Qualitative Variables March 3, 20041Political Science 552Qualitative VariablesDichotomous Predictor22110XXYβββ++=X1=PID X2=Gender (0 male, 1 female)11021100 XXYβββββ+=⋅++=()112021101 XXYββββββ++=⋅++=220XYββ+=0200βββ=⋅+=Y20201ββββ+=⋅+=YDummy Variables-Gender.* FT-BUSH PID GENDER. gen gender=(v001029==2). regress v000361 v000523 gender------------------------------------------------------------------------------v000361 | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+----------------------------------------------------------------v000523 | 6.887741 .254927 27.02 0.000 6.387688 7.387794gender | 1.469969 1.070683 1.37 0.170 -.6302344 3.570172_cons | 36.43924 1.106661 32.93 0.000 34.26846 38.61001------------------------------------------------------------------------------. . predict yhatG(option xb assumed; fitted values). twoway (scatter v000361 v000523, jitter(3)) (line yhatG v000523 if gender==1> , sort) (line yhatG v000523 if gender!=1, sort)Qualitative Variables March 3, 200420 20 40 60 80 1000 2 4 6K1x. Pa rt y ID su mm aryC1c/C1c.T. Thermometer George W Bush Fitted valuesFitted valuest-test equivalency. ttest v000361, by(v001029)Two-sample t test with equal variancesGroup Obs Mean Std. Err. Std. Dev.1. MALE 668 57.04192 .9476304 24.492172. 2. FEMAL 851 55.81199 .8678922 25.31807combined 1519 56.35286 .6403584 24.95755diff 1.22993 1.290152Degrees of freedom: 1517Ha: diff < 0 Ha: diff != 0 Ha: diff > 0t = 0.9533 t = 0.9533 t = 0.9533P < t = 0.8297 P > |t| = 0.3406 P > t = 0.1703. gen gender=(v001029==2). regress v000361 genderv000361 Coef. Std. Err. t P>|t|gender -1.22993 1.290152 -0.95 0.341 _cons 57.04192 .9656656 59.07 0.000Three or More Categories55443322110XXXXXYββββββ+++++=554433221100XXXXXXYββββββ+++++=054321 XXXXX ==+++Qualitative Variables March 3, 20043Multi-Category Example. xi: regress v000361 v000523 i.regionv000361 Coef. Std. Err. t P>t v000523 6.849912 .2510766 27.28 0.000_Iregion_2 -.096798 1.626896 -0.06 0.953_Iregion_3 5.911701 1.53034 3.86 0.000 _Iregion_4 -2.327671 1.680044 -1.39 0.166_cons 3 5.77408 1.427326 25.06 0.000. predict yhat(option xb assumed; fitted values)(31 missing values generated). twoway (lfit yhat v000523 if region==1) (lfit yhat v000523 if region==2)> (lfit yhat v000523 if region==3) (lfit yhat v000523 if region==4)Plot of Multi-Category30 40 50 60 70 80Fitted values0 2 4 6K1 x. Pa rt y ID su mm aryFitted values Fitted valuesFitted values Fitted valuesANOVA on Region. recode v000079 (1/19 = 1 "East")(20/39 = 2 "Midwest")(40/59 = 3 "South/Border> ")(60/79 = 4 "West")(96 = .),gen(region)oneway v000361 region, tabulate| Summary of C1c/C1c.T. Thermometer| George W Bushregion | Mean Std. Dev. Freq.--------------+------------------------------------East | 54 25 264Midwest | 54 25 383South/Bor | 61 25 540West | 52 25 330--------------+------------------------------------Total | 56 25 1517Analysis of VarianceSource SS df MS F Prob > F------------------------------------------------------------------------Between groups 19259.4678 3 6419.82259 10.51 0.0000Within groups 924177.917 1513 610.824796------------------------------------------------------------------------Total 943437.384 1516 622.320174Qualitative Variables March 3, 20044Region as Dummy Variable. xi: regress v000361 i.regioni.region _Iregion_1-4 (naturally coded; _Iregion_1 omitted)Source | SS df MS Number of obs = 1517----------------+------------------------------ F( 3, 1513) = 10.51Model | 19259.4678 3 6419.82259 Prob > F = 0.0000Residual | 924177.917 1513 610.824796 R-squared = 0.0204-----------------+------------------------------ Adj R-squared = 0.0185Total | 943437.384 1516 622.320174 Root MSE = 24.715------------------------------------------------------------------------------v000361 | Coef. Std. Err. t P>|t| -------------+----------------------------------------------------------------_Iregion_2 | -.1112232 1.977011 -0.06 0.955_Iregion_3 | 6.498316 1.856041 3.50 0.000_Iregion_4 | -2.125758 2.040763 -1.04 0.298 _cons | 54.49242 1.521095 35.82 0.000------------------------------------------------------------------------------Modifying Omitted Category. char region[omit] 3. xi: regress v000361 i.regioni.region _Iregion_1-4 (naturally coded; _Iregion_3 omitted)Source | SS df MS Number of obs = 1517---------------+------------------------------ F( 3, 1513) = 10.51Model | 19259.4678 3 6419.82259 Prob > F = 0.0000Residual | 924177.917 1513 610.824796 R-squared = 0.0204---------------+------------------------------ Adj R-squared = 0.0185Total | 943437.384 1516 622.320174 Root MSE = 24.715------------------------------------------------------------------------------v000361 | Coef. Std. Err. t P>|t| -------------+----------------------------------------------------------------_Iregion_1 | -6.498316 1.856041 -3.50 0.000 _Iregion_2 | -6.60954 1.65106 -4.00 0.000 _Iregion_4 | -8.624074 1.726888 -4.99 0.000 _cons | 60.99074 1.063559 57.35 0.000 ------------------------------------------------------------------------------Effect Coding. recode _Iregion* (0 = -1) if (region==3). regress v000361 _Iregion*Source SS df MS Number of obs = 1517F( 3, 1513) = 10.51Model 19259.4678 3 6419.82259 Prob > F = 0.0000Residual 924177.917 1513 610.824796 R-squared = 0.0204Adj R-squared = 0.0185Total 943437.384 1516 622.320174 Root MSE = 24.715v000361 Coef. Std. Err. t P>t_Iregion_1 -1.065334 1.259974 -0.85