[Stata Program]
data gpa;
input gpa greq grev mat ar;
cards;
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
proc reg simple corr;
model gpa = greq grev mat ar / stb p r;
plot gpa*greq='*';
plot gpa*grev='*';
plot gpa*mat='*';
plot gpa*ar='*';
plot student. * obs.='*';
plot student. * predicted.='*';
plot student. * greq='*';
plot student. * grev='*';
plot student. * mat='*';
plot student. * ar='*';
run;
[Stata Output]
The SAS System 10:59 Wednesday, January 27, 1999
Descriptive Statistics
Variables Sum Mean Uncorrected SS
INTERCEP 30 1 30
GREQ 16960 565.33333333 9656600
GREV 17260 575.33333333 10130200
MAT 2010 67 137150
AR 107 3.5666666667 402.02
GPA 99.4 3.3133333333 339.78
Variables Variance Std Deviation
INTERCEP 0 0
GREQ 2363.6781609 48.617673339
GREV 6894.7126437 83.034406385
MAT 85.517241379 9.2475532645
AR 0.7029885057 0.8384440982
GPA 0.359816092 0.5998467237
Correlation
CORR GREQ GREV MAT AR GPA
GREQ 1.0000 0.4681 0.2669 0.5078 0.6111
GREV 0.4681 1.0000 0.4257 0.4053 0.5815
MAT 0.2669 0.4257 1.0000 0.5248 0.6042
AR 0.5078 0.4053 0.5248 1.0000 0.6207
GPA 0.6111 0.5815 0.6042 0.6207 1.0000
Model: MODEL1
Dependent Variable: GPA
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 4 6.68313 1.67078 11.134 0.0001
Error 25 3.75153 0.15006
C Total 29 10.43467
Root MSE 0.38738 R-square 0.6405
Dep Mean 3.31333 Adj R-sq 0.5829
C.V. 11.69147
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 -1.738107 0.95073990 -1.828 0.0795
GREQ 1 0.003998 0.00183065 2.184 0.0385
GREV 1 0.001524 0.00105016 1.451 0.1593
MAT 1 0.020896 0.00954884 2.188 0.0382
AR 1 0.144234 0.11300126 1.276 0.2135
Standardized
Variable DF Estimate
INTERCEP 1 0.00000000
GREQ 1 0.32406205
GREV 1 0.21091228
MAT 1 0.32214467
AR 1 0.20160444
Dep Var Predict Std Err Std Err Student
Obs GPA Value Predict Residual Residual Residual
1 3.2000 3.3313 0.191 -0.1313 0.337 -0.390
2 4.1000 3.8132 0.136 0.2868 0.363 0.791
3 3.0000 2.7912 0.137 0.2088 0.362 0.576
4 2.6000 2.8297 0.118 -0.2297 0.369 -0.623
5 3.7000 3.1740 0.153 0.5260 0.356 1.478
6 4.0000 3.6744 0.189 0.3256 0.338 0.963
7 4.3000 4.1085 0.152 0.1915 0.356 0.538
8 2.7000 3.0228 0.168 -0.3228 0.349 -0.924
9 3.6000 3.5931 0.147 0.0069 0.359 0.019
10 4.1000 3.5899 0.152 0.5101 0.356 1.433
11 2.7000 2.7944 0.180 -0.0944 0.343 -0.275
12 2.9000 2.7299 0.124 0.1701 0.367 0.463
13 2.5000 2.7297 0.130 -0.2297 0.365 -0.629
14 3.0000 3.4304 0.193 -0.4304 0.336 -1.281
15 3.3000 4.0876 0.174 -0.7876 0.346 -2.276
16 3.2000 3.3313 0.191 -0.1313 0.337 -0.390
17 4.1000 3.8132 0.136 0.2868 0.363 0.791
18 3.0000 2.7912 0.137 0.2088 0.362 0.576
19 2.6000 2.8297 0.118 -0.2297 0.369 -0.623
20 3.7000 3.1740 0.153 0.5260 0.356 1.478
21 4.0000 3.6744 0.189 0.3256 0.338 0.963
22 4.3000 4.1085 0.152 0.1915 0.356 0.538
23 2.7000 3.0228 0.168 -0.3228 0.349 -0.924
24 3.6000 3.5931 0.147 0.0069 0.359 0.019
25 4.1000 3.5899 0.152 0.5101 0.356 1.433
26 2.7000 2.7944 0.180 -0.0944 0.343 -0.275
27 2.9000 2.7299 0.124 0.1701 0.367 0.463
28 2.5000 2.7297 0.130 -0.2297 0.365 -0.629
29 3.0000 3.4304 0.193 -0.4304 0.336 -1.281
30 3.3000 4.0876 0.174 -0.7876 0.346 -2.276
Cook's
Obs -2-1-0 1 2 D
1 | | | 0.010
2 | |* | 0.018
3 | |* | 0.009
4 | *| | 0.008
5 | |** | 0.081
6 | |* | 0.058
7 | |* | 0.011
8 | *| | 0.039
9 | | | 0.000
10 | |** | 0.075
11 | | | 0.004
12 | | | 0.005
13 | *| | 0.010
14 | **| | 0.108
15 | ****| | 0.262
16 | | | 0.010
17 | |* | 0.018
18 | |* | 0.009
19 | *| | 0.008
20 | |** | 0.081
21 | |* | 0.058
22 | |* | 0.011
23 | *| | 0.039
24 | | | 0.000
25 | |** | 0.075
26 | | | 0.004
27 | | | 0.005
28 | *| | 0.010
29 | **| | 0.108
30 | ****| | 0.262
Sum of Residuals 0
Sum of Squared Residuals 3.7515
Predicted Resid SS (Press) 5.6417
[Dependent Variable vs Inpependent Variable (GREQ)]
-----+-------+-------+-------+-------+-------+-------+-------+-------+------
4.4 + +
| |
| * |
| |
| |
4.2 + +
| |
| * * |
| |
| |
4.0 + * +
| |
| |
| |
| |
3.8 + +
| |
GPA | * |
| |
| |
3.6 + * +
| |
| |
| |
| |
3.4 + +
| |
| * |
| |
| |
3.2 + * +
| |
| |
| |
| |
3.0 + * * +
| |
| * |
| |
| |
2.8 + +
| |
| * * |
| |
| |
2.6 + * +
| |
| * |
| |
| |
2.4 + +
-----+-------+-------+-------+-------+-------+-------+-------+-------+------
500 520 540 560 580 600 620 640 660
GREQ
[Dependent Variable vs Inpependent Variable (GREV)]
-+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+--
4.4 + +
| |
| * |
| |
| |
4.2 + +
| |
| * * |
| |
| |
4.0 + * +
| |
| |
| |
| |
3.8 + +
| |
GPA | * |
| |
| |
3.6 + * +
| |
| |
| |
| |
3.4 + +
| |
| * |
| |
| |
3.2 + * +
| |
| |
| |
| |
3.0 +* * +
| |
| * |
| |
| |
2.8 + +
| |
| * * |
| |
| |
2.6 + * +
| |
| * |
| |
| |
2.4 + +
-+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+--
480 500 520 540 560 580 600 620 640 660 680 700 720
GREV
[Dependent Variable vs Inpependent Variable (MAT)]
-+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+--
4.4 + +
| |
| * |
| |
| |
4.2 + +
| |
| * |
| |
| |
4.0 + * +
| |
| |
| |
| |
3.8 + +
| |
GPA | * |
| |
| |
3.6 + * +
| |
| |
| |
| |
3.4 + +
| |
| * |
| |
| |
3.2 + * +
| |
| |
| |
| |
3.0 + * +
| |
|* |
| |
| |
2.8 + +
| |
|* * |
| |
| |
2.6 +* +
| |
|* |
| |
| |
2.4 + +
-+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+--
55.0 57.5 60.0 62.5 65.0 67.5 70.0 72.5 75.0 77.5 80.0 82.5 85.0
MAT
[Dependent Variable vs Inpependent Variable (AR)]
-----+----+----+----+----+----+----+----+----+----+----+----+----+----+-----
4.4 + +
| |
| * |
| |
| |
4.2 + +
| |
| * * |
| |
| |
4.0 + * +
| |
| |
| |
| |
3.8 + +
| |
GPA | * |
| |
| |
3.6 + * +
| |
| |
| |
| |
3.4 + +
| |
| * |
| |
| |
3.2 + * +
| |
| |
| |
| |
3.0 + * * +
| |
| * |
| |
| |
2.8 + +
| |
| * * |
| |
| |
2.6 + * +
| |
| * |
| |
| |
2.4 + +
-----+----+----+----+----+----+----+----+----+----+----+----+----+----+-----
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0
AR
[Standardized Residual vs Observation]
----+----+----+----+----+----+----+----+----+----+----+----+----+----
STUDENT | |
1.5 + * * +
| * * |
| |
| |
| |
| |
1.0 + * * +
| |
| |
| * * |
| |
| * * |
0.5 + * * * * +
| |
S | |
t | |
u | |
d | |
e 0.0 + * * +
n | |
t | |
i | * * |
z | |
e | * * |
d -0.5 + +
| * * |
R | * * |
e | |
s | |
i | * * |
d -1.0 + +
u | |
a | |
l | * * |
| |
| |
-1.5 + +
| |
| |
| |
| |
| |
-2.0 + +
| |
| |
| * * |
| |
| |
-2.5 + +
| |
----+----+----+----+----+----+----+----+----+----+----+----+----+----
0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5 30.0
Observation Number OBS NUM
[Standardized Residual vs Predicted Variable]
------+------+------+------+------+------+------+------+------+------
STUDENT | |
1.5 + * +
| * |
| |
| |
| |
| |
1.0 + * +
| |
| |
| * |
| |
| * |
0.5 + * * +
| |
S | |
t | |
u | |
d | |
e 0.0 + * +
n | |
t | |
i | * |
z | |
e | * |
d -0.5 + +
| * |
R | * |
e | |
s | |
i | * |
d -1.0 + +
u | |
a | |
l | * |
| |
| |
-1.5 + +
| |
| |
| |
| |
| |
-2.0 + +
| |
| |
| * |
| |
| |
-2.5 + +
| |
------+------+------+------+------+------+------+------+------+------
2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2
Predicted Value of GPA PRED
[Standardized Residual vs Independent Variable (GREQ)]
------+------+------+------+------+------+------+------+------+------
STUDENT | |
1.5 + * +
| * |
| |
| |
| |
| |
1.0 + * +
| |
| |
| * |
| |
| * |
0.5 + * * +
| |
S | |
t | |
u | |
d | |
e 0.0 + * +
n | |
t | |
i | * |
z | |
e | * |
d -0.5 + +
| * |
R | * |
e | |
s | |
i | * |
d -1.0 + +
u | |
a | |
l | * |
| |
| |
-1.5 + +
| |
| |
| |
| |
| |
-2.0 + +
| |
| |
| * |
| |
| |
-2.5 + +
| |
------+------+------+------+------+------+------+------+------+------
500 520 540 560 580 600 620 640 660
GREQ
[Standardized Residual vs Independent Variable (GREV)]
----+----+----+----+----+----+----+----+----+----+----+----+----+----
STUDENT | |
1.5 + * +
| * |
| |
| |
| |
| |
1.0 + * +
| |
| |
| * |
| |
| * |
0.5 + * * +
| |
S | |
t | |
u | |
d | |
e 0.0 + * +
n | |
t | |
i | * |
z | |
e | * |
d -0.5 + +
| * |
R | * |
e | |
s | |
i | * |
d -1.0 + +
u | |
a | |
l | * |
| |
| |
-1.5 + +
| |
| |
| |
| |
| |
-2.0 + +
| |
| |
| * |
| |
| |
-2.5 + +
| |
----+----+----+----+----+----+----+----+----+----+----+----+----+----
480 500 520 540 560 580 600 620 640 660 680 700 720
GREV
[Standardized Residual vs Independent Variable (MAT)]
----+----+----+----+----+----+----+----+----+----+----+----+----+----
STUDENT | |
1.5 + * +
| * |
| |
| |
| |
| |
1.0 + * +
| |
| |
| * |
| |
| * |
0.5 + * * +
| |
S | |
t | |
u | |
d | |
e 0.0 + * +
n | |
t | |
i | * |
z | |
e | * |
d -0.5 + +
| * |
R | * |
e | |
s | |
i | * |
d -1.0 + +
u | |
a | |
l | * |
| |
| |
-1.5 + +
| |
| |
| |
| |
| |
-2.0 + +
| |
| |
| * |
| |
| |
-2.5 + +
| |
----+----+----+----+----+----+----+----+----+----+----+----+----+----
55.0 57.5 60.0 62.5 65.0 67.5 70.0 72.5 75.0 77.5 80.0 82.5 85.0
MAT
[Standardized Residual vs Independent Variable (AR)]
-+----+----+----+----+----+----+----+----+----+----+----+----+----+--
STUDENT | |
1.5 + * +
| * |
| |
| |
| |
| |
1.0 + * +
| |
| |
| * |
| |
| * |
0.5 + * * +
| |
S | |
t | |
u | |
d | |
e 0.0 + * +
n | |
t | |
i | * |
z | |
e | * |
d -0.5 + +
| * |
R | * |
e | |
s | |
i | * |
d -1.0 + +
u | |
a | |
l | * |
| |
| |
-1.5 + +
| |
| |
| |
| |
| |
-2.0 + +
| |
| |
| * |
| |
| |
-2.5 + +
| |
-+----+----+----+----+----+----+----+----+----+----+----+----+----+--
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0
AR