 625 540 65 2.7
4.1 575 680 75 4.5
3.0 520 480 65 2.5
2.6 545 520 55 3.1
3.7 520 490 75 3.6
4.0 655 535 65 4.3
4.3 630 720 75 4.6
2.7 500 500 75 3.0
3.6 605 575 65 4.7
4.1 555 690 75 3.4
2.7 505 545 55 3.7
2.9 540 515 55 2.6
2.5 520 520 55 3.1
3.0 585 710 65 2.7
3.3 600 610 85 5.0
3.2 625 540 65 2.7
4.1 575 680 75 4.5
3.0 520 480 65 2.5
2.6 545 520 55 3.1
3.7 520 490 75 3.6
4.0 655 535 65 4.3
4.3 630 720 75 4.6
2.7 500 500 75 3.0
3.6 605 575 65 4.7
4.1 555 690 75 3.4
2.7 505 545 55 3.7
2.9 540 515 55 2.6
2.5 520 520 55 3.1
3.0 585 710 65 2.7
3.3 600 610 85 5.0
end data.
set highres=off.
Regression variables=gpa,greq,grev,mat,ar
/descriptives=mean,stddev,corr,n
/statistics=r,anova,cha,ci,coeff,tol,history
/dependent= gpa
/method=enter
/residuals=histogram,normprob,outliers
/casewise=default
/scatterplot=(gpa,greq) (gpa,grev) (gpa,mat) (gpa,ar) (*sresid,*pred)
(*sresid,greq)(*sresid,grev) (*sresid,mat) (*sresid,ar).
OUTPUT:
22 Dec 99 Multiple Regression Example Page 2
16:43:19 UCLA OAC IBM RS6000 AIX 3.2.5/4.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Listwise Deletion of Missing Data
Mean Std Dev Label
GPA 3.313 .600
GREQ 565.333 48.618
GREV 575.333 83.034
MAT 67.000 9.248
AR 3.567 .838
N of Cases = 30
Correlation:
GPA GREQ GREV MAT AR
GPA 1.000 .611 .581 .604 .621
GREQ .611 1.000 .468 .267 .508
GREV .581 .468 1.000 .426 .405
MAT .604 .267 .426 1.000 .525
AR .621 .508 .405 .525 1.000
22 Dec 99 Multiple Regression Example Page 3
16:43:19 UCLA OAC IBM RS6000 AIX 3.2.5/4.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. GPA
Descriptive Statistics are printed on Page 2
Block Number 1. Method: Enter
Variable(s) Entered on Step Number 1.. AR
2.. GREV
3.. MAT
4.. GREQ
Multiple R .80030 Analysis of Variance
R Square .64047 R Square Change .64047 DF Sum of Squares Mean Square
Adjusted R Square .58295 F Change 11.13400 Regression 4 6.68313 1.67078
Standard Error .38738 Signif F Change .0000 Residual 25 3.75153 .15006
F = 11.13400 Signif F = .0000
------------------------------------------ Variables in the Equation ------------------------------------------
Variable B SE B 95% Confdnce Intrvl B Beta Tolerance VIF T Sig T
GREQ .003998 .001831 2.27987E-04 .007769 .324062 .653236 1.531 2.184 .0385
GREV .001524 .001050 -6.39208E-04 .003687 .210912 .680518 1.469 1.451 .1593
MAT .020896 .009549 .001230 .040562 .322145 .663614 1.507 2.188 .0382
AR .144234 .113001 -.088497 .376964 .201604 .576442 1.735 1.276 .2135
(Constant) -1.738107 .950740 -3.696192 .219979 -1.828 .0795
End Block Number 1 All requested variables entered.
22 Dec 99 Multiple Regression Example Page 4
16:43:19 UCLA OAC IBM RS6000 AIX 3.2.5/4.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. GPA
Summary table
-------------
Step MultR Rsq AdjRsq F(Eqn) SigF RsqCh FCh SigCh Variable BetaIn Correl
1 In: AR .6207 .6207
2 In: GREV .3947 .5815
3 In: MAT .2900 .6042
4 .8003 .6405 .5829 11.134 .000 .6405 11.134 .000 In: GREQ .3241 .6111
>Note # 12650
>No outliers found. No casewise plot produced.
* * * * * * * * * * * * * * * * * * * * * * * * * * * * *
Residuals Statistics:
Min Max Mean Std Dev N
*PRED 2.7297 4.1085 3.3133 .4801 30
*ZPRED -1.2157 1.6564 .0000 1.0000 30
*SEPRED .1184 .1928 .1563 .0246 30
*ADJPRED 2.7105 4.2868 3.3212 .4925 30
*RESID -.7876 .5260 .0000 .3597 30
*ZRESID -2.0332 1.3578 .0000 .9285 30
*SRESID -2.2758 1.4777 -.0092 1.0275 30
*DRESID -.9868 .6230 -.0079 .4410 30
*SDRESID -2.5042 1.5156 -.0209 1.0693 30
*MAHAL 1.7438 6.2196 3.8667 1.5001 30
*COOK D .0000 .2619 .0465 .0673 30
*LEVER .0601 .2145 .1333 .0517 30
Total Cases = 30
22 Dec 99 Multiple Regression Example Page 5
16:43:19 UCLA OAC IBM RS6000 AIX 3.2.5/4.
Outliers - Standardized Residual
Case # *ZRESID
30 -2.03322
15 -2.03322
20 1.35776
5 1.35776
25 1.31691
10 1.31691
29 -1.11095
14 -1.11095
21 .84060
6 .84060
* * * * * * * * * * * * * * * * * * * * * * * * * * * * *
Histogram - Standardized Residual
N Exp N (* = 1 Cases, . : = Normal Curve)
0 .02 Out
0 .05 3.00
0 .12 2.67
0 .27 2.33
0 .55 2.00 .
0 1.00 1.67 .
4 1.65 1.33 *:**
2 2.42 1.00 *:
4 3.19 .67 **:*
4 3.76 .33 ***:
2 3.97 .00 ** .
4 3.76 -.33 ***:
6 3.19 -.67 **:***
2 2.42 -1.00 *:
0 1.65 -1.33 .
0 1.00 -1.67 .
2 .55 -2.00 :*
0 .27 -2.33
0 .12 -2.67
0 .05 -3.00
0 .02 Out
22 Dec 99 Multiple Regression Example Page 6
16:43:19 UCLA OAC IBM RS6000 AIX 3.2.5/4.
Normal Probability (P-P) Plot
Standardized Residual
1.0 +---------+---------+---------+---------.
| . |
| *.***|
| . |
| .** |
.75 + ** +
| ***.* |
E | ** . |
x | . |
p | . |
e .5 + *.* +
c | . |
t | .** |
e | ** |
d | ***.* |
.25 + . +
| **. |
| * *. |
| . |
| . |
+**-------+---------+---------+---------+ Observed
.25 .5 .75 1.0
22 Dec 99 Multiple Regression Example Page 7
16:43:19 UCLA OAC IBM RS6000 AIX 3.2.5/4.
Standardized Scatterplot Standardized Scatterplot
Across - GREQ Down - GPA Across - GREV Down - GPA
Out ++-----+-----+-----+-----+-----+-----++ Out ++-----+-----+-----+-----+-----+-----++
3 + + Symbols: 3 + + Symbols:
| | | |
| | Max N | | Max N
2 + + 2 + +
| : | . 1.0 | : | . 1.0
| : : | : 2.0 | * | : 2.0
1 + : + 1 + : + * 4.0
| : | | : |
| : | | : |
0 + : + 0 + : +
| : | | : |
| : : : | | : : : |
-1 + :: + -1 + : : +
| : : | | * |
| | | |
-2 + + -2 + +
| | | |
| | | |
-3 + + -3 + +
Out ++-----+-----+-----+-----+-----+-----++ Out ++-----+-----+-----+-----+-----+-----++
-3 -2 -1 0 1 2 3 Out -3 -2 -1 0 1 2 3 Out
Standardized Scatterplot Standardized Scatterplot
Across - MAT Down - GPA Across - AR Down - GPA
Out ++-----+-----+-----+-----+-----+-----++ Out ++-----+-----+-----+-----+-----+-----++
3 + + Symbols: 3 + + Symbols:
| | | |
| | Max N | | Max N
2 + + 2 + +
| : | . 1.0 | : | . 1.0
| * | : 2.0 | : : | : 2.0
1 + : + * 4.0 1 + : + * 4.0
| : | | : |
| : | | : |
0 + : + 0 + : +
| : | | : |
| : * | | ::: |
-1 + : : + -1 + : : +
| * | | * |
| | | |
-2 + + -2 + +
| | | |
| | | |
-3 + + -3 + +
Out ++-----+-----+-----+-----+-----+-----++ Out ++-----+-----+-----+-----+-----+-----++
-3 -2 -1 0 1 2 3 Out -3 -2 -1 0 1 2 3 Out
22 Dec 99 Multiple Regression Example Page 8
16:43:19 UCLA OAC IBM RS6000 AIX 3.2.5/4.
Standardized Scatterplot Standardized Scatterplot
Across - *PRED Down - *SRESID Across - GREQ Down - *SRESID
Out ++-----+-----+-----+-----+-----+-----++ Out ++-----+-----+-----+-----+-----+-----++
3 + + Symbols: 3 + + Symbols:
| | | |
| | Max N | | Max N
2 + + 2 + +
| | . 1.0 | | . 1.0
| : : | : 2.0 | : : | : 2.0
1 + : + 1 + : +
| : : : | | : : : |
| : | | : |
0 + : + 0 + : +
| : : | | : : |
| :: | | : : |
-1 + : + -1 + : +
| : | | : |
| | | |
-2 + + -2 + +
| : | | : |
| | | |
-3 + + -3 + +
Out ++-----+-----+-----+-----+-----+-----++ Out ++-----+-----+-----+-----+-----+-----++
-3 -2 -1 0 1 2 3 Out -3 -2 -1 0 1 2 3 Out
Standardized Scatterplot Standardized Scatterplot
Across - GREV Down - *SRESID Across - MAT Down - *SRESID
Out ++-----+-----+-----+-----+-----+-----++ Out ++-----+-----+-----+-----+-----+-----++
3 + + Symbols: 3 + + Symbols:
| | | |
| | Max N | | Max N
2 + + 2 + +
| | . 1.0 | | . 1.0
| : : | : 2.0 | * | : 2.0
1 + : + * 4.0 1 + : + * 4.0
| : : : | | : * |
| : | | : |
0 + : + 0 + : +
| :: | | : : |
| * | | * |
-1 + : + -1 + : +
| : | | : |
| | | |
-2 + + -2 + +
| : | | : |
| | | |
-3 + + -3 + +
Out ++-----+-----+-----+-----+-----+-----++ Out ++-----+-----+-----+-----+-----+-----++
-3 -2 -1 0 1 2 3 Out -3 -2 -1 0 1 2 3 Out
22 Dec 99 Multiple Regression Example Page 9
16:43:19 UCLA OAC IBM RS6000 AIX 3.2.5/4.
Standardized Scatterplot
Across - AR Down - *SRESID
Out ++-----+-----+-----+-----+-----+-----++
3 + + Symbols:
| |
| | Max N
2 + +
| | . 1.0
| :: | : 2.0
1 + : + * 4.0
| : * |
| : |
0 + : +
| : : |
| * |
-1 + : +
| : |
| |
-2 + +
| : |
| |
-3 + +
Out ++-----+-----+-----+-----+-----+-----++
-3 -2 -1 0 1 2 3 Out
22 Dec 99 Multiple Regression Example Page 10
16:43:19 UCLA OAC IBM RS6000 AIX 3.2.5/4.
Preceding task required .08 seconds CPU time; .09 seconds elapsed.
48 0
47 command lines read.
0 errors detected.
0 warnings issued.
0 seconds CPU time.
0 seconds elapsed time.
End of job.