STA429/1007 F 2004 Handout 5
Regression with Categorical Independent Variables (Shorter version)
First, a piece of mathread.sas showing the format for apparent nationality.
------------------------------------------------------------------------------------------
value natfmt
1 = 'Chinese'
2 = 'Japanese'
3 = 'Korean'
4 = 'Vietnamese'
5 = 'Other Asian'
6 = 'Eastern European'
7 = 'Hispanic'
8 = 'English-speaking'
9 = 'French'
10 = 'Italian'
11 = 'Greek'
12 = 'Germanic'
13 = 'Other European'
14 = 'Middle-Eastern'
15 = 'Pakistani'
16 = 'East Indian'
17 = 'Sub-Saharan'
18 = 'OTHER' ;
------------------------------------------------------------------------------------------
/********************** mathcat1.sas **********************/
title 'Regression with Categorical IV: Math data';
options linesize=79 pagesize=2000 noovp formdlim='_';
libname math '/homes/students/u0/stats/brunner/mathlib';
/* Full path to permanent SAS datasets */
libname library '/homes/students/u0/stats/brunner/mathlib';
/* SAS will seach for permanently stored formats ONLY in a
place called "library." */
proc freq data=math.explore;
tables nation1 nation2;
proc glm data=math.explore;
class nation2;
model grade=nation2;
means nation2;
proc format;
value ethfmt 1 = 'Chinese'
2 = 'Other Asian'
3 = 'Eastern European'
4 = 'English-speaking'
5 = 'Other European'
6 = 'Middle Eastern'
7 = 'East Indian'
8 = 'Other';
data ecat;
set math.explore;
n1 = nation1;
if n1=. then ethnic1=.;
else if n1=1 then ethnic1 = 1; /* Chinese */
else if 2 <= n1 <= 5 then ethnic1 = 2; /* Other Asian */
else if n1=6 then ethnic1 = 3; /* Eastern European */
else if n1=8 then ethnic1 = 4; /* English-speaking */
else if n1=7 or 9 <= n1 <= 13 then ethnic1 = 5; /* Other European */
else if n1=14 then ethnic1 = 6; /* Middle Eastern */
else if n1=16 then ethnic1 = 7; /* East Indian */
else ethnic1=8; /* Other */
label ethnic1 = 'Ethnicity of Name Acc to Rater1';
n2 = nation2;
if n2=. then ethnic2=.;
else if n2=1 then ethnic2 = 1; /* Chinese */
else if 2 <= n2 <= 5 then ethnic2 = 2; /* Other Asian */
else if n2=6 then ethnic2 = 3; /* Eastern European */
else if n2=8 then ethnic2 = 4; /* English-speaking */
else if n2=7 or 9 <= n2 <= 13 then ethnic2 = 5; /* Other European */
else if n2=14 then ethnic2 = 6; /* Middle Eastern */
else if n2=16 then ethnic2 = 7; /* East Indian */
else ethnic2=8; /* Other */
label ethnic2 = 'Ethnicity of Name Acc to Rater2';
format ethnic1 ethnic2 ethfmt.;
/* I like rater1, but I like rater2 even more */
/* Make all 8 dummy vars, but use only 7 if model has intercept. */
if ethnic2=. then e1=.;
else if ethnic2 = 1 then e1=1; else e1=0;
if ethnic2=. then e2=.;
else if ethnic2 = 2 then e2=1; else e2=0;
if ethnic2=. then e3=.;
else if ethnic2 = 3 then e3=1; else e3=0;
if ethnic2=. then e4=.;
else if ethnic2 = 4 then e4=1; else e4=0;
if ethnic2=. then e5=.;
else if ethnic2 = 5 then e5=1; else e5=0;
if ethnic2=. then e6=.;
else if ethnic2 = 6 then e6=1; else e6=0;
if ethnic2=. then e7=.;
else if ethnic2 = 7 then e7=1; else e7=0;
if ethnic2=. then e8=.;
else if ethnic2 = 8 then e8=1; else e8=0;
proc freq;
tables nation1*ethnic1 nation2*ethnic2 / norow nocol nopercent missing;
tables ethnic1*ethnic2;
tables ethnic2*(e1-e8) / norow nocol nopercent missing;
tables sex;
proc glm;
class ethnic2;
model grade=ethnic2;
proc reg;
model grade=e1-e7;
allsame: test e1=e2=e3=e4=e5=e6=e7=0;
proc reg;
model grade=e1-e8 / noint;
sameall: test e1=e2=e3=e4=e5=e6=e7=e8;
proc reg;
title3 'Include Sex and Ethnicity in the regression';
model grade = gpa hscalc precalc calc sex e2-e8;
hschool: test gpa=hscalc=0;
dtest: test precalc=calc=0;
compare: test precalc=calc;
EthBack: test e2=e3=e4=e5=e6=e7=e8=0;
proc glm;
class sex ethnic2;
model grade = sex ethnic2 sex*ethnic2;
means sex ethnic2 sex*ethnic2;
_______________________________________________________________________________
Nationality of name acc to rater1
Cumulative Cumulative
nation1 Frequency Percent Frequency Percent
---------------------------------------------------------------------
Chinese 73 13.30 73 13.30
Japanese 2 0.36 75 13.66
Korean 12 2.19 87 15.85
Vietnamese 16 2.91 103 18.76
Other Asian 23 4.19 126 22.95
Eastern European 61 11.11 187 34.06
Hispanic 35 6.38 222 40.44
English-speaking 96 17.49 318 57.92
French 7 1.28 325 59.20
Italian 22 4.01 347 63.21
Greek 8 1.46 355 64.66
Germanic 11 2.00 366 66.67
Other European 25 4.55 391 71.22
Middle-Eastern 64 11.66 455 82.88
Pakistani 2 0.36 457 83.24
East Indian 72 13.11 529 96.36
Sub-Saharan 2 0.36 531 96.72
OTHER 18 3.28 549 100.00
Frequency Missing = 30
We did the proc glm just to get the means in this compact format.
The GLM Procedure
Level of ------------grade------------
nation2 N Mean Std Dev
Chinese 66 61.2727273 21.1823914
East Indian 57 64.3157895 19.7259419
Eastern European 48 56.0833333 19.9625536
English-speaking 73 56.6301370 17.2107096
French 9 52.0000000 20.4205779
Germanic 10 57.7000000 22.6374812
Greek 6 60.5000000 9.1815031
Hispanic 17 60.5294118 16.9893998
Italian 21 56.0000000 17.7341479
Japanese 1 36.0000000 .
Korean 4 71.7500000 17.5570499
Middle-Eastern 40 59.6750000 19.5505754
OTHER 5 56.4000000 11.6318528
Other Asian 6 45.6666667 12.5485723
Other European 7 47.4285714 26.2923128
Pakistani 1 50.0000000 .
Sub-Saharan 4 50.7500000 6.3966137
Vietnamese 10 58.4000000 21.8794678
Skipping some checks ...
Table of ethnic1 by ethnic2
ethnic1(Ethnicity of Name Acc to Rater1)
ethnic2(Ethnicity of Name Acc to Rater2)
Frequency |
Percent |
Row Pct |
Col Pct |Chinese |Other |Eastern |English-| Total
| |Asian |European|speaking|
-----------------+--------+--------+--------+--------+
Chinese | 71 | 2 | 0 | 0 | 73
| 12.93 | 0.36 | 0.00 | 0.00 | 13.30
| 97.26 | 2.74 | 0.00 | 0.00 |
| 73.96 | 5.71 | 0.00 | 0.00 |
-----------------+--------+--------+--------+--------+
Other Asian | 15 | 25 | 2 | 1 | 53
| 2.73 | 4.55 | 0.36 | 0.18 | 9.65
| 28.30 | 47.17 | 3.77 | 1.89 |
| 15.63 | 71.43 | 3.08 | 1.05 |
-----------------+--------+--------+--------+--------+
Eastern European | 0 | 1 | 50 | 0 | 61
| 0.00 | 0.18 | 9.11 | 0.00 | 11.11
| 0.00 | 1.64 | 81.97 | 0.00 |
| 0.00 | 2.86 | 76.92 | 0.00 |
-----------------+--------+--------+--------+--------+
English-speaking | 4 | 4 | 1 | 79 | 96
| 0.73 | 0.73 | 0.18 | 14.39 | 17.49
| 4.17 | 4.17 | 1.04 | 82.29 |
| 4.17 | 11.43 | 1.54 | 83.16 |
-----------------+--------+--------+--------+--------+
Other European | 0 | 1 | 7 | 14 | 108
| 0.00 | 0.18 | 1.28 | 2.55 | 19.67
| 0.00 | 0.93 | 6.48 | 12.96 |
| 0.00 | 2.86 | 10.77 | 14.74 |
-----------------+--------+--------+--------+--------+
Middle Eastern | 0 | 0 | 2 | 0 | 64
| 0.00 | 0.00 | 0.36 | 0.00 | 11.66
| 0.00 | 0.00 | 3.13 | 0.00 |
| 0.00 | 0.00 | 3.08 | 0.00 |
-----------------+--------+--------+--------+--------+
East Indian | 0 | 0 | 1 | 1 | 72
| 0.00 | 0.00 | 0.18 | 0.18 | 13.11
| 0.00 | 0.00 | 1.39 | 1.39 |
| 0.00 | 0.00 | 1.54 | 1.05 |
-----------------+--------+--------+--------+--------+
Other | 6 | 2 | 2 | 0 | 22
| 1.09 | 0.36 | 0.36 | 0.00 | 4.01
| 27.27 | 9.09 | 9.09 | 0.00 |
| 6.25 | 5.71 | 3.08 | 0.00 |
-----------------+--------+--------+--------+--------+
Total 96 35 65 95 549
17.49 6.38 11.84 17.30 100.00
(Continued)
Table of ethnic1 by ethnic2
ethnic1(Ethnicity of Name Acc to Rater1)
ethnic2(Ethnicity of Name Acc to Rater2)
Frequency |
Percent |
Row Pct |
Col Pct |Other E|Middle |East |Other | Total
|uropean |Eastern |Indian | |
-----------------+--------+--------+--------+--------+
Chinese | 0 | 0 | 0 | 0 | 73
| 0.00 | 0.00 | 0.00 | 0.00 | 13.30
| 0.00 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.00 | 0.00 | 0.00 |
-----------------+--------+--------+--------+--------+
Other Asian | 1 | 2 | 5 | 2 | 53
| 0.18 | 0.36 | 0.91 | 0.36 | 9.65
| 1.89 | 3.77 | 9.43 | 3.77 |
| 0.99 | 3.51 | 5.81 | 14.29 |
-----------------+--------+--------+--------+--------+
Eastern European | 4 | 0 | 3 | 3 | 61
| 0.73 | 0.00 | 0.55 | 0.55 | 11.11
| 6.56 | 0.00 | 4.92 | 4.92 |
| 3.96 | 0.00 | 3.49 | 21.43 |
-----------------+--------+--------+--------+--------+
English-speaking | 7 | 0 | 0 | 1 | 96
| 1.28 | 0.00 | 0.00 | 0.18 | 17.49
| 7.29 | 0.00 | 0.00 | 1.04 |
| 6.93 | 0.00 | 0.00 | 7.14 |
-----------------+--------+--------+--------+--------+
Other European | 83 | 1 | 1 | 1 | 108
| 15.12 | 0.18 | 0.18 | 0.18 | 19.67
| 76.85 | 0.93 | 0.93 | 0.93 |
| 82.18 | 1.75 | 1.16 | 7.14 |
-----------------+--------+--------+--------+--------+
Middle Eastern | 1 | 50 | 8 | 3 | 64
| 0.18 | 9.11 | 1.46 | 0.55 | 11.66
| 1.56 | 78.13 | 12.50 | 4.69 |
| 0.99 | 87.72 | 9.30 | 21.43 |
-----------------+--------+--------+--------+--------+
East Indian | 1 | 1 | 67 | 1 | 72
| 0.18 | 0.18 | 12.20 | 0.18 | 13.11
| 1.39 | 1.39 | 93.06 | 1.39 |
| 0.99 | 1.75 | 77.91 | 7.14 |
-----------------+--------+--------+--------+--------+
Other | 4 | 3 | 2 | 3 | 22
| 0.73 | 0.55 | 0.36 | 0.55 | 4.01
| 18.18 | 13.64 | 9.09 | 13.64 |
| 3.96 | 5.26 | 2.33 | 21.43 |
-----------------+--------+--------+--------+--------+
Total 101 57 86 14 549
18.40 10.38 15.66 2.55 100.00
Frequency Missing = 30
Skipping checks of e1-e8 ...
Cumulative Cumulative
sex Frequency Percent Frequency Percent
-----------------------------------------------------------
Male 285 51.72 285 51.72
Female 266 48.28 551 100.00
Frequency Missing = 28
_______________________________________________________________________________
Regression with Categorical IV: Math data 6
16:43 Wednesday, October 13, 2004
The GLM Procedure
Class Level Information
Class Levels Values
ethnic2 8 Chinese East Indian Eastern European English-speaking
Middle Eastern Other Other Asian Other European
Number of observations 579
NOTE: Due to missing values, only 385 observations can be used in this
analysis.
_______________________________________________________________________________
Regression with Categorical IV: Math data 7
16:43 Wednesday, October 13, 2004
The GLM Procedure
Dependent Variable: grade Final mark (if any)
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 7 3695.1830 527.8833 1.43 0.1925
Error 377 139351.2430 369.6319
Corrected Total 384 143046.4260
R-Square Coeff Var Root MSE grade Mean
0.025832 32.77514 19.22581 58.65974
Source DF Type I SS Mean Square F Value Pr > F
ethnic2 7 3695.182958 527.883280 1.43 0.1925
Source DF Type III SS Mean Square F Value Pr > F
ethnic2 7 3695.182958 527.883280 1.43 0.1925
_______________________________________________________________________________
Regression with Categorical IV: Math data 8
16:43 Wednesday, October 13, 2004
The REG Procedure
Model: MODEL1
Dependent Variable: grade Final mark (if any)
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 7 3695.18296 527.88328 1.43 0.1925
Error 377 139351 369.63194
Corrected Total 384 143046
Root MSE 19.22581 R-Square 0.0258
Dependent Mean 58.65974 Adj R-Sq 0.0077
Coeff Var 32.77514
Parameter Estimates
Parameter Standard
Variable Label DF Estimate Error t Value Pr > |t|
Intercept Intercept 1 53.50000 6.07974 8.80 <.0001
e1 1 7.77273 6.52408 1.19 0.2343
e2 1 2.73810 7.38679 0.37 0.7111
e3 1 2.58333 6.68310 0.39 0.6993
e4 1 3.13014 6.48280 0.48 0.6295
e5 1 2.85714 6.49951 0.44 0.6605
e6 1 6.17500 6.79735 0.91 0.3642
e7 1 10.81579 6.59151 1.64 0.1017
_______________________________________________________________________________
Regression with Categorical IV: Math data 9
16:43 Wednesday, October 13, 2004
The REG Procedure
Model: MODEL1
Test allsame Results for Dependent Variable grade
Mean
Source DF Square F Value Pr > F
Numerator 7 527.88328 1.43 0.1925
Denominator 377 369.63194
_______________________________________________________________________________
The REG Procedure
Model: MODEL1
Dependent Variable: grade Final mark (if any)
NOTE: No intercept in model. R-Square is redefined.
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 8 1328467 166058 449.25 <.0001
Error 377 139351 369.63194
Uncorrected Total 385 1467818
Root MSE 19.22581 R-Square 0.9051
Dependent Mean 58.65974 Adj R-Sq 0.9030
Coeff Var 32.77514
Parameter Estimates
Parameter Standard
Variable Label DF Estimate Error t Value Pr > |t|
e1 1 61.27273 2.36653 25.89 <.0001
e2 1 56.23810 4.19542 13.40 <.0001
e3 1 56.08333 2.77501 20.21 <.0001
e4 1 56.63014 2.25021 25.17 <.0001
e5 1 56.35714 2.29792 24.53 <.0001
e6 1 59.67500 3.03987 19.63 <.0001
e7 1 64.31579 2.54652 25.26 <.0001
e8 1 53.50000 6.07974 8.80 <.0001
_______________________________________________________________________________
Test sameall Results for Dependent Variable grade
Mean
Source DF Square F Value Pr > F
Numerator 7 527.88328 1.43 0.1925
Denominator 377 369.63194
_______________________________________________________________________________
Regression with Categorical IV: Math data 12
16:43 Wednesday, October 13, 2004
Include Sex and Ethnicity in the regression
The REG Procedure
Model: MODEL1
Dependent Variable: grade Final mark (if any)
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 12 43590 3632.50289 18.77 <.0001
Error 276 53413 193.52377
Corrected Total 288 97003
Root MSE 13.91128 R-Square 0.4494
Dependent Mean 60.61246 Adj R-Sq 0.4254
Coeff Var 22.95119
Parameter Estimates
Parameter Standard
Variable Label DF Estimate Error t Value
Intercept Intercept 1 -72.84682 11.68505 -6.23
gpa High School GPA 1 1.18286 0.18253 6.48
hscalc HS Calculus 1 0.33347 0.10016 3.33
precalc Number precalculus correct 1 1.73408 0.58004 2.99
calc Number calculus correct 1 0.69419 0.39547 1.76
sex 1 1.07063 1.72557 0.62
e2 1 -0.13357 3.85211 -0.03
e3 1 -0.59464 3.23489 -0.18
e4 1 -1.77769 2.87413 -0.62
e5 1 -0.06677 2.94415 -0.02
e6 1 -2.17740 3.45108 -0.63
e7 1 2.88897 2.99501 0.96
e8 1 1.64621 5.74186 0.29
Parameter Estimates
Variable Label DF Pr > |t|
Intercept Intercept 1 <.0001
gpa High School GPA 1 <.0001
hscalc HS Calculus 1 0.0010
precalc Number precalculus correct 1 0.0030
calc Number calculus correct 1 0.0803
sex 1 0.5355
e2 1 0.9724
e3 1 0.8543
e4 1 0.5367
e5 1 0.9819
e6 1 0.5286
e7 1 0.3356
e8 1 0.7746
_______________________________________________________________________________
Regression with Categorical IV: Math data 13
16:43 Wednesday, October 13, 2004
Include Sex and Ethnicity in the regression
The REG Procedure
Model: MODEL1
Test hschool Results for Dependent Variable grade
Mean
Source DF Square F Value Pr > F
Numerator 2 11413 58.98 <.0001
Denominator 276 193.52377
_______________________________________________________________________________
Regression with Categorical IV: Math data 14
16:43 Wednesday, October 13, 2004
Include Sex and Ethnicity in the regression
The REG Procedure
Model: MODEL1
Test dtest Results for Dependent Variable grade
Mean
Source DF Square F Value Pr > F
Numerator 2 1711.22289 8.84 0.0002
Denominator 276 193.52377
_______________________________________________________________________________
Regression with Categorical IV: Math data 15
16:43 Wednesday, October 13, 2004
Include Sex and Ethnicity in the regression
The REG Procedure
Model: MODEL1
Test compare Results for Dependent Variable grade
Mean
Source DF Square F Value Pr > F
Numerator 1 322.00651 1.66 0.1982
Denominator 276 193.52377
_______________________________________________________________________________
Regression with Categorical IV: Math data 16
16:43 Wednesday, October 13, 2004
Include Sex and Ethnicity in the regression
The REG Procedure
Model: MODEL1
Test EthBack Results for Dependent Variable grade
Mean
Source DF Square F Value Pr > F
Numerator 7 98.29303 0.51 0.8283
Denominator 276 193.52377
_______________________________________________________________________________
Sex by ethnicity 2-way ANOVA
Regression with Categorical IV: Math data 17
16:43 Wednesday, October 13, 2004
Include Sex and Ethnicity in the regression
The GLM Procedure
Class Level Information
Class Levels Values
sex 2 Female Male
ethnic2 8 Chinese East Indian Eastern European English-speaking
Middle Eastern Other Other Asian Other European
Number of observations 579
NOTE: Due to missing values, only 383 observations can be used in this
analysis.
_______________________________________________________________________________
Regression with Categorical IV: Math data 18
16:43 Wednesday, October 13, 2004
Include Sex and Ethnicity in the regression
The GLM Procedure
Dependent Variable: grade Final mark (if any)
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 15 6847.6569 456.5105 1.23 0.2454
Error 367 136069.8940 370.7627
Corrected Total 382 142917.5509
R-Square Coeff Var Root MSE grade Mean
0.047913 32.82331 19.25520 58.66319
Source DF Type I SS Mean Square F Value Pr > F
sex 1 110.794519 110.794519 0.30 0.5849
ethnic2 7 3504.025570 500.575081 1.35 0.2256
sex*ethnic2 7 3232.836800 461.833829 1.25 0.2768
Source DF Type III SS Mean Square F Value Pr > F
sex 1 316.814991 316.814991 0.85 0.3559
ethnic2 7 3542.751451 506.107350 1.37 0.2189
sex*ethnic2 7 3232.836800 461.833829 1.25 0.2768
_______________________________________________________________________________
Regression with Categorical IV: Math data 19
16:43 Wednesday, October 13, 2004
Include Sex and Ethnicity in the regression
The GLM Procedure
Level of ------------grade------------
sex N Mean Std Dev
Female 193 58.1295337 18.4319923
Male 190 59.2052632 20.2598196
Level of ------------grade------------
ethnic2 N Mean Std Dev
Chinese 66 61.2727273 21.1823914
East Indian 56 64.2857143 19.9031421
Eastern European 48 56.0833333 19.9625536
English-speaking 72 56.7222222 17.3133688
Middle Eastern 40 59.6750000 19.5505754
Other 10 53.5000000 9.1195760
Other Asian 21 56.2380952 20.1367941
Other European 70 56.3571429 18.8718299
Level of Level of ------------grade------------
sex ethnic2 N Mean Std Dev
Female Chinese 24 62.5416667 17.2475056
Female East Indian 24 63.2083333 18.9965195
Female Eastern European 32 57.5312500 17.4946708
Female English-speaking 40 57.5750000 18.0851086
Female Middle Eastern 17 63.7647059 14.9102708
Female Other 6 49.6666667 5.4650404
Female Other Asian 12 47.6666667 19.5696116
Female Other European 38 55.3421053 20.9481681
Male Chinese 42 60.5476190 23.3020489
Male East Indian 32 65.0937500 20.8208323
Male Eastern European 16 53.1875000 24.5498642
Male English-speaking 32 55.6562500 16.5209727
Male Middle Eastern 23 56.6521739 22.2130361
Male Other 4 59.2500000 11.2361025
Male Other Asian 9 67.6666667 15.1657509
Male Other European 32 57.5625000 16.3153154