Chapter 7 Binary or Zeroone or Dummy Variables Dummy Variables Example Example WAGE1 Data Set We want to fit the model The term female is a dummy variable and takes into account the effect of female vs male ID: 769252
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Chapter 7 – Binary or Zero/one or Dummy Variables
Dummy Variables – Example
Example – WAGE1 Data Set We want to fit the model : The term female is a dummy variable and takes into account the effect of female vs. male.
Example – WAGE1 Data Set We want to fit the model : The regression equation is wage = 0.623 - 2.27 female + 0.506 educ Predictor Coef SE Coef T PConstant 0.6228 0.6725 0.93 0.355female -2.2734 0.2790 -8.15 0.000educ 0.50645 0.05039 10.05 0.000S = 3.18552 R-Sq = 25.9% R-Sq(adj) = 25.6%
Example – WAGE1 Data Set We want to fit the model : Interpretation of fitted model: wage = 0.623 - 2.27 female + 0.506 educ The coefficient on female measures the average difference in hourly wage between a woman and a man (for this model).
Graphical Interpretation of Sex Effect
Example – WAGE1 Data Set Interpretation of fitted model: wage = 0.623 - 2.27 female + 0.506 educ The wage differential between females and males of -2.27 dollars per hour is due to sex of the individual and, potentially, factors we have not controlled for.
Example – WAGE1 Data Set Now, fit the model : This allows us to test the hypotheses: Ho: -> mean wage same for the sexes H1:-> mean wage different for the sexes
H o : H 1: The regression equation is wage = 7.10 - 2.51 female Predictor Coef SE Coef T PConstant 7.0995 0.2100 33.81 0.000female -2.5118 0.3034 -8.28 0.000
H o : H 1:The alternative hypothesis is supported – there is a statistically significant difference in mean wage between the sexes, p-value ≈ 0
wage = 7.10 - 2.51 female Estimated mean wage of males is $7.10 per hour Estimate mean wage of females is $7.10 – 2.51 = $4.59 per hour
Example – WAGE1 Data Set What is the effect (if any) on wage of a person’s marital status? (Did you check your regression assumptions?)
Example – WAGE1 Data Set Examine the effect on wage of a few of the other dummy variables in this data set.
Example – WAGE1 Data Set What is the interpretation of a dummy variable if the response is log(y)? Now, fit the model : Log(
Example – WAGE1 Data Set lwage = 1.81 - 0.397 female Predictor Coef SE Coef T PConstant 1.81357 0.02981 60.83 0.000Female -0.39722 0.04307 -9.22 0.000 About 40% decrease in hourly wage if individual is female!
Example – WAGE1 Data Set How do we handle multiple dummy variables at once? Consider the two variables married and female. We have four categories: single male, single female, married male, and married female.
We have four categories: single male, single female, married male, and married female. Need to create three new dummy variables Marriedmale Marriedfemale SinglefemaleSingle Male000Married Male100Single Female001Married Female 0 1 0
We have four categories: single male, single female, married male, and married female. Need to create three new dummy variables In order to create the dummy variables marriedmale , marriedfemale, and singlefemale, use the calculator and a nested and statement within an if statement in Minitab.
We have four categories: single male, single female, married male, and married female. wage = 5.17 + 2.82 marriedmale - 0.602 marriedfemale - 0.556 singlefemalePredictor Coef SE Coef T PConstant 5.1680 0.3614 14.30 0.000marriedmale 2.8150 0.4363 6.45 0.000marriedfemale -0.6021 0.4645 -1.30 0.195singlefemale - 0.5564 0.4736 -1.18 0.241S = 3.35181 R-Sq = 18.1% R-Sq(adj) = 17.6%
Did you check the assumptions of homoskedasticity and normality?
We have four categories: single male, single female, married male, and married female. lwage = 1.52 + 0.427 marriedmale - 0.0797 marriedfemale - 0.132 singlefemalePredictor Coef SE Coef T PConstant 1.52081 0.05099 29.83 0.000marriedmale 0.42668 0.06155 6.93 0.000marriedfemale -0.07974 0.06552 -1.22 0.224 singlefemale -0.13164 0.06680 -1.97 0.049S = 0.472836 R-Sq = 21.3% R-Sq(adj) = 20.9%
Did you check the assumptions of homoskedasticity and normality?
lwage = 0.321 + 0.213 marriedmale - 0.198 marriedfemale - 0.110 singlefemale + 0.0789 educ + 0.0268 exper - 0.000535 expersq + 0.0291 tenure - 0.000533 tenursqPredictor Coef SE Coef T PConstant 0.3214 0.1000 3.21 0.001marriedmale 0.21268 0.05536 3.84 0.000 marriedfemale -0.19827 0.05784 -3.43 0.001singlefemale -0.11035 0.05574 1.98 0.048educ 0.078910 0.006694 11.79 0.000exper 0.026801 0.005243 5.11 0.000expersq -0.0005352 0.0001104 -4.85 0.000tenure 0.029088 0.006762 4.30 0.000 tenursq - 0.0005331 0.0002312 - 2.31 0.022 S = 0.393290 R-Sq = 46.1% R-Sq(adj) = 45.3%
Did you check the assumptions of homoskedasticity and normality?
Example – BEAUTY Data Set Do looks affect hourly wage? Variable: looks Has five levels: 1, 2, 3, 4, 5 Make dummy variables where: 1, 2 – below average3 – average4, 5 – above average
Example – BEAUTY Data Set Do looks affect hourly wage? Make dummy variables where: 1, 2 – below average 3 – average4, 5 – above averageYou only need two dummy variables: belowaverage and aboveaverage
Example – BEAUTY Data Set Do looks affect hourly wage? Your conclusions? Did you check assumptions?
Example – BEAUTY Data Set Do looks affect hourly wage? Now, run a separate analysis for females and for males. Your conclusions? Did you check assumptions?
Dummy Variables and the Interaction Term Consider the Wage1 data set. Response: log(wage) Predictor variables: female, married, female*married, educ, exper, exper^2, tenure, and tenure^2.NOTE: need to run this model in general linear regression of Minitab
Dummy Variables and the Interaction Term Term Coef SE Coef T PConstant 0.321378 0.100009 3.2135 0.001female -0.110350 0.055742 -1.9797 0.048married 0.212676 0.055357 3.8419 0.000female*married -0.300593 0.071767 -4.1885 0.000educ 0.078910 0.006694 11.7873 0.000 exper 0.026801 0.005243 5.1118 0.000expersq -0.000535 0.000110 -4.8471 0.000tenure 0.029088 0.006762 4.3016 0.000tenursq -0.000533 0.000231 -2.3056 0.022Summary of ModelR-Sq = 46.09% R-Sq(adj) = 45.25%
Dummy Variables and the Interaction Term lwage = 0.321378 - 0.11035 female + 0.212676 married + 0.0789103 educ + 0.0268006 exper - 0.000535245 expersq + 0.0290875 tenure -0.000533142 tenursq - 0.300593 female*marriedInterpretation of dummy variables coefficients.
Example – Problem C7.2 Complete C7.2 ( i ), (iii), and (iv) in class