7 Multiple Regression Analysis
Also covered using Python and Stata
7.1 Example 7.1. Multiple Regression Analysis with Qualitative Information
Average wage difference between men and women in the sample
wage_fem <- lm(wage ~ female + educ + exper + tenure + 1, data=wage1)
stargazer(wage_fem, type="text", align=TRUE)##
## ===============================================
## Dependent variable:
## ---------------------------
## wage
## -----------------------------------------------
## female -1.811***
## (0.265)
##
## educ 0.572***
## (0.049)
##
## exper 0.025**
## (0.012)
##
## tenure 0.141***
## (0.021)
##
## Constant -1.568**
## (0.725)
##
## -----------------------------------------------
## Observations 526
## R2 0.364
## Adjusted R2 0.359
## Residual Std. Error 2.958 (df = 521)
## F Statistic 74.398*** (df = 4; 521)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01Average wage for men in the sample
##
## ===============================================
## Dependent variable:
## ---------------------------
## wage
## -----------------------------------------------
## female -2.512***
## (0.303)
##
## Constant 7.099***
## (0.210)
##
## -----------------------------------------------
## Observations 526
## R2 0.116
## Adjusted R2 0.114
## Residual Std. Error 3.476 (df = 524)
## F Statistic 68.537*** (df = 1; 524)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01Average wage for men and women in the sample
## Group.1 x
## 1 0 7.099489
## 2 1 4.5876597.2 Example 7.2. Effect of computer ownership on collage GPA
colGPA_ur <- lm(colGPA ~ PC + hsGPA + ACT + 1, data=gpa1)
stargazer(colGPA_ur, type="text", align=TRUE)##
## ===============================================
## Dependent variable:
## ---------------------------
## colGPA
## -----------------------------------------------
## PC 0.157***
## (0.057)
##
## hsGPA 0.447***
## (0.094)
##
## ACT 0.009
## (0.011)
##
## Constant 1.264***
## (0.333)
##
## -----------------------------------------------
## Observations 141
## R2 0.219
## Adjusted R2 0.202
## Residual Std. Error 0.333 (df = 137)
## F Statistic 12.834*** (df = 3; 137)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01## Linear hypothesis test
##
## Hypothesis:
## hsGPA = 0
## ACT = 0
##
## Model 1: restricted model
## Model 2: colGPA ~ PC + hsGPA + ACT + 1
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 139 18.436
## 2 137 15.149 2 3.2873 14.865 1.437e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
## ===============================================
## Dependent variable:
## ---------------------------
## colGPA
## -----------------------------------------------
## PC 0.170***
## (0.063)
##
## Constant 2.989***
## (0.040)
##
## -----------------------------------------------
## Observations 141
## R2 0.050
## Adjusted R2 0.043
## Residual Std. Error 0.364 (df = 139)
## F Statistic 7.314*** (df = 1; 139)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01## Group.1 x
## 1 0 2.989412
## 2 1 3.1589297.3 Example 7.3. Effect of Training Grants on hours of training
jtrain88 <- subset(jtrain, jtrain$year==1988)
jobb_reg <- lm(hrsemp ~ grant + lsales + lemploy + 1, data=jtrain88)
stargazer(jobb_reg, type="text", align=TRUE)##
## ===============================================
## Dependent variable:
## ---------------------------
## hrsemp
## -----------------------------------------------
## grant 26.254***
## (5.592)
##
## lsales -0.985
## (3.540)
##
## lemploy -6.070
## (3.883)
##
## Constant 46.665
## (43.412)
##
## -----------------------------------------------
## Observations 105
## R2 0.237
## Adjusted R2 0.214
## Residual Std. Error 24.380 (df = 101)
## F Statistic 10.444*** (df = 3; 101)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.017.4 Example 7.4. Housing price regression
hrpice_reg <- lm(lprice ~ llotsize + lsqrft + bdrms + colonial + 1, data=hprice1)
stargazer(hrpice_reg, type="text", align=TRUE)##
## ===============================================
## Dependent variable:
## ---------------------------
## lprice
## -----------------------------------------------
## llotsize 0.168***
## (0.038)
##
## lsqrft 0.707***
## (0.093)
##
## bdrms 0.027
## (0.029)
##
## colonial 0.054
## (0.045)
##
## Constant -1.350**
## (0.651)
##
## -----------------------------------------------
## Observations 88
## R2 0.649
## Adjusted R2 0.632
## Residual Std. Error 0.184 (df = 83)
## F Statistic 38.378*** (df = 4; 83)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.017.5 Example 7.5. Hourly wage equation
wage_reg <- lm(lwage ~ female + educ + exper + expersq + tenure + tenursq + 1, data=wage1)
stargazer(wage_reg, type="text", align=TRUE)##
## ===============================================
## Dependent variable:
## ---------------------------
## lwage
## -----------------------------------------------
## female -0.297***
## (0.036)
##
## educ 0.080***
## (0.007)
##
## exper 0.029***
## (0.005)
##
## expersq -0.001***
## (0.0001)
##
## tenure 0.032***
## (0.007)
##
## tenursq -0.001**
## (0.0002)
##
## Constant 0.417***
## (0.099)
##
## -----------------------------------------------
## Observations 526
## R2 0.441
## Adjusted R2 0.434
## Residual Std. Error 0.400 (df = 519)
## F Statistic 68.177*** (df = 6; 519)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01## female
## -0.25659257.6 Example 7.6. Hourly wage equation
marrmale <- (wage1$female==0 & wage1$married==1)
marrfem <- (wage1$female==1 & wage1$married==1)
singfem <- (wage1$female==1 & wage1$married==0)
singmale <- (wage1$female==0 & wage1$married==0)
wage_sf = lm(lwage ~ marrmale + marrfem + singfem + educ + exper + expersq + tenure + tenursq + 1, data=wage1)
stargazer(wage_sf, type="text", align=TRUE)##
## ===============================================
## Dependent variable:
## ---------------------------
## lwage
## -----------------------------------------------
## marrmale 0.213***
## (0.055)
##
## marrfem -0.198***
## (0.058)
##
## singfem -0.110**
## (0.056)
##
## educ 0.079***
## (0.007)
##
## exper 0.027***
## (0.005)
##
## expersq -0.001***
## (0.0001)
##
## tenure 0.029***
## (0.007)
##
## tenursq -0.001**
## (0.0002)
##
## Constant 0.321***
## (0.100)
##
## -----------------------------------------------
## Observations 526
## R2 0.461
## Adjusted R2 0.453
## Residual Std. Error 0.393 (df = 517)
## F Statistic 55.246*** (df = 8; 517)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01wage_sm = lm(lwage ~ marrmale + marrfem + singmale + educ + exper + expersq + tenure + tenursq + 1, data=wage1)
stargazer(wage_sm, type="text", align=TRUE)##
## ===============================================
## Dependent variable:
## ---------------------------
## lwage
## -----------------------------------------------
## marrmale 0.323***
## (0.050)
##
## marrfem -0.088*
## (0.052)
##
## singmale 0.110**
## (0.056)
##
## educ 0.079***
## (0.007)
##
## exper 0.027***
## (0.005)
##
## expersq -0.001***
## (0.0001)
##
## tenure 0.029***
## (0.007)
##
## tenursq -0.001**
## (0.0002)
##
## Constant 0.211**
## (0.097)
##
## -----------------------------------------------
## Observations 526
## R2 0.461
## Adjusted R2 0.453
## Residual Std. Error 0.393 (df = 517)
## F Statistic 55.246*** (df = 8; 517)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.017.7 Example 7.7. Effects of physical attractiveness on wage
beauty0<-subset(beauty, beauty$female==0)
beauty_reg0 <- lm(lwage ~ belavg + abvavg + educ + exper + expersq + union + married + black + south + goodhlth + 1, data=beauty0)
stargazer(beauty_reg0, type="text", align=TRUE)##
## ===============================================
## Dependent variable:
## ---------------------------
## lwage
## -----------------------------------------------
## belavg -0.165***
## (0.053)
##
## abvavg -0.025
## (0.038)
##
## educ 0.061***
## (0.007)
##
## exper 0.046***
## (0.006)
##
## expersq -0.001***
## (0.0001)
##
## union 0.149***
## (0.036)
##
## married 0.064
## (0.044)
##
## black -0.257***
## (0.076)
##
## south 0.085**
## (0.043)
##
## goodhlth 0.001
## (0.070)
##
## Constant 0.478***
## (0.120)
##
## -----------------------------------------------
## Observations 824
## R2 0.255
## Adjusted R2 0.246
## Residual Std. Error 0.469 (df = 813)
## F Statistic 27.819*** (df = 10; 813)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01beauty1<-subset(beauty, beauty$female==1)
beauty_reg1 <- lm(lwage ~ belavg + abvavg + educ + exper + expersq + union + married + black + south + goodhlth + 1, data=beauty1)
stargazer(beauty_reg1, type="text", align=TRUE)##
## ===============================================
## Dependent variable:
## ---------------------------
## lwage
## -----------------------------------------------
## belavg -0.114*
## (0.066)
##
## abvavg 0.069
## (0.049)
##
## educ 0.076***
## (0.009)
##
## exper 0.029***
## (0.007)
##
## expersq -0.0005***
## (0.0002)
##
## union 0.293***
## (0.054)
##
## married -0.062
## (0.044)
##
## black 0.144**
## (0.069)
##
## south 0.008
## (0.060)
##
## goodhlth 0.113
## (0.081)
##
## Constant -0.077
## (0.144)
##
## -----------------------------------------------
## Observations 436
## R2 0.278
## Adjusted R2 0.261
## Residual Std. Error 0.451 (df = 425)
## F Statistic 16.399*** (df = 10; 425)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.017.8 Example 7.8. Effects of law school rankings on starting salaries
r61_100 <- (lawsch85$rank>60 & lawsch85$rank<=100)
lawsch85 <- cbind(lawsch85, r61_100)
lawsch85_reg = lm(lsalary ~ top10 + r11_25 + r26_40 + r41_60 + r61_100 + LSAT + GPA + llibvol + lcost + 1, data=lawsch85)
stargazer(lawsch85_reg, type="text", align=TRUE)##
## ===============================================
## Dependent variable:
## ---------------------------
## lsalary
## -----------------------------------------------
## top10 0.700***
## (0.053)
##
## r11_25 0.594***
## (0.039)
##
## r26_40 0.375***
## (0.034)
##
## r41_60 0.263***
## (0.028)
##
## r61_100 0.132***
## (0.021)
##
## LSAT 0.006*
## (0.003)
##
## GPA 0.014
## (0.074)
##
## llibvol 0.036
## (0.026)
##
## lcost 0.001
## (0.025)
##
## Constant 9.165***
## (0.411)
##
## -----------------------------------------------
## Observations 136
## R2 0.911
## Adjusted R2 0.905
## Residual Std. Error 0.086 (df = 126)
## F Statistic 143.199*** (df = 9; 126)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01## Linear hypothesis test
##
## Hypothesis:
## LSAT = 0
## GPA = 0
## llibvol = 0
## lcost = 0
##
## Model 1: restricted model
## Model 2: lsalary ~ top10 + r11_25 + r26_40 + r41_60 + r61_100 + LSAT +
## GPA + llibvol + lcost + 1
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 130 0.99409
## 2 126 0.92411 4 0.069978 2.3853 0.0547 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 17.10 Example 7.10. Log hourly wage equation
wage_reg <- lm(lwage ~ female*educ + exper + expersq + tenure + tenursq + 1, data=wage1)
stargazer(wage_reg, type="text", align=TRUE)##
## ===============================================
## Dependent variable:
## ---------------------------
## lwage
## -----------------------------------------------
## female -0.227
## (0.168)
##
## educ 0.082***
## (0.008)
##
## exper 0.029***
## (0.005)
##
## expersq -0.001***
## (0.0001)
##
## tenure 0.032***
## (0.007)
##
## tenursq -0.001**
## (0.0002)
##
## female:educ -0.006
## (0.013)
##
## Constant 0.389***
## (0.119)
##
## -----------------------------------------------
## Observations 526
## R2 0.441
## Adjusted R2 0.433
## Residual Std. Error 0.400 (df = 518)
## F Statistic 58.371*** (df = 7; 518)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01## Linear hypothesis test
##
## Hypothesis:
## female = 0
## female:educ = 0
##
## Model 1: restricted model
## Model 2: lwage ~ female * educ + exper + expersq + tenure + tenursq +
## 1
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 520 93.911
## 2 518 82.922 2 10.99 34.325 1.002e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 17.11 Example 7.11. Effects of race on baseball player salaries
mlb1<-subset(mlb1, mlb1$percblck!=0)
mlb1_reg <- lm(lsalary ~ years + gamesyr + bavg + hrunsyr + rbisyr + runsyr + fldperc + allstar + black + hispan + black:percblck + hispan:perchisp + 1, data=mlb1)
stargazer(mlb1_reg, type="text", align=TRUE)##
## ===============================================
## Dependent variable:
## ---------------------------
## lsalary
## -----------------------------------------------
## years 0.067***
## (0.013)
##
## gamesyr 0.009***
## (0.003)
##
## bavg 0.001
## (0.002)
##
## hrunsyr 0.015
## (0.016)
##
## rbisyr 0.004
## (0.008)
##
## runsyr 0.007
## (0.005)
##
## fldperc 0.001
## (0.002)
##
## allstar 0.008***
## (0.003)
##
## black -0.198
## (0.125)
##
## hispan -0.190
## (0.153)
##
## black:percblck 0.012**
## (0.005)
##
## hispan:perchisp 0.020**
## (0.010)
##
## Constant 10.344***
## (2.183)
##
## -----------------------------------------------
## Observations 330
## R2 0.638
## Adjusted R2 0.624
## Residual Std. Error 0.713 (df = 317)
## F Statistic 46.482*** (df = 12; 317)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01linearHypothesis (mlb1_reg, c("black = 0","hispan = 0","hispan:perchisp = 0", "black:percblck = 0"))## Linear hypothesis test
##
## Hypothesis:
## black = 0
## hispan = 0
## hispan:perchisp = 0
## black:percblck = 0
##
## Model 1: restricted model
## Model 2: lsalary ~ years + gamesyr + bavg + hrunsyr + rbisyr + runsyr +
## fldperc + allstar + black + hispan + black:percblck + hispan:perchisp +
## 1
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 321 166.67
## 2 317 161.28 4 5.3886 2.6479 0.03348 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1mlb1_reg_r <- lm(lsalary ~ years + gamesyr + bavg + hrunsyr + rbisyr + runsyr + fldperc + allstar + 1, data=mlb1)
stargazer(mlb1_reg_r, type="text", align=TRUE)##
## ===============================================
## Dependent variable:
## ---------------------------
## lsalary
## -----------------------------------------------
## years 0.067***
## (0.013)
##
## gamesyr 0.009**
## (0.003)
##
## bavg 0.001
## (0.002)
##
## hrunsyr 0.014
## (0.017)
##
## rbisyr 0.005
## (0.008)
##
## runsyr 0.008*
## (0.005)
##
## fldperc 0.001
## (0.002)
##
## allstar 0.007**
## (0.003)
##
## Constant 10.637***
## (2.199)
##
## -----------------------------------------------
## Observations 330
## R2 0.626
## Adjusted R2 0.616
## Residual Std. Error 0.721 (df = 321)
## F Statistic 67.023*** (df = 8; 321)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.017.12 Equation [7.22] (Page 222)
gpa3 <- subset(gpa3, gpa3$spring==1)
gpa3_reg <- lm(cumgpa ~ female*sat + hsperc + female:hsperc + tothrs + female:tothrs + 1, data=gpa3)
stargazer(gpa3_reg, type="text", align=TRUE)##
## ===============================================
## Dependent variable:
## ---------------------------
## cumgpa
## -----------------------------------------------
## female -0.353
## (0.411)
##
## sat 0.001***
## (0.0002)
##
## hsperc -0.008***
## (0.001)
##
## tothrs 0.002***
## (0.001)
##
## female:sat 0.001*
## (0.0004)
##
## female:hsperc -0.001
## (0.003)
##
## female:tothrs -0.0001
## (0.002)
##
## Constant 1.481***
## (0.207)
##
## -----------------------------------------------
## Observations 366
## R2 0.406
## Adjusted R2 0.394
## Residual Std. Error 0.468 (df = 358)
## F Statistic 34.946*** (df = 7; 358)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01## Linear hypothesis test
##
## Hypothesis:
## female:tothrs = 0
## female:sat = 0
## female:hsperc = 0
##
## Model 1: restricted model
## Model 2: cumgpa ~ female * sat + hsperc + female:hsperc + tothrs + female:tothrs +
## 1
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 361 79.362
## 2 358 78.355 3 1.0072 1.5339 0.20547.13 Equation [7.25] (Page 224)
gpa3_reg_r <- lm(cumgpa ~ female + sat + hsperc + tothrs + 1, data=gpa3)
stargazer(gpa3_reg_r, type="text", align=TRUE)##
## ===============================================
## Dependent variable:
## ---------------------------
## cumgpa
## -----------------------------------------------
## female 0.310***
## (0.059)
##
## sat 0.001***
## (0.0002)
##
## hsperc -0.008***
## (0.001)
##
## tothrs 0.002***
## (0.001)
##
## Constant 1.329***
## (0.180)
##
## -----------------------------------------------
## Observations 366
## R2 0.398
## Adjusted R2 0.392
## Residual Std. Error 0.469 (df = 361)
## F Statistic 59.739*** (df = 4; 361)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.017.14 Equation [7.29] (Page 225)
mroz_reg <- lm(inlf ~ nwifeinc + educ + exper + expersq + age + kidslt6 + kidsge6 + 1, data=mroz)
stargazer(mroz_reg, type="text", align=TRUE)##
## ===============================================
## Dependent variable:
## ---------------------------
## inlf
## -----------------------------------------------
## nwifeinc -0.003**
## (0.001)
##
## educ 0.038***
## (0.007)
##
## exper 0.039***
## (0.006)
##
## expersq -0.001***
## (0.0002)
##
## age -0.016***
## (0.002)
##
## kidslt6 -0.262***
## (0.034)
##
## kidsge6 0.013
## (0.013)
##
## Constant 0.586***
## (0.154)
##
## -----------------------------------------------
## Observations 753
## R2 0.264
## Adjusted R2 0.257
## Residual Std. Error 0.427 (df = 745)
## F Statistic 38.218*** (df = 7; 745)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.017.15 Example 7.12. A linear probability model of arrest
arr86 <- (crime1$narr86 > 0)
crime1 <- cbind(crime1, arr86)
crime_reg <- lm(arr86 ~ pcnv + avgsen + tottime + ptime86 + qemp86 + 1, data=crime1)
stargazer(crime_reg, type="text", align=TRUE)##
## ===============================================
## Dependent variable:
## ---------------------------
## arr86
## -----------------------------------------------
## pcnv -0.162***
## (0.021)
##
## avgsen 0.006
## (0.006)
##
## tottime -0.002
## (0.005)
##
## ptime86 -0.022***
## (0.005)
##
## qemp86 -0.043***
## (0.005)
##
## Constant 0.441***
## (0.017)
##
## -----------------------------------------------
## Observations 2,725
## R2 0.047
## Adjusted R2 0.046
## Residual Std. Error 0.437 (df = 2719)
## F Statistic 27.030*** (df = 5; 2719)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01## Linear hypothesis test
##
## Hypothesis:
## avgsen = 0
## tottime = 0
##
## Model 1: restricted model
## Model 2: arr86 ~ pcnv + avgsen + tottime + ptime86 + qemp86 + 1
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 2721 520.38
## 2 2719 519.97 2 0.40531 1.0597 0.34677.16 Equation [7.32] (Page 228)
crime_reg_2 <- lm(arr86 ~ pcnv + avgsen + tottime + ptime86 + qemp86 + black + hispan + 1, data=crime1)
stargazer(crime_reg_2, type="text", align=TRUE)##
## ===============================================
## Dependent variable:
## ---------------------------
## arr86
## -----------------------------------------------
## pcnv -0.152***
## (0.021)
##
## avgsen 0.005
## (0.006)
##
## tottime -0.003
## (0.005)
##
## ptime86 -0.024***
## (0.005)
##
## qemp86 -0.038***
## (0.005)
##
## black 0.170***
## (0.024)
##
## hispan 0.096***
## (0.021)
##
## Constant 0.380***
## (0.019)
##
## -----------------------------------------------
## Observations 2,725
## R2 0.068
## Adjusted R2 0.066
## Residual Std. Error 0.433 (df = 2717)
## F Statistic 28.405*** (df = 7; 2717)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.017.17 Equation [7.33] (Page 229)
jtrain <- subset(jtrain, jtrain$year==1988)
jobb_reg <- lm(lscrap ~ grant + lsales + lemploy + 1, data=jtrain)
stargazer(jobb_reg, type="text", align=TRUE)##
## ===============================================
## Dependent variable:
## ---------------------------
## lscrap
## -----------------------------------------------
## grant -0.052
## (0.431)
##
## lsales -0.455
## (0.373)
##
## lemploy 0.639*
## (0.365)
##
## Constant 4.987
## (4.656)
##
## -----------------------------------------------
## Observations 50
## R2 0.072
## Adjusted R2 0.011
## Residual Std. Error 1.385 (df = 46)
## F Statistic 1.182 (df = 3; 46)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.017.18 Equation [7.35] (Page 231)
fert_reg <- lm(children ~ age + educ + 1, data=fertil2)
stargazer(fert_reg, type="text", align=TRUE)##
## ===============================================
## Dependent variable:
## ---------------------------
## children
## -----------------------------------------------
## age 0.175***
## (0.003)
##
## educ -0.090***
## (0.006)
##
## Constant -1.997***
## (0.094)
##
## -----------------------------------------------
## Observations 4,361
## R2 0.560
## Adjusted R2 0.559
## Residual Std. Error 1.475 (df = 4358)
## F Statistic 2,767.702*** (df = 2; 4358)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.017.19 Equation [7.37] (Page 232)
fert_reg_2 <- lm(children ~ age + educ + electric + 1, data=fertil2)
stargazer(fert_reg_2, type="text", align=TRUE)##
## ===============================================
## Dependent variable:
## ---------------------------
## children
## -----------------------------------------------
## age 0.177***
## (0.003)
##
## educ -0.079***
## (0.006)
##
## electric -0.362***
## (0.068)
##
## Constant -2.071***
## (0.095)
##
## -----------------------------------------------
## Observations 4,358
## R2 0.562
## Adjusted R2 0.562
## Residual Std. Error 1.471 (df = 4354)
## F Statistic 1,862.831*** (df = 3; 4354)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01