Chapter 7: Multiple Regression Analysis with Qualitative Information
library(wooldridge)Estimating dummy variables that reflect qualitative information works quite the same way in R as it does with quantitative variables. You just add it as an independent variable into the formula of the model.
# Example 7.1
data("wage1")
lm.7.1.1 <- lm(wage ~ female + educ + exper + tenure, data = wage1)
summary(lm.7.1.1)##
## Call:
## lm(formula = wage ~ female + educ + exper + tenure, data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.7675 -1.8080 -0.4229 1.0467 14.0075
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.56794 0.72455 -2.164 0.0309 *
## female -1.81085 0.26483 -6.838 2.26e-11 ***
## educ 0.57150 0.04934 11.584 < 2e-16 ***
## exper 0.02540 0.01157 2.195 0.0286 *
## tenure 0.14101 0.02116 6.663 6.83e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.958 on 521 degrees of freedom
## Multiple R-squared: 0.3635, Adjusted R-squared: 0.3587
## F-statistic: 74.4 on 4 and 521 DF, p-value: < 2.2e-16lm.7.1.2 <- lm(wage ~ female, data = wage1)
summary(lm.7.1.2)##
## Call:
## lm(formula = wage ~ female, data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.5995 -1.8495 -0.9877 1.4260 17.8805
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.0995 0.2100 33.806 < 2e-16 ***
## female -2.5118 0.3034 -8.279 1.04e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.476 on 524 degrees of freedom
## Multiple R-squared: 0.1157, Adjusted R-squared: 0.114
## F-statistic: 68.54 on 1 and 524 DF, p-value: 1.042e-15# Example 7.2
data("gpa1")
lm.7.2 <- lm(colGPA ~ PC + hsGPA + ACT, data = gpa1)
summary(lm.7.2)##
## Call:
## lm(formula = colGPA ~ PC + hsGPA + ACT, data = gpa1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.7901 -0.2622 -0.0107 0.2334 0.7570
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.263520 0.333125 3.793 0.000223 ***
## PC 0.157309 0.057287 2.746 0.006844 **
## hsGPA 0.447242 0.093647 4.776 4.54e-06 ***
## ACT 0.008659 0.010534 0.822 0.412513
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3325 on 137 degrees of freedom
## Multiple R-squared: 0.2194, Adjusted R-squared: 0.2023
## F-statistic: 12.83 on 3 and 137 DF, p-value: 1.932e-07# Example 7.3
data("jtrain")
# Since we do not use the whole data, but just observations from 1988
# we have to manipulate the sampe
jtrain <- jtrain[jtrain$d88==1,]
# We choose those observation, where in each row of the sampel it holds
# that jtrain$d88==1.
# Then we estimate the usual regression.
lm.7.3 <- lm(hrsemp ~ grant + lsales + lemploy, data = jtrain)
summary(lm.7.3)##
## Call:
## lm(formula = hrsemp ~ grant + lsales + lemploy, data = jtrain)
##
## Residuals:
## Min 1Q Median 3Q Max
## -36.874 -13.128 -3.642 4.770 119.618
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 46.6651 43.4121 1.075 0.285
## grant 26.2545 5.5918 4.695 8.4e-06 ***
## lsales -0.9846 3.5399 -0.278 0.781
## lemploy -6.0699 3.8829 -1.563 0.121
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 24.38 on 101 degrees of freedom
## (52 observations deleted due to missingness)
## Multiple R-squared: 0.2368, Adjusted R-squared: 0.2141
## F-statistic: 10.44 on 3 and 101 DF, p-value: 4.804e-06# Example 7.4
data("hprice1")
lm.7.4 <- lm(lprice ~ llotsize + lsqrft + bdrms + colonial, data = hprice1)
summary(lm.7.4)##
## Call:
## lm(formula = lprice ~ llotsize + lsqrft + bdrms + colonial, data = hprice1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.69479 -0.09750 -0.01619 0.09151 0.70228
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.34959 0.65104 -2.073 0.0413 *
## llotsize 0.16782 0.03818 4.395 3.25e-05 ***
## lsqrft 0.70719 0.09280 7.620 3.69e-11 ***
## bdrms 0.02683 0.02872 0.934 0.3530
## colonial 0.05380 0.04477 1.202 0.2330
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1841 on 83 degrees of freedom
## Multiple R-squared: 0.6491, Adjusted R-squared: 0.6322
## F-statistic: 38.38 on 4 and 83 DF, p-value: < 2.2e-16# Example 7.5
lm.7.5 <- lm(lwage ~ female + educ + exper + expersq + tenure + tenursq, data = wage1)
summary(lm.7.5)##
## Call:
## lm(formula = lwage ~ female + educ + exper + expersq + tenure +
## tenursq, data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.83160 -0.25658 -0.02126 0.25500 1.13370
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.4166910 0.0989279 4.212 2.98e-05 ***
## female -0.2965110 0.0358055 -8.281 1.04e-15 ***
## educ 0.0801967 0.0067573 11.868 < 2e-16 ***
## exper 0.0294324 0.0049752 5.916 6.00e-09 ***
## expersq -0.0005827 0.0001073 -5.431 8.65e-08 ***
## tenure 0.0317139 0.0068452 4.633 4.56e-06 ***
## tenursq -0.0005852 0.0002347 -2.493 0.013 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3998 on 519 degrees of freedom
## Multiple R-squared: 0.4408, Adjusted R-squared: 0.4343
## F-statistic: 68.18 on 6 and 519 DF, p-value: < 2.2e-16For the more accurate estimate extract the coefficient on female from the summary function, paste it into the exp function and subract 1.
exp(summary(lm.7.5)$coeff[2,1])-1## [1] -0.2565925For the estimate of the percentage by which a man’s wage exceed a compareable woman’s wage we just put a minus sign in front of the coefficient.
exp(-summary(lm.7.5)$coeff[2,1])-1## [1] 0.3451573The central command that allows you to create dummy variables is as.numeric. It gives a vector which is one if the conditions that are stated in parentheses are true and zero otherwise.
# Example 7.6
# Generate the subgroup dummies
marrmale <- as.numeric(wage1$female==0 & wage1$married==1)
marrfem <- as.numeric(wage1$female==1 & wage1$married==1)
singfem <- as.numeric(wage1$female==1 & wage1$married==0)
lm.7.6.1 <- lm(lwage ~ marrmale + marrfem + singfem + educ + exper + expersq + tenure + tenursq, data = wage1)
summary(lm.7.6.1)##
## Call:
## lm(formula = lwage ~ marrmale + marrfem + singfem + educ + exper +
## expersq + tenure + tenursq, data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.89697 -0.24060 -0.02689 0.23144 1.09197
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.3213781 0.1000090 3.213 0.001393 **
## marrmale 0.2126757 0.0553572 3.842 0.000137 ***
## marrfem -0.1982676 0.0578355 -3.428 0.000656 ***
## singfem -0.1103502 0.0557421 -1.980 0.048272 *
## educ 0.0789103 0.0066945 11.787 < 2e-16 ***
## exper 0.0268006 0.0052428 5.112 4.50e-07 ***
## expersq -0.0005352 0.0001104 -4.847 1.66e-06 ***
## tenure 0.0290875 0.0067620 4.302 2.03e-05 ***
## tenursq -0.0005331 0.0002312 -2.306 0.021531 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3933 on 517 degrees of freedom
## Multiple R-squared: 0.4609, Adjusted R-squared: 0.4525
## F-statistic: 55.25 on 8 and 517 DF, p-value: < 2.2e-16singmale <- as.numeric(wage1$female==0)*as.numeric(wage1$married==0)
lm.7.6.2 <- lm(lwage ~ marrmale + singmale + singfem + educ + exper + expersq + tenure + tenursq, data=wage1)
summary(lm.7.6.2)##
## Call:
## lm(formula = lwage ~ marrmale + singmale + singfem + educ + exper +
## expersq + tenure + tenursq, data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.89697 -0.24060 -0.02689 0.23144 1.09197
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.1231105 0.1057937 1.164 0.245089
## marrmale 0.4109433 0.0457709 8.978 < 2e-16 ***
## singmale 0.1982676 0.0578355 3.428 0.000656 ***
## singfem 0.0879174 0.0523481 1.679 0.093664 .
## educ 0.0789103 0.0066945 11.787 < 2e-16 ***
## exper 0.0268006 0.0052428 5.112 4.50e-07 ***
## expersq -0.0005352 0.0001104 -4.847 1.66e-06 ***
## tenure 0.0290875 0.0067620 4.302 2.03e-05 ***
## tenursq -0.0005331 0.0002312 -2.306 0.021531 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3933 on 517 degrees of freedom
## Multiple R-squared: 0.4609, Adjusted R-squared: 0.4525
## F-statistic: 55.25 on 8 and 517 DF, p-value: < 2.2e-16# Example 7.7
data("beauty")
lm.7.7 <- lm(lwage ~ belavg + abvavg + educ + exper + expersq + service + married + black, data = beauty)
summary(lm.7.7)##
## Call:
## lm(formula = lwage ~ belavg + abvavg + educ + exper + expersq +
## service + married + black, data = beauty)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.74211 -0.29201 0.01702 0.30052 3.04504
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.1353690 0.0856441 1.581 0.114222
## belavg -0.1610574 0.0447131 -3.602 0.000328 ***
## abvavg -0.0065951 0.0323216 -0.204 0.838350
## educ 0.0822901 0.0059115 13.920 < 2e-16 ***
## exper 0.0446750 0.0047555 9.394 < 2e-16 ***
## expersq -0.0006421 0.0001056 -6.079 1.61e-09 ***
## service -0.2772843 0.0335089 -8.275 3.26e-16 ***
## married 0.1229036 0.0325837 3.772 0.000170 ***
## black -0.0861601 0.0554701 -1.553 0.120611
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5025 on 1251 degrees of freedom
## Multiple R-squared: 0.2901, Adjusted R-squared: 0.2856
## F-statistic: 63.91 on 8 and 1251 DF, p-value: < 2.2e-16Unfortunatly, the results are not the same as in the book, resp. the paper by Hamermesh and Biddle (1994)
In the next example the conditions used in the are a bit more sophisticated, but follow the same logic as above.
# Example 7.8
data("lawsch85")
# Generate dummies which is not necessary here, but I
# wanted to show you how it is done.
# However, you must create the last (r61.100) since it is not contained
# in the downloaded data.
top10 <- as.numeric(lawsch85$rank <= 10)
r11.25 <- as.numeric(lawsch85$rank >= 11 & lawsch85$rank <= 25)
r26.40 <- as.numeric(lawsch85$rank >= 26 & lawsch85$rank <= 40)
r41.60 <- as.numeric(lawsch85$rank >= 41 & lawsch85$rank <= 60)
r61.100 <- as.numeric(lawsch85$rank >= 61 & lawsch85$rank <= 100)
lm.7.8 <- lm(lsalary ~ top10 + r11_25 + r26_40 + r41_60 + r61.100 + LSAT + GPA + llibvol + lcost, data = lawsch85)
summary(lm.7.8)##
## Call:
## lm(formula = lsalary ~ top10 + r11_25 + r26_40 + r41_60 + r61.100 +
## LSAT + GPA + llibvol + lcost, data = lawsch85)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.294888 -0.039691 -0.001683 0.043888 0.277497
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.1652942 0.4114243 22.277 < 2e-16 ***
## top10 0.6995659 0.0534920 13.078 < 2e-16 ***
## r11_25 0.5935433 0.0394400 15.049 < 2e-16 ***
## r26_40 0.3750763 0.0340812 11.005 < 2e-16 ***
## r41_60 0.2628190 0.0279621 9.399 3.18e-16 ***
## r61.100 0.1315949 0.0210419 6.254 5.71e-09 ***
## LSAT 0.0056909 0.0030630 1.858 0.0655 .
## GPA 0.0137257 0.0741919 0.185 0.8535
## llibvol 0.0363619 0.0260165 1.398 0.1647
## lcost 0.0008411 0.0251360 0.033 0.9734
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.08564 on 126 degrees of freedom
## (20 observations deleted due to missingness)
## Multiple R-squared: 0.9109, Adjusted R-squared: 0.9046
## F-statistic: 143.2 on 9 and 126 DF, p-value: < 2.2e-16# Equation 7.14
# Generate the interaction term
femmarr <- wage1$female*wage1$married
lm.e7.14 <- lm(lwage ~ female + married + femmarr + educ + exper + expersq + tenure + tenursq, data = wage1)
summary(lm.e7.14)##
## Call:
## lm(formula = lwage ~ female + married + femmarr + educ + exper +
## expersq + tenure + tenursq, data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.89697 -0.24060 -0.02689 0.23144 1.09197
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.3213781 0.1000090 3.213 0.001393 **
## female -0.1103502 0.0557421 -1.980 0.048272 *
## married 0.2126757 0.0553572 3.842 0.000137 ***
## femmarr -0.3005931 0.0717670 -4.188 3.30e-05 ***
## educ 0.0789103 0.0066945 11.787 < 2e-16 ***
## exper 0.0268006 0.0052428 5.112 4.50e-07 ***
## expersq -0.0005352 0.0001104 -4.847 1.66e-06 ***
## tenure 0.0290875 0.0067620 4.302 2.03e-05 ***
## tenursq -0.0005331 0.0002312 -2.306 0.021531 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3933 on 517 degrees of freedom
## Multiple R-squared: 0.4609, Adjusted R-squared: 0.4525
## F-statistic: 55.25 on 8 and 517 DF, p-value: < 2.2e-16# Example 7.9
# No data found
# Example 7.10
femmarr <- wage1$female*wage1$married
lm.7.10 <- lm(lwage ~ female + educ + femmarr + exper + expersq + tenure + tenursq, data = wage1)
# Yields slightly different results
summary(lm.7.10)##
## Call:
## lm(formula = lwage ~ female + educ + femmarr + exper + expersq +
## tenure + tenursq, data = wage1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.87420 -0.24795 -0.01231 0.24709 1.12173
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.3799992 0.1001423 3.795 0.000165 ***
## female -0.2373598 0.0454727 -5.220 2.60e-07 ***
## educ 0.0812642 0.0067544 12.031 < 2e-16 ***
## femmarr -0.1106204 0.0526998 -2.099 0.036295 *
## exper 0.0321299 0.0051227 6.272 7.52e-10 ***
## expersq -0.0006285 0.0001091 -5.758 1.46e-08 ***
## tenure 0.0313651 0.0068248 4.596 5.42e-06 ***
## tenursq -0.0005820 0.0002339 -2.488 0.013170 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3985 on 518 degrees of freedom
## Multiple R-squared: 0.4455, Adjusted R-squared: 0.438
## F-statistic: 59.45 on 7 and 518 DF, p-value: < 2.2e-16# Test for d0 and d1
lm.7.10.t <- lm(lwage ~ + educ + exper + expersq + tenure + tenursq, data = wage1)
# F= 36.717. The book's value is a bit lower.
anova(lm.7.10,lm.7.10.t)## Analysis of Variance Table
##
## Model 1: lwage ~ female + educ + femmarr + exper + expersq + tenure +
## tenursq
## Model 2: lwage ~ +educ + exper + expersq + tenure + tenursq
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 518 82.251
## 2 520 93.911 -2 -11.66 36.717 1.224e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Example 7.11
data("mlb1")
lm.7.11 <- lm(lsalary ~ years + gamesyr + bavg + hrunsyr +
rbisyr + runsyr + fldperc + allstar +
black + hispan + blckpb + hispph, data = mlb1)
summary(lm.7.11)##
## Call:
## lm(formula = lsalary ~ years + gamesyr + bavg + hrunsyr + rbisyr +
## runsyr + fldperc + allstar + black + hispan + blckpb + hispph,
## data = mlb1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.6762 -0.4397 -0.0699 0.4891 2.1993
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.3436845 2.1825380 4.739 3.24e-06 ***
## years 0.0673458 0.0128915 5.224 3.18e-07 ***
## gamesyr 0.0088778 0.0033837 2.624 0.00912 **
## bavg 0.0009451 0.0015133 0.625 0.53271
## hrunsyr 0.0146206 0.0164522 0.889 0.37486
## rbisyr 0.0044938 0.0075750 0.593 0.55344
## runsyr 0.0072029 0.0045671 1.577 0.11576
## fldperc 0.0010865 0.0021195 0.513 0.60857
## allstar 0.0075307 0.0028735 2.621 0.00920 **
## black -0.1980080 0.1254968 -1.578 0.11561
## hispan -0.1900089 0.1530902 -1.241 0.21547
## blckpb 0.0124513 0.0049628 2.509 0.01261 *
## hispph 0.0200863 0.0097933 2.051 0.04109 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7133 on 317 degrees of freedom
## (23 observations deleted due to missingness)
## Multiple R-squared: 0.6376, Adjusted R-squared: 0.6239
## F-statistic: 46.48 on 12 and 317 DF, p-value: < 2.2e-16# Equation 7.22
data("gpa3")
lm.e7.22 <- lm(cumgpa ~ female + sat + I(female*sat) +
hsperc + I(female*hsperc) +
tothrs + I(female*tothrs), data = gpa3[gpa3$term==2,])
summary(lm.e7.22)##
## Call:
## lm(formula = cumgpa ~ female + sat + I(female * sat) + hsperc +
## I(female * hsperc) + tothrs + I(female * tothrs), data = gpa3[gpa3$term ==
## 2, ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.51370 -0.28645 -0.02306 0.27555 1.24760
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.4808117 0.2073336 7.142 5.17e-12 ***
## female -0.3534862 0.4105293 -0.861 0.38979
## sat 0.0010516 0.0001811 5.807 1.40e-08 ***
## I(female * sat) 0.0007506 0.0003852 1.949 0.05211 .
## hsperc -0.0084516 0.0013704 -6.167 1.88e-09 ***
## I(female * hsperc) -0.0005498 0.0031617 -0.174 0.86206
## tothrs 0.0023441 0.0008624 2.718 0.00688 **
## I(female * tothrs) -0.0001158 0.0016277 -0.071 0.94331
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4678 on 358 degrees of freedom
## Multiple R-squared: 0.4059, Adjusted R-squared: 0.3943
## F-statistic: 34.95 on 7 and 358 DF, p-value: < 2.2e-16# Equation 7.29
data("mroz")
lm.e7.29 <- lm(inlf ~ nwifeinc + educ + exper + expersq +
age + kidslt6 + kidsge6, data = mroz)
summary(lm.e7.29)##
## Call:
## lm(formula = inlf ~ nwifeinc + educ + exper + expersq + age +
## kidslt6 + kidsge6, data = mroz)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.93432 -0.37526 0.08833 0.34404 0.99417
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.5855192 0.1541780 3.798 0.000158 ***
## nwifeinc -0.0034052 0.0014485 -2.351 0.018991 *
## educ 0.0379953 0.0073760 5.151 3.32e-07 ***
## exper 0.0394924 0.0056727 6.962 7.38e-12 ***
## expersq -0.0005963 0.0001848 -3.227 0.001306 **
## age -0.0160908 0.0024847 -6.476 1.71e-10 ***
## kidslt6 -0.2618105 0.0335058 -7.814 1.89e-14 ***
## kidsge6 0.0130122 0.0131960 0.986 0.324415
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4271 on 745 degrees of freedom
## Multiple R-squared: 0.2642, Adjusted R-squared: 0.2573
## F-statistic: 38.22 on 7 and 745 DF, p-value: < 2.2e-16# Example 7.12
data("crime1")
# Generate arr86
arr86 <- as.numeric(crime1$narr86 > 0)
lm.7.12 <- lm(arr86 ~ pcnv + avgsen + tottime + ptime86 + qemp86, data = crime1)
summary(lm.7.12)##
## Call:
## lm(formula = arr86 ~ pcnv + avgsen + tottime + ptime86 + qemp86,
## data = crime1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.5577 -0.2889 -0.2157 0.5734 0.8931
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.440615 0.017233 25.568 < 2e-16 ***
## pcnv -0.162445 0.021237 -7.649 2.79e-14 ***
## avgsen 0.006113 0.006452 0.947 0.344
## tottime -0.002262 0.004978 -0.454 0.650
## ptime86 -0.021966 0.004635 -4.739 2.25e-06 ***
## qemp86 -0.042829 0.005405 -7.925 3.31e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4373 on 2719 degrees of freedom
## Multiple R-squared: 0.04735, Adjusted R-squared: 0.0456
## F-statistic: 27.03 on 5 and 2719 DF, p-value: < 2.2e-16# Equation 7.23
lm.e7.23 <- lm(arr86 ~ pcnv + avgsen + tottime + ptime86 + qemp86 +
black + hispan, data = crime1)
summary(lm.e7.23)##
## Call:
## lm(formula = arr86 ~ pcnv + avgsen + tottime + ptime86 + qemp86 +
## black + hispan, data = crime1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.6127 -0.3035 -0.2208 0.5258 0.9255
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.380428 0.018727 20.314 < 2e-16 ***
## pcnv -0.152062 0.021065 -7.219 6.79e-13 ***
## avgsen 0.004619 0.006389 0.723 0.470
## tottime -0.002562 0.004926 -0.520 0.603
## ptime86 -0.023695 0.004595 -5.157 2.69e-07 ***
## qemp86 -0.038474 0.005402 -7.123 1.35e-12 ***
## black 0.169763 0.023674 7.171 9.56e-13 ***
## hispan 0.096187 0.020710 4.644 3.57e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4327 on 2717 degrees of freedom
## Multiple R-squared: 0.06819, Adjusted R-squared: 0.06579
## F-statistic: 28.41 on 7 and 2717 DF, p-value: < 2.2e-16# Equation 7.33
lm.e7.33 <- lm(lscrap ~ grant + lsales + lemploy, data = jtrain[jtrain$d88 == 1,])
summary(lm.e7.33)##
## Call:
## lm(formula = lscrap ~ grant + lsales + lemploy, data = jtrain[jtrain$d88 ==
## 1, ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4487 -0.9809 0.0621 0.8589 2.8299
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.98678 4.65559 1.071 0.2897
## grant -0.05178 0.43129 -0.120 0.9050
## lsales -0.45484 0.37332 -1.218 0.2293
## lemploy 0.63943 0.36514 1.751 0.0866 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.385 on 46 degrees of freedom
## (107 observations deleted due to missingness)
## Multiple R-squared: 0.07157, Adjusted R-squared: 0.01102
## F-statistic: 1.182 on 3 and 46 DF, p-value: 0.327# Equation 7.35
data("fertil2")
lm.e7.35 <- lm(children ~ age + educ, data = fertil2)
summary(lm.e7.35)##
## Call:
## lm(formula = children ~ age + educ, data = fertil2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.5700 -0.6955 -0.0760 0.7412 7.1294
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.996750 0.093969 -21.25 <2e-16 ***
## age 0.174831 0.002705 64.63 <2e-16 ***
## educ -0.089940 0.005983 -15.03 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.475 on 4358 degrees of freedom
## Multiple R-squared: 0.5595, Adjusted R-squared: 0.5593
## F-statistic: 2768 on 2 and 4358 DF, p-value: < 2.2e-16# Equation 7.37
lm.e7.37 <- lm(children ~ age + educ + electric, data = fertil2)
summary(lm.e7.37)##
## Call:
## lm(formula = children ~ age + educ + electric, data = fertil2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.6019 -0.6814 -0.0619 0.7476 7.1061
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.071091 0.094741 -21.861 < 2e-16 ***
## age 0.176999 0.002729 64.855 < 2e-16 ***
## educ -0.078751 0.006319 -12.462 < 2e-16 ***
## electric -0.361758 0.068032 -5.317 1.1e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.471 on 4354 degrees of freedom
## (3 observations deleted due to missingness)
## Multiple R-squared: 0.5621, Adjusted R-squared: 0.5618
## F-statistic: 1863 on 3 and 4354 DF, p-value: < 2.2e-16