THE SAS CODE USED:
data temp;
input zip income lottery black pop;
label
zip = 'zip code'
income = '1997 median household income'
lottery = '1997 lottery sales (millions)'
black = 'percent Black'
pop = 'total pop'
;
cards;
20019 29230 21.3 98.6 59402
20018 34612 13.5 95.7 18174
20032 26688 11.2 95.6 39928
20020 30980 17.4 95.4 54429
20001 23621 15.5 88.4 34683
20011 40368 18.9 88.2 63092
20002 36477 26.4 82.3 56843
20012 57877 6.8 78.9 15033
20017 46743 4.8 70.9 19584
20010 31924 8.5 63.4 29043
20024 41967 8.6 60.7 11592
20003 50348 9.2 58.3 24889
20005 34240 7.6 48.1 9932
20009 38242 9 45.6 46845
20015 84519 0.8 8.0 14497
20037 48695 2.2 6.5 11109
20016 69206 4.1 5.6 31099
20036 43175 3.5 5.4 4074
20006 32414 4.1 5.1 2308
20008 59636 1.5 5.0 26557
20007 61105 2.7 4.6 27184
;
proc reg;
model lottery = black /stb;
weight pop;
title 'black, with pop weight';
proc reg;
model lottery = income /stb;
weight pop;
title 'income, with pop weight';
proc reg;
model lottery = black income /stb;
weight pop;
title 'black and income with pop weight';
run;
OUTPUT:
BLACK, WITH POP WEIGHT
Model: MODEL1
Dependent Variable: LOTTERY 1997 lottery sales (millions)
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 1 21771119.307 21771119.307 31.621 0.0001
Error 19 13081376.946 688493.52347
C Total 20 34852496.253
Root MSE 829.75510 R-square 0.6247
Dep Mean 12.83514 Adj R-sq 0.6049
C.V. 6464.71156
Parameter Estimates
Parameter Standard T for H0: Standardized
Variable DF Estimate Error Parameter=0 Prob > |T| Estimate
INTERCEP 1 0.975225 2.36539722 0.412 0.6847 0.00000000
BLACK 1 0.179092 0.03184823 5.623 0.0001 0.79035724
Variable
Variable DF Label
INTERCEP 1 Intercept
BLACK 1 percent Black
INCOME, WITH POP WEIGHT
Model: MODEL1
Dependent Variable: LOTTERY 1997 lottery sales (millions)
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 1 14577908.614 14577908.614 13.661 0.0015
Error 19 20274587.639 1067083.56
C Total 20 34852496.253
Root MSE 1032.99737 R-square 0.4183
Dep Mean 12.83514 Adj R-sq 0.3877
C.V. 8048.19402
Parameter Estimates
Parameter Standard T for H0: Standardized
Variable DF Estimate Error Parameter=0 Prob > |T| Estimate
INTERCEP 1 27.221775 4.11435264 6.616 0.0001 0.00000000
INCOME 1 -0.000352 0.00009516 -3.696 0.0015 -0.64674141
Variable
Variable DF Label
INTERCEP 1 Intercept
INCOME 1 1997 median household income
BLACK AND INCOME WITH POP WEIGHT
Model: MODEL1
Dependent Variable: LOTTERY 1997 lottery sales (millions)
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 2 21775814.62 10887907.31 14.987 0.0001
Error 18 13076681.633 726482.31295
C Total 20 34852496.253
Root MSE 852.33932 R-square 0.6248
Dep Mean 12.83514 Adj R-sq 0.5831
C.V. 6640.66765
Parameter Estimates
Parameter Standard T for H0: Standardized
Variable DF Estimate Error Parameter=0 Prob > |T| Estimate
INTERCEP 1 1.655450 8.80318502 0.188 0.8529 0.00000000
BLACK 1 0.175463 0.05574371 3.148 0.0056 0.77434426
INCOME 1 -0.000010755 0.00013378 -0.080 0.9368 -0.01977713
Variable
Variable DF Label
INTERCEP 1 Intercept
BLACK 1 percent Black
INCOME 1 1997 median household income
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