Template Title

加载经常用的R包

library(pacman)
p_load(tidyverse,stringr,DT,skimr,DataExplorer,grf,glmnet,caret,tidytext,
       explore,patchwork,ggrepel,ggcorrplot,gghighlight,ggthemes,fpp2,
       forecast,magrittr,readxl,writexl,listviewer,car,tseries,vtable)

mtcars

##                      mpg cyl  disp  hp drat    wt  qsec vs am gear carb
## Mazda RX4           21.0   6 160.0 110 3.90 2.620 16.46  0  1    4    4
## Mazda RX4 Wag       21.0   6 160.0 110 3.90 2.875 17.02  0  1    4    4
## Datsun 710          22.8   4 108.0  93 3.85 2.320 18.61  1  1    4    1
## Hornet 4 Drive      21.4   6 258.0 110 3.08 3.215 19.44  1  0    3    1
## Hornet Sportabout   18.7   8 360.0 175 3.15 3.440 17.02  0  0    3    2
## Valiant             18.1   6 225.0 105 2.76 3.460 20.22  1  0    3    1
## Duster 360          14.3   8 360.0 245 3.21 3.570 15.84  0  0    3    4
## Merc 240D           24.4   4 146.7  62 3.69 3.190 20.00  1  0    4    2
## Merc 230            22.8   4 140.8  95 3.92 3.150 22.90  1  0    4    2
## Merc 280            19.2   6 167.6 123 3.92 3.440 18.30  1  0    4    4
## Merc 280C           17.8   6 167.6 123 3.92 3.440 18.90  1  0    4    4
## Merc 450SE          16.4   8 275.8 180 3.07 4.070 17.40  0  0    3    3
## Merc 450SL          17.3   8 275.8 180 3.07 3.730 17.60  0  0    3    3
## Merc 450SLC         15.2   8 275.8 180 3.07 3.780 18.00  0  0    3    3
## Cadillac Fleetwood  10.4   8 472.0 205 2.93 5.250 17.98  0  0    3    4
## Lincoln Continental 10.4   8 460.0 215 3.00 5.424 17.82  0  0    3    4
## Chrysler Imperial   14.7   8 440.0 230 3.23 5.345 17.42  0  0    3    4
## Fiat 128            32.4   4  78.7  66 4.08 2.200 19.47  1  1    4    1
## Honda Civic         30.4   4  75.7  52 4.93 1.615 18.52  1  1    4    2
## Toyota Corolla      33.9   4  71.1  65 4.22 1.835 19.90  1  1    4    1
## Toyota Corona       21.5   4 120.1  97 3.70 2.465 20.01  1  0    3    1
## Dodge Challenger    15.5   8 318.0 150 2.76 3.520 16.87  0  0    3    2
## AMC Javelin         15.2   8 304.0 150 3.15 3.435 17.30  0  0    3    2
## Camaro Z28          13.3   8 350.0 245 3.73 3.840 15.41  0  0    3    4
## Pontiac Firebird    19.2   8 400.0 175 3.08 3.845 17.05  0  0    3    2
## Fiat X1-9           27.3   4  79.0  66 4.08 1.935 18.90  1  1    4    1
## Porsche 914-2       26.0   4 120.3  91 4.43 2.140 16.70  0  1    5    2
## Lotus Europa        30.4   4  95.1 113 3.77 1.513 16.90  1  1    5    2
## Ford Pantera L      15.8   8 351.0 264 4.22 3.170 14.50  0  1    5    4
## Ferrari Dino        19.7   6 145.0 175 3.62 2.770 15.50  0  1    5    6
## Maserati Bora       15.0   8 301.0 335 3.54 3.570 14.60  0  1    5    8
## Volvo 142E          21.4   4 121.0 109 4.11 2.780 18.60  1  1    4    2

#一元线性回归
load("D:/Rworkspace/financial book data/Ch06/bankwage.Rdata")
names(bankwage)

## [1] "wage"     "edu"      "wage0"    "gender"   "minority" "job"

attach(bankwage)

lm_we <- lm(log(wage)~edu)
plot(log(wage)~edu)
abline(lm_we,col="green")#添加拟合线
summary(lm_we)

## 
## Call:
## lm(formula = log(wage) ~ edu)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.66260 -0.19303 -0.03559  0.16538  0.95223 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 9.062102   0.062738   144.4   <2e-16 ***
## edu         0.095963   0.004548    21.1   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2853 on 472 degrees of freedom
## Multiple R-squared:  0.4854, Adjusted R-squared:  0.4844 
## F-statistic: 445.3 on 1 and 472 DF,  p-value: < 2.2e-16

coef(lm_we)#查截距与斜率（回归系数）

## (Intercept)         edu 
##  9.06210165  0.09596304

#回归诊断
rbind(AIC(lm_we),BIC(lm_we))#AIC和BIC准则

##          [,1]
## [1,] 160.2177
## [2,] 172.7014

anova(lm_we)#方差分析

## Analysis of Variance Table
## 
## Response: log(wage)
##            Df Sum Sq Mean Sq F value    Pr(>F)    
## edu         1 36.251  36.251   445.3 < 2.2e-16 ***
## Residuals 472 38.424   0.081                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#画残差诊断图
par(mfrow=c(2,2))#将图形框分成2*2
plot(lm_we)
#图1红线接近水平线表示残差分布接近独立同分布，若散点分布无规律，表明没有非线性关系
#If you find equally spread residuals around a horizontal line without distinct patterns, that is a good indication you don’t have non-linear relationships.
#图2，可结合正态性检验判断
#图3，红线接近水平线表示不存在异方差。
#This plot shows if residuals are spread equally along the ranges of predictors. This is how you can check the assumption of equal variance (homoscedasticity). It’s good if you see a horizontal line with equally (randomly) spread points.
#图4，该图中看不到库克距离线，表明没有对实验结果影响大的观测点
#残差图详细解释见https://data.library.virginia.edu/diagnostic-plots/

#残差正态性检验
library(fBasics)

## Loading required package: timeDate

## Loading required package: timeSeries

## 
## Attaching package: 'fBasics'

## The following object is masked from 'package:car':
## 
##     densityPlot

basicStats(resid(lm_we))#由结果可知skewness大于0，左偏，波形有左侧长尾

##             resid.lm_we
## nobs         474.000000
## NAs            0.000000
## Minimum       -0.662598
## Maximum        0.952229
## 1. Quartile   -0.193032
## 3. Quartile    0.165382
## Mean           0.000000
## Median        -0.035591
## Sum            0.000000
## SE Mean        0.013091
## LCL Mean      -0.025724
## UCL Mean       0.025724
## Variance       0.081235
## Stdev          0.285017
## Skewness       0.516700
## Kurtosis       0.242913

jarqueberaTest(resid(lm_we))#不是正态

## 
## Title:
##  Jarque - Bera Normalality Test
## 
## Test Results:
##   STATISTIC:
##     X-squared: 22.5262
##   P VALUE:
##     Asymptotic p Value: 1.284e-05 
## 
## Description:
##  Sun May 17 09:14:03 2020 by user: Lenovo

normalTest(resid(lm_we),method = "jb",na.rm = T)#与上相同

## 
## Title:
##  Jarque - Bera Normalality Test
## 
## Test Results:
##   STATISTIC:
##     X-squared: 22.5262
##   P VALUE:
##     Asymptotic p Value: 1.284e-05 
## 
## Description:
##  Sun May 17 09:14:03 2020 by user: Lenovo

shapiro.test(resid(lm_we))#不是正态

## 
##  Shapiro-Wilk normality test
## 
## data:  resid(lm_we)
## W = 0.98184, p-value = 1.199e-05

#峰度默认为excess
kurtosis(resid(lm_we))#厚尾

## [1] 0.2429132
## attr(,"method")
## [1] "excess"

kurtosis(resid(lm_we),method = "moment")

## [1] 3.242913
## attr(,"method")
## [1] "moment"

#残差正态QQ图的画法二
library(car)
qqPlot(resid(lm_we),main = "Q-Q Plot")

## [1]  18 343

qqPlot(lm_we,main = "Studentized Q-Q Plot")

## [1]  18 343

#异方差检验
#car包提供的ncvTest()函数生成一个计分检验，
#零假设为误差方差不变，备择假设为误差方差随着拟合值水平的变化而变化。

ncvTest(lm_we)#p值小于0.05，所以拒绝原假设，方差变化，存在异方差

## Non-constant Variance Score Test 
## Variance formula: ~ fitted.values 
## Chisquare = 8.791185, Df = 1, p = 0.0030269

#异方差检验方案二
#lmtest包中的
library(lmtest)

## Loading required package: zoo

## 
## Attaching package: 'zoo'

## The following object is masked from 'package:timeSeries':
## 
##     time<-

## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

bptest(lm_we) #拒绝原假设，存在异方差.这得出的是学生化的结果。

## 
##  studentized Breusch-Pagan test
## 
## data:  lm_we
## BP = 7.7914, df = 1, p-value = 0.00525

#为保持与其他方法的结果的一致性可设置成非学生化检验
bptest(lm_we,studentize = F)

## 
##  Breusch-Pagan test
## 
## data:  lm_we
## BP = 8.7912, df = 1, p-value = 0.003027

#误差独立性检验(自相关检验),car包中
durbinWatsonTest(lm_we)#原假设为rho=0，没有自相关性。p<0.05,拒绝原假设，rho!=0,存在自相关。

##  lag Autocorrelation D-W Statistic p-value
##    1       0.1149518      1.764697   0.006
##  Alternative hypothesis: rho != 0

#判断异常值(非必要)
measure <- influence.measures(lm_we)
summary(measure)

## Potentially influential observations of
##   lm(formula = log(wage) ~ edu) :
## 
##     dfb.1_ dfb.edu dffit   cov.r   cook.d hat    
## 4    0.06  -0.05    0.06    1.01_*  0.00   0.01  
## 18  -0.10   0.14    0.21_*  0.96_*  0.02   0.00  
## 27  -0.03   0.04    0.04    1.01_*  0.00   0.01  
## 29  -0.25   0.29    0.33_*  0.97_*  0.05   0.01  
## 32  -0.20   0.23    0.26_*  0.99_*  0.03   0.01  
## 40   0.03  -0.05   -0.12    0.99_*  0.01   0.00  
## 65   0.06  -0.05    0.06    1.01_*  0.00   0.01  
## 90  -0.05   0.04   -0.05    1.01_*  0.00   0.01  
## 103 -0.16   0.19    0.21_*  1.00    0.02   0.01  
## 121  0.03  -0.06   -0.12    0.98_*  0.01   0.00  
## 130  0.00   0.00    0.00    1.02_*  0.00   0.01_*
## 137  0.00   0.00    0.00    1.02_*  0.00   0.02_*
## 139  0.03  -0.02    0.03    1.01_*  0.00   0.01  
## 144 -0.04   0.03   -0.04    1.01_*  0.00   0.01  
## 173 -0.05   0.06    0.07    1.02_*  0.00   0.01_*
## 209  0.02  -0.02    0.02    1.01_*  0.00   0.01  
## 218 -0.04   0.07    0.14    0.97_*  0.01   0.00  
## 232 -0.01   0.01    0.01    1.01_*  0.00   0.01  
## 241 -0.02   0.02   -0.02    1.01_*  0.00   0.01  
## 253 -0.03   0.03   -0.03    1.01_*  0.00   0.01  
## 256  0.01  -0.01   -0.01    1.01_*  0.00   0.01  
## 257 -0.04   0.05    0.05    1.01_*  0.00   0.01  
## 258  0.05  -0.04    0.05    1.01_*  0.00   0.01  
## 274 -0.08   0.10    0.16    0.98_*  0.01   0.00  
## 278  0.04  -0.04    0.04    1.01_*  0.00   0.01  
## 281  0.21  -0.19    0.22_*  0.99    0.02   0.01  
## 325 -0.03   0.03   -0.04    1.01_*  0.00   0.01  
## 338 -0.05   0.05   -0.05    1.01_*  0.00   0.01  
## 340  0.05  -0.05    0.06    1.01_*  0.00   0.01  
## 341  0.09  -0.07    0.14    0.98_*  0.01   0.00  
## 343 -0.10   0.14    0.21_*  0.96_*  0.02   0.00  
## 352  0.04  -0.04    0.05    1.01_*  0.00   0.01  
## 357 -0.02   0.02   -0.02    1.01_*  0.00   0.01  
## 362 -0.03   0.03   -0.03    1.01_*  0.00   0.01  
## 365  0.05  -0.04    0.05    1.01_*  0.00   0.01  
## 379  0.02  -0.02    0.02    1.01_*  0.00   0.01  
## 408 -0.04   0.04    0.05    1.01_*  0.00   0.01  
## 443  0.05  -0.05    0.05    1.01_*  0.00   0.01  
## 446 -0.10   0.13    0.20_*  0.96_*  0.02   0.00  
## 450 -0.01   0.01    0.01    1.01_*  0.00   0.01  
## 458 -0.04   0.05    0.05    1.01_*  0.00   0.01  
## 461  0.05  -0.05    0.05    1.01_*  0.00   0.01  
## 464  0.03  -0.04   -0.04    1.01_*  0.00   0.01

#偏离线性关系的一个最简单的情况就是解释变量的幂次进入回归。
#二次拟合（多项式回归 ）诊断
lm_we2 <- lm(log(wage)~edu+I(edu^2))
summary(lm_we2,corr=T)#corr=T会计算估计系数的相关性

## 
## Call:
## lm(formula = log(wage) ~ edu + I(edu^2))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.68571 -0.15861 -0.02415  0.16519  0.96679 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 11.132436   0.189092  58.873  < 2e-16 ***
## edu         -0.230009   0.028742  -8.002 9.58e-15 ***
## I(edu^2)     0.012229   0.001068  11.454  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2526 on 471 degrees of freedom
## Multiple R-squared:  0.5975, Adjusted R-squared:  0.5958 
## F-statistic: 349.7 on 2 and 471 DF,  p-value: < 2.2e-16
## 
## Correlation of Coefficients:
##          (Intercept) edu  
## edu      -0.99            
## I(edu^2)  0.96       -0.99

par(mfrow=c(2,2))
plot(lm_we2)

#由于edu和edu^2相关系数过高，所以采用正交多项式回归
#正交多项式回归
polm_we <- lm(log(wage)~poly(edu,2))
summary(polm_we,,corr=T)

## 
## Call:
## lm(formula = log(wage) ~ poly(edu, 2))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.68571 -0.15861 -0.02415  0.16519  0.96679 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    10.3568     0.0116  892.65   <2e-16 ***
## poly(edu, 2)1   6.0208     0.2526   23.84   <2e-16 ***
## poly(edu, 2)2   2.8933     0.2526   11.45   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2526 on 471 degrees of freedom
## Multiple R-squared:  0.5975, Adjusted R-squared:  0.5958 
## F-statistic: 349.7 on 2 and 471 DF,  p-value: < 2.2e-16
## 
## Correlation of Coefficients:
##               (Intercept) poly(edu, 2)1
## poly(edu, 2)1 0.00                     
## poly(edu, 2)2 0.00        0.00

par(mfrow=c(2,2))
plot(polm_we)

#残差正态性检验
normalTest(resid(polm_we),method = "jb",na.rm = T)

## 
## Title:
##  Jarque - Bera Normalality Test
## 
## Test Results:
##   STATISTIC:
##     X-squared: 41.315
##   P VALUE:
##     Asymptotic p Value: 1.068e-09 
## 
## Description:
##  Sun May 17 09:14:04 2020 by user: Lenovo

basicStats(resid(polm_we))#不服从正态分布

##             resid.polm_we
## nobs           474.000000
## NAs              0.000000
## Minimum         -0.685714
## Maximum          0.966785
## 1. Quartile     -0.158605
## 3. Quartile      0.165189
## Mean             0.000000
## Median          -0.024152
## Sum              0.000000
## SE Mean          0.011578
## LCL Mean        -0.022750
## UCL Mean         0.022750
## Variance         0.063537
## Stdev            0.252065
## Skewness         0.489820
## Kurtosis         1.044062

#异方差检验
ncvTest(polm_we)

## Non-constant Variance Score Test 
## Variance formula: ~ fitted.values 
## Chisquare = 28.29595, Df = 1, p = 1.0411e-07

bptest(polm_we,studentize = F) 

## 
##  Breusch-Pagan test
## 
## data:  polm_we
## BP = 28.573, df = 2, p-value = 6.244e-07

#存在异方差

#自相关检验
durbinWatsonTest(polm_we)#自相关

##  lag Autocorrelation D-W Statistic p-value
##    1        0.105941      1.778422    0.01
##  Alternative hypothesis: rho != 0

#多元连续变量线性回归
#在单变量线性回归的基础上增加一个变量wage0(员工起薪)
lm2_wew <- lm(log(wage)~edu+log(wage0))
summary(lm2_wew)

## 
## Call:
## lm(formula = log(wage) ~ edu + log(wage0))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.45035 -0.11750 -0.01215  0.11453  0.90229 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 1.646916   0.274598   5.998 3.99e-09 ***
## edu         0.023122   0.003894   5.938 5.59e-09 ***
## log(wage0)  0.868505   0.031835  27.282  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1778 on 471 degrees of freedom
## Multiple R-squared:  0.8006, Adjusted R-squared:  0.7997 
## F-statistic: 945.4 on 2 and 471 DF,  p-value: < 2.2e-16

#方差分析（方差即为总误差）方差分析主要针对整个模型
anova(lm_we,lm2_wew)#比较一元线性回归和多元线性回归

## Analysis of Variance Table
## 
## Model 1: log(wage) ~ edu
## Model 2: log(wage) ~ edu + log(wage0)
##   Res.Df    RSS Df Sum of Sq      F    Pr(>F)    
## 1    472 38.424                                  
## 2    471 14.892  1    23.532 744.29 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#异方差检验
ncvTest(lm2_wew)

## Non-constant Variance Score Test 
## Variance formula: ~ fitted.values 
## Chisquare = 13.41802, Df = 1, p = 0.00024922

bptest(lm2_wew,studentize = F)#存在异方差

## 
##  Breusch-Pagan test
## 
## data:  lm2_wew
## BP = 16.069, df = 2, p-value = 0.000324

#多重共线性检验
kappa(lm2_wew)## [10,100] 较强，>100，严重

## [1] 536.4418

#因子回归
#因子变量不是连续的数值变量，而是类型变量或者非0即1这样的虚拟变量
#如果原始数据为字符串，R会自动辨认，如果是数值，需要用factor()转换。
#加入性别变量
lm3_weg <- lm(log(wage)~edu+log(wage0)+gender)
summary(lm3_weg)

## 
## Call:
## lm(formula = log(wage) ~ edu + log(wage0) + gender)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.45101 -0.11130 -0.01224  0.10796  0.88370 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 1.932281   0.307832   6.277 7.85e-10 ***
## edu         0.023378   0.003883   6.021 3.50e-09 ***
## log(wage0)  0.836406   0.035468  23.582  < 2e-16 ***
## genderMale  0.039600   0.019551   2.025   0.0434 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1772 on 470 degrees of freedom
## Multiple R-squared:  0.8023, Adjusted R-squared:  0.801 
## F-statistic: 635.8 on 3 and 470 DF,  p-value: < 2.2e-16

#Wald检验是测试与一组解释变量相关的参数是否为零的多种方法之一。
waldtest(lm3_weg, .~. -log(wage0)) #检验log(wage0)的系数是否为0.

## Wald test
## 
## Model 1: log(wage) ~ edu + log(wage0) + gender
## Model 2: log(wage) ~ edu + gender
##   Res.Df Df      F    Pr(>F)    
## 1    470                        
## 2    471 -1 556.12 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#交互影响
#考虑性别和受教育年限的交互的影响
lm4_weg <- lm(log(wage)~edu+log(wage0)+gender+gender*edu)
summary(lm4_weg)

## 
## Call:
## lm(formula = log(wage) ~ edu + log(wage0) + gender + gender * 
##     edu)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.45056 -0.11127 -0.00943  0.10693  0.88486 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     1.885367   0.332427   5.672 2.48e-08 ***
## edu             0.024805   0.005433   4.565 6.38e-06 ***
## log(wage0)      0.839500   0.036441  23.037  < 2e-16 ***
## genderMale      0.071119   0.086097   0.826    0.409    
## edu:genderMale -0.002471   0.006573  -0.376    0.707    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1774 on 469 degrees of freedom
## Multiple R-squared:  0.8024, Adjusted R-squared:  0.8007 
## F-statistic:   476 on 4 and 469 DF,  p-value: < 2.2e-16

#方案二
lm4_weg1 <- lm(log(wage)~edu+log(wage0)+(gender+edu)^2)
summary(lm4_weg1)

## 
## Call:
## lm(formula = log(wage) ~ edu + log(wage0) + (gender + edu)^2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.45056 -0.11127 -0.00943  0.10693  0.88486 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     1.885367   0.332427   5.672 2.48e-08 ***
## edu             0.024805   0.005433   4.565 6.38e-06 ***
## log(wage0)      0.839500   0.036441  23.037  < 2e-16 ***
## genderMale      0.071119   0.086097   0.826    0.409    
## edu:genderMale -0.002471   0.006573  -0.376    0.707    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1774 on 469 degrees of freedom
## Multiple R-squared:  0.8024, Adjusted R-squared:  0.8007 
## F-statistic:   476 on 4 and 469 DF,  p-value: < 2.2e-16

#含有多个交互项的多元回归
lm5_wegm <- lm(log(wage)~edu+log(wage0)+(edu+gender+minority)^2)
summary(lm5_wegm)

## 
## Call:
## lm(formula = log(wage) ~ edu + log(wage0) + (edu + gender + minority)^2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.45697 -0.11790 -0.00293  0.10435  0.86635 
## 
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)             2.173917   0.339770   6.398 3.83e-10 ***
## edu                     0.029143   0.005551   5.250 2.32e-07 ***
## log(wage0)              0.804249   0.037496  21.449  < 2e-16 ***
## genderMale              0.044760   0.090223   0.496  0.62006    
## minorityYes             0.222798   0.102574   2.172  0.03035 *  
## edu:genderMale         -0.000342   0.006709  -0.051  0.95937    
## edu:minorityYes        -0.021623   0.007903  -2.736  0.00645 ** 
## genderMale:minorityYes  0.022999   0.041332   0.556  0.57817    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1757 on 466 degrees of freedom
## Multiple R-squared:  0.8074, Adjusted R-squared:  0.8045 
## F-statistic:   279 on 7 and 466 DF,  p-value: < 2.2e-16

lm5_wegm1<- lm(log(wage)~edu+log(wage0)+(edu+gender+minority)^3)
summary(lm5_wegm1)

## 
## Call:
## lm(formula = log(wage) ~ edu + log(wage0) + (edu + gender + minority)^3)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.45714 -0.11783 -0.00318  0.10515  0.86618 
## 
## Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 2.1838785  0.3430826   6.365 4.67e-10 ***
## edu                         0.0287972  0.0057725   4.989 8.60e-07 ***
## log(wage0)                  0.8036479  0.0376322  21.355  < 2e-16 ***
## genderMale                  0.0363215  0.0980328   0.371    0.711    
## minorityYes                 0.1850335  0.1991397   0.929    0.353    
## edu:genderMale              0.0003006  0.0073162   0.041    0.967    
## edu:minorityYes            -0.0186024  0.0157751  -1.179    0.239    
## genderMale:minorityYes      0.0740376  0.2342868   0.316    0.752    
## edu:genderMale:minorityYes -0.0040124  0.0181287  -0.221    0.825    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1759 on 465 degrees of freedom
## Multiple R-squared:  0.8074, Adjusted R-squared:  0.8041 
## F-statistic: 243.6 on 8 and 465 DF,  p-value: < 2.2e-16