Ca6_inear Regression_0408
Tung-Han Wu
2020/4/8
setwd(“C:/Users/User/Desktop/LearnR/CA/CAdata”)
x = c(18,23,25,35,65,54,34,56,72,19,23,42,18,39,37)
y = c(202,186,187,180,156,169,174,172,153,199,193,174,198,183,178)
plot(x,y, xlim=c(0,80), ylim=c(150,215))# make a plot
abline(lm(y ~ x)) # plot the regression line
lm(y ~ x) # the basic values of the regression analysis##
## Call:
## lm(formula = y ~ x)
##
## Coefficients:
## (Intercept) x
## 210.0485 -0.7977summary(lm(y ~ x)) #alternative code##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.9258 -2.5383 0.3879 3.1867 6.6242
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 210.04846 2.86694 73.27 < 2e-16 ***
## x -0.79773 0.06996 -11.40 3.85e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.578 on 13 degrees of freedom
## Multiple R-squared: 0.9091, Adjusted R-squared: 0.9021
## F-statistic: 130 on 1 and 13 DF, p-value: 3.848e-08library和require都可載入package 如果該package不存在， 執行到library會停止執行後續code require則會繼續執行。
library(ggplot2)
# require(ggplot2)
# print(qplot(x, y, xlim=c(0,80), ylim=c(150,220)))
# abline(lm(y ~ x))Numeric Functions in R
Multiple Regression with R
y = c(202,186,187,180,156,169,174,172,153,199,193,174,198,183,178)
x1 = c(18,23,25,35,65,54,34,56,72,19,23,42,18,39,37)
x2 = c(56,45,67,89,65,76,55,66,77,63,53,49,76,62,53)
fit= lm(y~x1+x2)
summary(fit)##
## Call:
## lm(formula = y ~ x1 + x2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.164 -2.733 -0.187 2.885 6.784
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 204.60635 6.55970 31.191 7.42e-13 ***
## x1 -0.81965 0.07426 -11.038 1.22e-07 ***
## x2 0.09865 0.10680 0.924 0.374
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.604 on 12 degrees of freedom
## Multiple R-squared: 0.9151, Adjusted R-squared: 0.901
## F-statistic: 64.7 on 2 and 12 DF, p-value: 3.737e-07R-squared 英文名稱 coefficient of determination
Multiple Regression with Categorical Predictors
將變項設為類別變項
y = c(202,186,187,180,156,169,174,172,153,199,193,174,198,183,178)
x1 = c(18,23,25,35,65,54,34,56,72,19,23,42,18,39,37)
x2 = c(56,45,67,89,65,76,55,66,77,63,53,49,76,62,53)
x3 = c(1,1,1,1,1,2,2,2,0,0,0,0,0,1,1)
fit= lm(y~x1+x2+factor(x3)) #用factor 宣告x3轉成類別變項
summary(fit)##
## Call:
## lm(formula = y ~ x1 + x2 + factor(x3))
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.1066 -2.5487 -0.8259 1.9912 7.3362
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 205.80831 7.33581 28.055 7.69e-11 ***
## x1 -0.81849 0.08383 -9.764 1.98e-06 ***
## x2 0.09552 0.11501 0.831 0.426
## factor(x3)1 -1.76090 2.90297 -0.607 0.558
## factor(x3)2 -1.12668 3.76855 -0.299 0.771
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.953 on 10 degrees of freedom
## Multiple R-squared: 0.9181, Adjusted R-squared: 0.8854
## F-statistic: 28.04 on 4 and 10 DF, p-value: 2.054e-05y = c(202,186,187,180,156,169,174,172,153,199,193,174,198,183,178)
x1 = c(18,23,25,35,65,54,34,56,72,19,23,42,18,39,37)
x2 = c(56,45,67,89,65,76,55,66,77,63,53,49,76,62,53)
x3 = c(1,1,1,1,1,2,2,2,0,0,0,0,0,1,1)
x3 = factor(x3)
newx3 = relevel(x3, ref = "2")
a = lm(y~x1+x2+newx3)
summary(a)##
## Call:
## lm(formula = y ~ x1 + x2 + newx3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.1066 -2.5487 -0.8259 1.9912 7.3362
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 204.68163 7.92081 25.841 1.73e-10 ***
## x1 -0.81849 0.08383 -9.764 1.98e-06 ***
## x2 0.09552 0.11501 0.831 0.426
## newx30 1.12668 3.76855 0.299 0.771
## newx31 -0.63422 3.58180 -0.177 0.863
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.953 on 10 degrees of freedom
## Multiple R-squared: 0.9181, Adjusted R-squared: 0.8854
## F-statistic: 28.04 on 4 and 10 DF, p-value: 2.054e-05不將變項設為類別變項
y = c(202,186,187,180,156,169,174,172,153,199,193,174,198,183,178)
x1 = c(18,23,25,35,65,54,34,56,72,19,23,42,18,39,37)
x2 = c(56,45,67,89,65,76,55,66,77,63,53,49,76,62,53)
x3 = c(1,1,1,1,1,2,2,2,0,0,0,0,0,1,1)
fit= lm(y~x1+x2+x3) #用factor 宣告x3轉成類別變項
summary(fit)##
## Call:
## lm(formula = y ~ x1 + x2 + x3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.301 -2.691 -1.098 2.572 7.484
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 205.05293 6.87760 29.815 7.13e-12 ***
## x1 -0.81148 0.07932 -10.230 5.89e-07 ***
## x2 0.09703 0.11072 0.876 0.40
## x3 -0.74955 1.77043 -0.423 0.68
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.77 on 11 degrees of freedom
## Multiple R-squared: 0.9165, Adjusted R-squared: 0.8937
## F-statistic: 40.24 on 3 and 11 DF, p-value: 3.193e-06y = c(202,186,187,180,156,169,174,172,153,199,193,174,198,183,178)
x1 = c(18,23,25,35,65,54,34,56,72,19,23,42,18,39,37)
x2 = c(56,45,67,89,65,76,55,66,77,63,53,49,76,62,53)
x3 = c("B","B","B","B","B","C","C","C","A","A","A","A","A","B","B")
fit= lm(y~x1+x2+x3)
summary(fit)##
## Call:
## lm(formula = y ~ x1 + x2 + x3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.1066 -2.5487 -0.8259 1.9912 7.3362
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 205.80831 7.33581 28.055 7.69e-11 ***
## x1 -0.81849 0.08383 -9.764 1.98e-06 ***
## x2 0.09552 0.11501 0.831 0.426
## x3B -1.76090 2.90297 -0.607 0.558
## x3C -1.12668 3.76855 -0.299 0.771
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.953 on 10 degrees of freedom
## Multiple R-squared: 0.9181, Adjusted R-squared: 0.8854
## F-statistic: 28.04 on 4 and 10 DF, p-value: 2.054e-05y = c(202,186,187,180,156,169,174,172,153,199,193,174,198,183,178)
x1 = c(18,23,25,35,65,54,34,56,72,19,23,42,18,39,37)
x2 = c(56,45,67,89,65,76,55,66,77,63,53,49,76,62,53)
x3 = c("F","F","F","F","F","F","F","M","M","M","M","M","M","M","M")
fit= lm(y~x1+x2+x3)
summary(fit)##
## Call:
## lm(formula = y ~ x1 + x2 + x3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.867 -2.234 -1.738 2.043 8.707
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 201.47962 6.23852 32.296 2.99e-12 ***
## x1 -0.83153 0.06823 -12.187 9.92e-08 ***
## x2 0.12109 0.09845 1.230 0.2444
## x3M 4.02377 2.20015 1.829 0.0946 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.211 on 11 degrees of freedom
## Multiple R-squared: 0.9349, Adjusted R-squared: 0.9172
## F-statistic: 52.67 on 3 and 11 DF, p-value: 8.171e-07aaa=read.csv("C:/Users/User/Desktop/LearnR/CA/CAdata/anova_data1.csv", header=T)
aaa## Dosage Score
## 1 a 30
## 2 a 38
## 3 a 35
## 4 a 41
## 5 a 27
## 6 a 24
## 7 b 32
## 8 b 26
## 9 b 31
## 10 b 29
## 11 b 27
## 12 b 35
## 13 b 21
## 14 b 25
## 15 c 17
## 16 c 21
## 17 c 20
## 18 c 19attach(aaa)
fit= lm(Score~Dosage)
summary(fit)##
## Call:
## lm(formula = Score ~ Dosage)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.500 -2.438 0.250 2.688 8.500
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 32.500 2.010 16.166 6.72e-11 ***
## Dosageb -4.250 2.659 -1.598 0.130880
## Dosagec -13.250 3.179 -4.168 0.000824 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.924 on 15 degrees of freedom
## Multiple R-squared: 0.5396, Adjusted R-squared: 0.4782
## F-statistic: 8.789 on 2 and 15 DF, p-value: 0.002977Multi-collinearity 多重共線姓
install.packages(“car”)
# Evaluate Collinearity
library(car)## Loading required package: carDatay = c(202,186,187,180,156,169,174,172,153,199,193,174,198,183,178)
x1 = c(18,23,25,35,65,54,34,56,72,19,23,42,18,39,37)
x2 = c(56,65,67,69,125,76,65,86,97,53,63,69,56,72,63)
fit= lm(y~x1+x2)
cor(x1, x2)## [1] 0.8668049vif(fit) #variance inflation factors## x1 x2
## 4.021729 4.021729y = c(202,186,187,180,156,169,174,172,153,199,193,174,198,183,178)
x1 = c(18,23,25,35,65,54,34,56,72,19,23,42,18,39,37)
x3 = c(16,25,27,39,65,46,35,56,87,13,23,49,16,32,23)
fit= lm(y~x1+x3)
cor(x1, x3)## [1] 0.9503016vif(fit)## x1 x3
## 10.31706 10.31706Multi Collinearity for Categorical Variables (補充)
http://stackoverflow.com/questions/33397689/multi-collinearity-for-categorical-variables
Residual analysis 回歸診斷
library(car) # package:car
y = c(202,186,187,180,156,169,174,172,153,199,193,174,198,183,178)
x1 = c(18,23,25,35,65,54,34,56,72,19,23,42,18,39,37)
x2 = c(56,45,67,89,65,76,55,66,77,63,53,49,76,62,53)
fit= lm(y~x1+x2)
summary(fit)##
## Call:
## lm(formula = y ~ x1 + x2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.164 -2.733 -0.187 2.885 6.784
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 204.60635 6.55970 31.191 7.42e-13 ***
## x1 -0.81965 0.07426 -11.038 1.22e-07 ***
## x2 0.09865 0.10680 0.924 0.374
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.604 on 12 degrees of freedom
## Multiple R-squared: 0.9151, Adjusted R-squared: 0.901
## F-statistic: 64.7 on 2 and 12 DF, p-value: 3.737e-07outlierTest(fit) # Bonferonnip-value for most extreme obs## No Studentized residuals with Bonferroni p < 0.05
## Largest |rstudent|:
## rstudent unadjusted p-value Bonferroni p
## 7 -2.127814 0.056795 0.85192qqPlot(fit, main="QQ Plot") #qqplot for studentizedresid
## [1] 7 8#畫殘差圖
par(mfrow=c(2,2))
plot(fit)
resid(fit)## 1 2 3 4 5 6 7
## 6.6232481 -4.1933786 -3.7242792 -4.6979492 -1.7408342 1.1578695 -8.1636447
## 8 9 10 11 12 13 14
## 6.7836355 -0.1870073 3.7523811 2.0174547 -1.0145391 0.6503314 4.2441036
## 15
## -1.5073916residualPlots(fit) # package: car, Tukey test for nonadditivity
## Test stat Pr(>|Test stat|)
## x1 0.8571 0.40966
## x2 -1.8647 0.08911 .
## Tukey test 0.8621 0.38862
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1殘插圖的值 正負3 比較好
Normality
方法一
Shapiro-Wilk test
#Sample size < 50
a<-rnorm(50, mean = 60, sd = 10)
shapiro.test## function (x)
## {
## DNAME <- deparse(substitute(x))
## stopifnot(is.numeric(x))
## x <- sort(x[complete.cases(x)])
## n <- length(x)
## if (is.na(n) || n < 3L || n > 5000L)
## stop("sample size must be between 3 and 5000")
## rng <- x[n] - x[1L]
## if (rng == 0)
## stop("all 'x' values are identical")
## if (rng < 1e-10)
## x <- x/rng
## res <- .Call(C_SWilk, x)
## RVAL <- list(statistic = c(W = res[1]), p.value = res[2],
## method = "Shapiro-Wilk normality test", data.name = DNAME)
## class(RVAL) <- "htest"
## return(RVAL)
## }
## <bytecode: 0x0000000012606d50>
## <environment: namespace:stats>(a)## [1] 83.45684 70.56542 48.60176 59.07326 55.00837 70.08762 75.87689 65.98744
## [9] 81.97664 49.31876 61.12105 59.37404 64.45662 51.90351 45.18661 55.15390
## [17] 46.67818 66.41711 53.97992 56.27781 48.45064 54.25767 64.22767 53.11206
## [25] 54.40701 57.65060 55.52188 66.06859 59.82486 48.89068 69.62759 56.01608
## [33] 55.22916 51.12721 70.11492 57.81674 46.98425 40.62899 51.51887 62.26380
## [41] 82.72806 50.49387 54.92946 66.97047 65.09214 53.91634 61.82253 58.62062
## [49] 72.02232 58.37658方法二
Kolmogorov-Smirnov test
檢查兩個分布
a<-rnorm(100, mean = 60, sd = 10)
b<-rnorm(100, mean = 60, sd = 8)
ks.test(a, b) # Do x and y come from the same distribution?##
## Two-sample Kolmogorov-Smirnov test
##
## data: a and b
## D = 0.14, p-value = 0.281
## alternative hypothesis: two-sided方法三
install.packages(“nortest”)
library(nortest)
lillie.test(a) #Lilliefors (Kolmogorov-Smirnov) test for normality##
## Lilliefors (Kolmogorov-Smirnov) normality test
##
## data: a
## D = 0.072953, p-value = 0.2124#Sample size > 50
pearson.test(a) #Pearson chi-square test for normality##
## Pearson chi-square normality test
##
## data: a
## P = 7.9, p-value = 0.6386sf.test(a) #Shapiro-Francia test for normality##
## Shapiro-Francia normality test
##
## data: a
## W = 0.9756, p-value = 0.05747Non-independence of Errors
#這一期和下一期是否相關 下面結果沒關
# Test for AutocorrelatedErrors
y = c(202,186,187,180,156,169,174,172,153,199,193,174,198,183,178)
x1 = c(88,23,35,25,65,94,24,36,72,59,23,82,28,99,37)
fit= lm(y~x1)
# durbinWatsonTest(fit)Equal variance test
使用F-test檢定變異數同質性的假設，將殘差取絕對值後依數值大小分為兩群，再檢定此群的變異數是否相同
y = c(202,186,187,180,156,169,174,172,153,199,193,174,198,183,178,177)
x1 = c(18,23,25,35,65,54,34,56,72,19,23,42,18,39,37,39)
fit= lm(y~x1)
res=abs(resid(fit)) # ads取絕對值
a=res[1:8] # 我選擇切一半
b=res[9:16]
var.test(a,b)##
## F test to compare two variances
##
## data: a and b
## F = 4.2844, num df = 7, denom df = 7, p-value = 0.07397
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
## 0.8577478 21.4000516
## sample estimates:
## ratio of variances
## 4.284372Identifying influential cases [排除極端值]
Cook’s d D > 4/n, where n is the number of observations cooks.distance(fit)
|DFFITS| >1 for small/medium data or >2sqrt(p/n) for large data 自變項數目(含截距項):p dffits(fit)
|DFBETAS| >1 for small/medium data or >2/sqrt(n) for large data dfbetas (fit)
aaa=read.csv("C:/Users/User/Desktop/LearnR/CA/CAdata/lowbwt.csv", header=T)
attach(aaa)
fit= lm(BWT~AGE+LWT+SMOKE)
summary(fit)##
## Call:
## lm(formula = BWT ~ AGE + LWT + SMOKE)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2069.89 -433.18 13.67 516.45 1813.75
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2362.720 300.687 7.858 3.11e-13 ***
## AGE 7.093 9.925 0.715 0.4757
## LWT 4.019 1.720 2.337 0.0205 *
## SMOKE -267.213 105.802 -2.526 0.0124 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 708.8 on 185 degrees of freedom
## Multiple R-squared: 0.06988, Adjusted R-squared: 0.05479
## F-statistic: 4.633 on 3 and 185 DF, p-value: 0.003781cooks.distance(fit) #越大越不好## 1 2 3 4 5 6
## 8.091231e-03 6.419186e-03 9.476283e-05 5.937741e-05 2.885089e-05 7.588305e-04
## 7 8 9 10 11 12
## 6.337463e-04 6.727997e-04 1.937808e-04 4.241809e-05 2.324249e-04 1.088990e-03
## 13 14 15 16 17 18
## 1.871643e-04 7.630093e-04 2.290077e-04 2.290077e-04 9.700582e-05 9.509760e-06
## 19 20 21 22 23 24
## 1.851577e-04 1.998491e-05 7.510465e-04 3.346710e-04 1.161106e-02 2.355037e-04
## 25 26 27 28 29 30
## 1.082100e-04 1.205737e-03 4.176751e-04 5.073280e-04 1.494260e-05 2.712675e-06
## 31 32 33 34 35 36
## 2.712675e-06 1.219782e-03 3.278110e-04 2.142058e-04 2.062418e-05 1.371800e-04
## 37 38 39 40 41 42
## 3.351273e-04 3.746905e-04 1.070923e-03 1.431487e-03 5.396954e-05 7.234268e-04
## 43 44 45 46 47 48
## 8.258035e-07 6.929410e-05 3.101368e-03 3.101368e-03 1.939120e-05 2.472959e-05
## 49 50 51 52 53 54
## 4.735950e-05 3.114932e-03 4.771181e-05 1.801726e-05 9.001905e-04 3.614989e-03
## 55 56 57 58 59 60
## 3.120697e-04 6.899062e-04 2.159992e-03 1.493096e-06 5.977599e-04 5.964558e-04
## 61 62 63 64 65 66
## 5.964558e-04 2.503049e-04 3.858828e-04 7.897966e-05 1.558962e-03 8.928576e-05
## 67 68 69 70 71 72
## 4.092882e-04 1.029237e-06 3.700017e-04 1.893643e-04 2.920325e-03 2.294233e-03
## 73 74 75 76 77 78
## 2.773707e-03 2.066998e-03 4.821409e-03 3.474504e-06 4.727477e-04 4.981517e-03
## 79 80 81 82 83 84
## 4.063533e-03 4.495877e-04 7.930186e-04 5.913623e-04 2.327173e-03 1.238137e-03
## 85 86 87 88 89 90
## 1.259416e-03 8.012113e-03 3.297179e-03 1.278362e-03 1.879113e-03 1.638709e-03
## 91 92 93 94 95 96
## 1.326998e-03 1.700527e-03 1.099909e-02 1.085207e-02 9.889287e-03 2.183452e-03
## 97 98 99 100 101 102
## 1.809873e-03 6.976488e-03 6.976488e-03 2.856290e-03 3.313486e-03 1.249258e-02
## 103 104 105 106 107 108
## 3.693451e-03 3.665054e-03 3.510126e-03 3.639327e-03 6.449399e-03 3.739138e-03
## 109 110 111 112 113 114
## 1.244639e-02 8.349879e-03 5.151642e-03 6.148936e-03 1.200573e-02 1.109605e-02
## 115 116 117 118 119 120
## 1.476529e-02 4.580693e-03 1.229218e-02 5.143057e-03 4.728238e-03 1.616729e-02
## 121 122 123 124 125 126
## 6.220598e-03 5.376079e-03 6.450495e-03 5.307676e-03 5.547980e-03 1.366785e-02
## 127 128 129 130 131 132
## 1.603014e-02 1.983679e-02 1.312272e-02 2.080437e-01 4.293705e-02 3.263085e-02
## 133 134 135 136 137 138
## 1.051408e-01 1.856065e-02 2.317522e-02 1.573253e-02 1.386106e-02 8.108206e-03
## 139 140 141 142 143 144
## 7.900945e-03 1.506383e-02 1.619219e-02 6.036581e-03 6.868416e-03 1.216299e-02
## 145 146 147 148 149 150
## 6.103057e-03 8.091529e-03 4.157642e-02 8.254824e-03 6.357383e-03 5.051545e-03
## 151 152 153 154 155 156
## 7.480706e-03 5.567301e-03 3.176305e-03 3.763557e-03 4.452047e-03 4.023523e-03
## 157 158 159 160 161 162
## 2.770079e-03 2.420780e-03 4.530571e-03 1.726846e-03 2.053625e-03 3.632937e-03
## 163 164 165 166 167 168
## 3.255539e-03 5.757275e-03 1.351428e-03 1.432390e-03 2.800003e-03 3.483477e-03
## 169 170 171 172 173 174
## 2.419495e-03 3.745330e-03 7.471918e-03 9.385954e-04 8.327085e-04 3.545521e-03
## 175 176 177 178 179 180
## 1.787122e-03 2.663582e-03 9.309099e-04 8.489235e-04 6.079712e-04 2.383996e-03
## 181 182 183 184 185 186
## 3.321447e-03 1.612051e-03 6.350367e-03 2.941222e-04 6.258374e-04 2.022937e-03
## 187 188 189
## 2.115936e-04 2.966937e-03 5.424351e-04dffits(fit) #單獨看## 1 2 3 4 5 6
## -0.179914000 -0.160202747 -0.019417664 -0.015370239 -0.010713697 -0.054989664
## 7 8 9 10 11 12
## -0.050246992 -0.051755603 -0.027768367 -0.012990921 -0.030412579 -0.065869694
## 13 14 15 16 17 18
## -0.027290931 -0.055115545 0.030187525 0.030187525 -0.019645779 0.006150929
## 19 20 21 22 23 24
## -0.027145661 0.008916797 -0.054679642 -0.036493530 -0.215360607 -0.030614644
## 25 26 27 28 29 30
## -0.020750888 -0.069307531 0.040772503 -0.044941482 -0.007710262 -0.003285131
## 31 32 33 34 35 36
## -0.003285131 0.069701168 0.036115927 -0.029197827 -0.009058400 0.023363020
## 37 38 39 40 41 42
## 0.036521261 0.038618096 -0.065284206 0.075494924 0.014653267 -0.053659000
## 43 44 45 46 47 48
## 0.001812558 -0.016604339 0.111226479 0.111226479 -0.008783332 0.009919062
## 49 50 51 52 53 54
## 0.013727069 0.111472856 0.013778092 0.008466560 0.059885828 0.120063580
## 55 56 57 58 59 60
## 0.035244281 0.052408927 0.092835312 0.002437234 0.048787475 0.048731203
## 61 62 63 64 65 66
## 0.048731203 0.031565322 0.039195560 0.017727166 0.078839232 0.018847926
## 67 68 69 70 71 72
## 0.040369311 0.002023536 0.038379365 0.027451448 0.108011165 0.095622841
## 73 74 75 76 77 78
## 0.105261089 0.090782325 0.138793575 -0.003717917 0.043390976 0.141030925
## 79 80 81 82 83 84
## 0.127508635 0.042298938 0.056221278 0.048515006 0.096331302 0.070269096
## 85 86 87 88 89 90
## 0.070890078 0.179289320 0.114798650 0.071427017 0.086500650 0.080897366
## 91 92 93 94 95 96
## 0.072776860 0.082401829 0.209440825 0.208894189 0.199225990 0.093350667
## 97 98 99 100 101 102
## 0.084954884 0.167231926 0.167231926 0.106791230 0.115170118 0.223709886
## 103 104 105 106 107 108
## 0.121637669 0.121176568 0.118568284 0.120382796 0.160710580 0.122231338
## 109 110 111 112 113 114
## 0.224154892 0.182759960 0.143380065 0.157119821 0.219910617 0.210941923
## 115 116 117 118 119 120
## 0.243772117 0.135518767 0.222219768 0.143656863 0.137845326 0.255446161
## 121 122 123 124 125 126
## 0.157951088 0.146845777 0.161221587 0.146231560 0.149535064 0.234759725
## 127 128 129 130 131 132
## 0.253635921 0.284569959 0.231710634 0.928254331 -0.423350535 -0.369040853
## 133 134 135 136 137 138
## -0.661196522 -0.275773528 -0.307010801 -0.253604805 -0.237123720 -0.181397529
## 139 140 141 142 143 144
## -0.179032282 -0.246506827 -0.255032054 -0.155403508 -0.166420854 -0.221449194
## 145 146 147 148 149 150
## -0.156261252 -0.180243270 -0.411162345 -0.182127918 -0.159832965 -0.142467791
## 151 152 153 154 155 156
## -0.173190803 -0.149382299 -0.112631944 -0.122661730 -0.133796506 -0.126781610
## 157 158 159 160 161 162
## -0.105180936 -0.098321535 -0.134836735 -0.082941286 -0.090481954 -0.120564787
## 163 164 165 166 167 168
## -0.114113318 -0.151880133 -0.073379463 -0.075564538 -0.105760584 -0.117961703
## 169 170 171 172 173 174
## -0.098186236 -0.122276949 -0.172811222 -0.061147348 -0.057586852 -0.118964710
## 175 176 177 178 179 180
## -0.084492600 -0.103065407 -0.060900524 -0.058140702 -0.049201278 -0.097536734
## 181 182 183 184 185 186
## -0.115281769 -0.080182797 -0.159243637 -0.034210600 -0.049910239 -0.089778361
## 187 188 189
## -0.029016966 -0.108830921 -0.046473168dfbetas(fit) ## (Intercept) AGE LWT SMOKE
## 1 0.0160060747 0.0864256263 -1.387811e-01 0.0575249813
## 2 0.0979099409 -0.1198860010 -3.351505e-02 0.0495883262
## 3 -0.0088939901 0.0045793665 7.150718e-03 -0.0127458496
## 4 -0.0057128399 0.0022398909 5.317694e-03 -0.0106035667
## 5 -0.0057755905 0.0045911641 2.972994e-03 -0.0065748705
## 6 -0.0289439230 0.0171016737 5.888033e-03 0.0331851589
## 7 -0.0265161183 0.0072827427 1.403639e-02 0.0304493308
## 8 -0.0445905152 0.0290981334 1.928274e-02 0.0239340188
## 9 0.0088831303 -0.0165788239 5.257476e-03 -0.0177625540
## 10 0.0004875270 -0.0048779425 4.386967e-03 -0.0089766643
## 11 -0.0255492804 0.0104690069 1.714251e-02 0.0143743286
## 12 -0.0167292421 0.0369171503 -3.017182e-02 0.0309215784
## 13 -0.0186179329 0.0009531490 1.798879e-02 0.0133951440
## 14 0.0010956054 -0.0376791397 2.737873e-02 0.0209661978
## 15 0.0177918118 -0.0118100252 -1.156816e-02 0.0176815469
## 16 0.0177918118 -0.0118100252 -1.156816e-02 0.0176815469
## 17 -0.0177582499 0.0127318135 7.211076e-03 0.0080459626
## 18 -0.0001686781 0.0016540231 -1.483045e-03 0.0045247264
## 19 -0.0172355993 0.0110739285 4.576002e-03 0.0156171117
## 20 -0.0021256823 0.0047548912 -2.071636e-03 0.0059151563
## 21 0.0144801977 -0.0432480079 1.580320e-02 0.0190222467
## 22 0.0003384117 -0.0258629791 2.033155e-02 0.0123618840
## 23 0.1756475551 -0.1292281727 -1.255099e-01 0.0403646231
## 24 0.0011151414 -0.0177285051 9.762435e-03 0.0146578431
## 25 -0.0046574631 -0.0055279535 6.274295e-03 0.0120674856
## 26 0.0377182840 -0.0246902455 -3.884585e-02 0.0268530315
## 27 0.0178736623 -0.0231085676 -7.747184e-06 0.0249129333
## 28 0.0207422626 -0.0250713246 -1.165012e-02 0.0192785071
## 29 0.0043723517 -0.0012903729 -4.507792e-03 -0.0048407799
## 30 -0.0026129094 0.0020548841 6.837295e-04 0.0015788692
## 31 -0.0026129094 0.0020548841 6.837295e-04 0.0015788692
## 32 0.0217324685 0.0144418196 -4.394638e-02 0.0404849357
## 33 -0.0168939466 0.0298157634 -8.228504e-03 0.0166775013
## 34 0.0077669138 -0.0030741615 -1.445491e-02 0.0146485749
## 35 -0.0014067662 -0.0022856702 1.695102e-03 0.0053873528
## 36 -0.0116711904 0.0129447453 2.220269e-03 0.0153979358
## 37 0.0057036404 -0.0163813380 9.300644e-03 0.0245926634
## 38 -0.0089292193 0.0173237487 -5.965309e-03 0.0272941533
## 39 0.0525838647 -0.0196805625 -4.991404e-02 -0.0268289634
## 40 -0.0239501201 0.0578672552 -2.777601e-02 0.0365019693
## 41 -0.0052613276 -0.0040842277 1.124646e-02 0.0074485959
## 42 0.0073864435 0.0248051663 -4.328112e-02 0.0157579546
## 43 0.0004973624 -0.0001082106 -2.149949e-05 -0.0011358037
## 44 0.0001185447 0.0061733038 -1.016363e-02 0.0075432669
## 45 0.0715038163 -0.0374153828 -5.686971e-02 0.0599818535
## 46 0.0715038163 -0.0374153828 -5.686971e-02 0.0599818535
## 47 0.0033548757 -0.0069252274 1.085666e-03 0.0031103982
## 48 0.0051689352 -0.0055181953 1.214002e-03 -0.0053409362
## 49 0.0052476681 0.0020122368 -5.395271e-03 -0.0080082721
## 50 0.0519217371 0.0038967108 -7.338145e-02 0.0618228430
## 51 0.0069466827 -0.0021440944 -3.215554e-03 -0.0084303469
## 52 0.0025866158 -0.0004261537 -5.390524e-04 -0.0053111739
## 53 0.0029177732 -0.0071821055 3.520523e-03 0.0460998131
## 54 -0.0093713241 0.0752604715 -6.521492e-02 0.0606911701
## 55 0.0257007120 -0.0169192677 -8.447383e-03 -0.0190302884
## 56 0.0435025275 -0.0350101749 -1.185301e-02 -0.0235906099
## 57 0.0327529642 -0.0143411368 -2.893890e-02 0.0649913075
## 58 -0.0012820902 0.0014866892 6.705890e-04 -0.0009529334
## 59 0.0375865185 -0.0145838943 -2.402059e-02 -0.0254020446
## 60 0.0360800408 -0.0319907248 -4.828496e-03 -0.0236250679
## 61 0.0360800408 -0.0319907248 -4.828496e-03 -0.0236250679
## 62 0.0135795739 -0.0002640427 -9.001036e-03 -0.0192781898
## 63 0.0169459247 0.0062508105 -1.907464e-02 -0.0218878001
## 64 -0.0053246289 0.0094247645 1.671536e-03 -0.0086348518
## 65 -0.0220270212 0.0259133895 2.658806e-03 0.0589836984
## 66 -0.0006836441 -0.0083602448 1.309845e-02 -0.0073423613
## 67 0.0154326277 0.0059176953 -1.586671e-02 -0.0235511618
## 68 -0.0014561022 0.0001160779 1.825160e-03 0.0006708564
## 69 0.0126774086 -0.0183270936 1.158027e-02 -0.0206994972
## 70 -0.0016043741 -0.0073854739 1.614913e-02 -0.0131774134
## 71 0.0285192423 -0.0055132458 -3.240144e-02 0.0780376750
## 72 -0.0609297136 0.0602196195 1.919144e-02 0.0563418008
## 73 0.0165663084 0.0056259942 -2.794000e-02 0.0780293419
## 74 0.0739920802 -0.0616391966 -1.755772e-02 -0.0410433786
## 75 0.0467891156 -0.0901222269 3.058250e-02 0.0787079853
## 76 0.0010178407 0.0015812015 -3.358243e-03 0.0006980907
## 77 -0.0031561820 0.0080581941 8.084954e-03 -0.0252132777
## 78 -0.0741664123 0.1026347534 -6.935697e-03 0.0790955007
## 79 0.0381457288 -0.0393901206 -1.027058e-02 0.0912072003
## 80 -0.0155510262 -0.0077587848 3.551802e-02 -0.0130771807
## 81 0.0195205611 -0.0117979319 2.249993e-03 -0.0347690154
## 82 -0.0330916741 0.0298748841 2.127911e-02 -0.0145751891
## 83 -0.0048869479 0.0665666793 -4.419812e-02 -0.0373398030
## 84 0.0382897139 -0.0311187946 -5.986000e-04 -0.0405912493
## 85 0.0268237828 -0.0018975383 -1.347660e-02 -0.0440808019
## 86 0.0822832433 -0.1004646215 -6.148143e-03 0.1092602638
## 87 0.0920411663 -0.0474330101 -4.837324e-02 -0.0587370084
## 88 0.0195994398 -0.0042642281 -8.472253e-04 -0.0447583363
## 89 -0.0646243145 0.0644226346 3.102263e-02 -0.0196140349
## 90 0.0354326301 -0.0146913086 -9.060464e-03 -0.0502068711
## 91 0.0095105881 0.0055365983 2.853041e-03 -0.0448880146
## 92 0.0310083220 -0.0291040873 1.120359e-02 -0.0488144910
## 93 -0.0863864569 -0.0713128840 1.890503e-01 0.0688574577
## 94 0.0435988201 0.0612320637 -1.214828e-01 0.1258895121
## 95 0.0671616672 -0.1293625437 4.389849e-02 0.1129784021
## 96 -0.0274218685 0.0589076695 -3.066624e-03 -0.0424747887
## 97 -0.0422688169 0.0451839737 2.797504e-02 -0.0353910767
## 98 0.0088370734 -0.0758279432 6.651468e-02 0.1078042285
## 99 0.0088370734 -0.0758279432 6.651468e-02 0.1078042285
## 100 -0.0389556321 0.0734424794 -1.328193e-03 -0.0446016772
## 101 0.0497929899 0.0183670438 -5.604788e-02 -0.0643139295
## 102 -0.0547072463 -0.0916388437 1.677271e-01 0.1078226523
## 103 0.0525891903 0.0193984728 -5.919533e-02 -0.0679255752
## 104 0.0633044221 0.0035294892 -5.684797e-02 -0.0691101774
## 105 0.0752825805 -0.0483693026 -1.998731e-02 -0.0682132630
## 106 -0.0673624843 -0.0110190302 1.131315e-01 -0.0204575935
## 107 -0.0115789275 0.1117540258 -6.943183e-02 -0.0630294613
## 108 -0.0209482988 -0.0329506156 8.675457e-02 -0.0502247574
## 109 0.0935981514 -0.1091846989 -1.225596e-02 0.1448999594
## 110 0.0296860872 -0.1234745533 1.158357e-01 -0.0598481700
## 111 -0.1053282214 0.0734571157 8.573394e-02 -0.0373270608
## 112 0.1114086768 -0.0931419502 -1.683026e-02 -0.0810885816
## 113 -0.0873462288 0.1287021769 -1.625402e-02 0.1438280987
## 114 -0.0549283206 0.1722761128 -7.088949e-02 -0.0670643749
## 115 -0.0528473026 -0.0880447386 1.615304e-01 0.1375130779
## 116 -0.0301655006 0.0754549565 -4.690689e-03 -0.0669117275
## 117 0.1344538870 -0.1819684315 4.559006e-02 -0.0853929956
## 118 -0.0242552825 0.0816506317 -1.723771e-02 -0.0709125733
## 119 0.0309388933 0.0367214427 -4.167928e-02 -0.0801626636
## 120 0.2318280312 -0.1462544496 -1.133372e-01 -0.1080034988
## 121 0.0135782958 -0.0735387578 9.153771e-02 -0.0709477786
## 122 -0.0565399075 0.0290143318 7.945047e-02 -0.0672364974
## 123 0.1017154370 -0.0418895027 -5.026522e-02 -0.0942226567
## 124 0.0553572594 -0.0293804238 -1.589143e-03 -0.0907756167
## 125 0.0120454915 0.0349574850 -9.518093e-03 -0.0896530263
## 126 -0.0497782473 0.1767660428 -7.238840e-02 -0.0882432508
## 127 -0.1824500911 0.1876677899 8.528654e-02 -0.0630457093
## 128 0.1047827980 -0.1143723014 -2.183830e-02 0.1940161375
## 129 0.0859915889 0.0332842029 -8.633538e-02 -0.1362181611
## 130 -0.4671330923 0.8862767577 -2.119728e-01 -0.1385824393
## 131 0.1009228736 -0.2257521225 9.835685e-02 -0.2808390427
## 132 0.0850820055 -0.2375172592 4.875908e-02 0.1678853509
## 133 0.5507403159 -0.3824014950 -3.407104e-01 -0.3002492472
## 134 -0.1057714987 -0.0785647838 1.577439e-01 0.1411731297
## 135 -0.1524173880 -0.0858638371 2.361907e-01 0.1260701892
## 136 0.0902407800 -0.0946731584 -8.481423e-02 0.1239556865
## 137 -0.1427882305 -0.0166879676 1.555175e-01 0.1178261159
## 138 -0.0379276269 -0.0179340722 1.633140e-02 0.1123780373
## 139 -0.0262461840 -0.0144576821 -2.382096e-03 0.1106713699
## 140 0.0602830311 0.0700439240 -1.528708e-01 -0.1504466827
## 141 0.0635654069 -0.1857481068 1.069404e-01 -0.1264879941
## 142 -0.0927773240 0.0402221874 8.238770e-02 -0.0874417872
## 143 -0.0475855880 -0.0459501104 6.752396e-02 0.0935097490
## 144 -0.1403257068 0.1645720434 -2.602789e-02 0.0987829713
## 145 -0.0362638219 -0.0458290741 9.577572e-02 -0.0911890921
## 146 0.0078978273 0.0666537619 -7.939347e-02 -0.1195302035
## 147 0.1236788904 0.1313621675 -3.571786e-01 0.1096530663
## 148 0.0675317826 -0.0042882021 -8.577943e-02 -0.1281922643
## 149 -0.1144746168 0.0299939161 8.442331e-02 0.0849475598
## 150 -0.0815497289 0.0618206842 7.816488e-03 0.0824194217
## 151 -0.0832032151 -0.0488244094 1.283004e-01 0.0743426076
## 152 -0.1219569855 0.0585976597 6.995140e-02 0.0747855482
## 153 -0.0506944303 0.0412999695 2.506045e-02 -0.0744758035
## 154 0.0103708790 -0.0454623302 3.310259e-02 -0.0870489435
## 155 -0.0068109258 -0.0069922895 -2.227796e-02 0.0808050055
## 156 -0.0445992014 0.0742574049 -1.712173e-02 -0.0773882870
## 157 -0.0326696809 0.0320670692 1.051935e-02 -0.0750270089
## 158 -0.0047904480 0.0117916987 -5.780053e-03 -0.0756874297
## 159 0.0129511451 -0.0641300360 1.412024e-02 0.0718197725
## 160 -0.0491922311 0.0102755350 5.509754e-02 -0.0426457296
## 161 -0.0499388919 0.0469996897 1.816423e-02 -0.0534926634
## 162 -0.0462419952 -0.0343475548 6.896371e-02 0.0617191518
## 163 -0.0839840116 0.0386599184 4.475680e-02 0.0622540278
## 164 -0.0504991630 0.0962422627 -6.354910e-02 0.0687170803
## 165 -0.0377281481 0.0325528540 1.677467e-02 -0.0457738840
## 166 -0.0226060327 0.0233434878 6.086578e-03 -0.0540514762
## 167 -0.0771299811 0.0180498212 6.038900e-02 0.0545795484
## 168 -0.0429100138 -0.0446622177 7.954214e-02 0.0524196004
## 169 0.0181130533 -0.0672708756 4.528569e-02 -0.0500721918
## 170 -0.1022177090 0.0877355019 2.387310e-02 0.0519368859
## 171 0.0823416649 0.0232218356 -1.339762e-01 -0.0899651830
## 172 -0.0175840331 0.0191306426 3.729478e-03 -0.0438440129
## 173 -0.0109123392 -0.0108865350 2.582083e-02 -0.0391074216
## 174 -0.0948284579 0.0881560184 1.389432e-02 0.0508143721
## 175 -0.0353054931 0.0010895052 2.214137e-02 0.0518788544
## 176 0.0566303491 -0.0627533986 -1.083136e-02 -0.0645476221
## 177 -0.0029672115 0.0073037980 -3.580175e-03 -0.0468809210
## 178 -0.0266831596 0.0325790942 1.993746e-03 -0.0354313824
## 179 -0.0104397107 -0.0034066076 1.746383e-02 -0.0351895648
## 180 -0.0712168720 0.0644657374 7.846217e-03 0.0472984439
## 181 0.0380587539 -0.0269379012 -5.134276e-02 0.0567505493
## 182 -0.0609698982 0.0250292850 3.694969e-02 0.0424469877
## 183 0.1004684778 -0.0134877031 -1.202743e-01 -0.0824274772
## 184 -0.0235332423 0.0222017804 8.504356e-03 -0.0163239061
## 185 -0.0011619578 -0.0258462684 2.824756e-02 -0.0273855606
## 186 -0.0805572980 0.0634071912 2.748089e-02 0.0352292255
## 187 -0.0101771452 -0.0031569306 1.685521e-02 -0.0177792076
## 188 -0.0494435460 0.0760852839 -3.451561e-02 0.0486355261
## 189 -0.0056953382 0.0108955013 -3.645666e-03 -0.0348291929influence.measures(fit) #一起看## Influence measures of
## lm(formula = BWT ~ AGE + LWT + SMOKE) :
##
## dfb.1_ dfb.AGE dfb.LWT dfb.SMOK dffit cov.r cook.d hat inf
## 1 0.016006 0.086426 -1.39e-01 0.057525 -0.17991 1.031 8.09e-03 0.03065
## 2 0.097910 -0.119886 -3.35e-02 0.049588 -0.16020 1.030 6.42e-03 0.02729
## 3 -0.008894 0.004579 7.15e-03 -0.012746 -0.01942 1.040 9.48e-05 0.01754
## 4 -0.005713 0.002240 5.32e-03 -0.010604 -0.01537 1.038 5.94e-05 0.01617
## 5 -0.005776 0.004591 2.97e-03 -0.006575 -0.01071 1.042 2.89e-05 0.01967
## 6 -0.028944 0.017102 5.89e-03 0.033185 -0.05499 1.025 7.59e-04 0.00993
## 7 -0.026516 0.007283 1.40e-02 0.030449 -0.05025 1.026 6.34e-04 0.00985
## 8 -0.044591 0.029098 1.93e-02 0.023934 -0.05176 1.039 6.73e-04 0.01920
## 9 0.008883 -0.016579 5.26e-03 -0.017763 -0.02777 1.043 1.94e-04 0.02123
## 10 0.000488 -0.004878 4.39e-03 -0.008977 -0.01299 1.040 4.24e-05 0.01725
## 11 -0.025549 0.010469 1.71e-02 0.014374 -0.03041 1.040 2.32e-04 0.01820
## 12 -0.016729 0.036917 -3.02e-02 0.030922 -0.06587 1.032 1.09e-03 0.01571
## 13 -0.018618 0.000953 1.80e-02 0.013395 -0.02729 1.038 1.87e-04 0.01606
## 14 0.001096 -0.037679 2.74e-02 0.020966 -0.05512 1.042 7.63e-04 0.02244
## 15 0.017792 -0.011810 -1.16e-02 0.017682 0.03019 1.043 2.29e-04 0.02128
## 16 0.017792 -0.011810 -1.16e-02 0.017682 0.03019 1.043 2.29e-04 0.02128
## 17 -0.017758 0.012732 7.21e-03 0.008046 -0.01965 1.048 9.70e-05 0.02563
## 18 -0.000169 0.001654 -1.48e-03 0.004525 0.00615 1.038 9.51e-06 0.01520
## 19 -0.017236 0.011074 4.58e-03 0.015617 -0.02715 1.032 1.85e-04 0.01124
## 20 -0.002126 0.004755 -2.07e-03 0.005915 0.00892 1.042 2.00e-05 0.01941
## 21 0.014480 -0.043248 1.58e-02 0.019022 -0.05468 1.045 7.51e-04 0.02471
## 22 0.000338 -0.025863 2.03e-02 0.012362 -0.03649 1.051 3.35e-04 0.02840
## 23 0.175648 -0.129228 -1.26e-01 0.040365 -0.21536 1.068 1.16e-02 0.05862 *
## 24 0.001115 -0.017729 9.76e-03 0.014658 -0.03061 1.035 2.36e-04 0.01410
## 25 -0.004657 -0.005528 6.27e-03 0.012067 -0.02075 1.031 1.08e-04 0.01009
## 26 0.037718 -0.024690 -3.88e-02 0.026853 -0.06931 1.035 1.21e-03 0.01847
## 27 0.017874 -0.023109 -7.75e-06 0.024913 0.04077 1.041 4.18e-04 0.02022
## 28 0.020742 -0.025071 -1.17e-02 0.019279 -0.04494 1.035 5.07e-04 0.01564
## 29 0.004372 -0.001290 -4.51e-03 -0.004841 -0.00771 1.046 1.49e-05 0.02322
## 30 -0.002613 0.002055 6.84e-04 0.001579 -0.00329 1.040 2.71e-06 0.01728
## 31 -0.002613 0.002055 6.84e-04 0.001579 -0.00329 1.040 2.71e-06 0.01728
## 32 0.021732 0.014442 -4.39e-02 0.040485 0.06970 1.041 1.22e-03 0.02278
## 33 -0.016894 0.029816 -8.23e-03 0.016678 0.03612 1.068 3.28e-04 0.04335 *
## 34 0.007767 -0.003074 -1.45e-02 0.014649 -0.02920 1.033 2.14e-04 0.01214
## 35 -0.001407 -0.002286 1.70e-03 0.005387 -0.00906 1.032 2.06e-05 0.00950
## 36 -0.011671 0.012945 2.22e-03 0.015398 0.02336 1.043 1.37e-04 0.02066
## 37 0.005704 -0.016381 9.30e-03 0.024593 0.03652 1.039 3.35e-04 0.01761
## 38 -0.008929 0.017324 -5.97e-03 0.027294 0.03862 1.038 3.75e-04 0.01704
## 39 0.052584 -0.019681 -4.99e-02 -0.026829 -0.06528 1.088 1.07e-03 0.06217 *
## 40 -0.023950 0.057867 -2.78e-02 0.036502 0.07549 1.059 1.43e-03 0.03782
## 41 -0.005261 -0.004084 1.12e-02 0.007449 0.01465 1.058 5.40e-05 0.03463
## 42 0.007386 0.024805 -4.33e-02 0.015758 -0.05366 1.058 7.23e-04 0.03553
## 43 0.000497 -0.000108 -2.15e-05 -0.001136 0.00181 1.031 8.26e-07 0.00873
## 44 0.000119 0.006173 -1.02e-02 0.007543 -0.01660 1.038 6.93e-05 0.01569
## 45 0.071504 -0.037415 -5.69e-02 0.059982 0.11123 1.037 3.10e-03 0.02458
## 46 0.071504 -0.037415 -5.69e-02 0.059982 0.11123 1.037 3.10e-03 0.02458
## 47 0.003355 -0.006925 1.09e-03 0.003110 -0.00878 1.046 1.94e-05 0.02300
## 48 0.005169 -0.005518 1.21e-03 -0.005341 0.00992 1.035 2.47e-05 0.01260
## 49 0.005248 0.002012 -5.40e-03 -0.008008 0.01373 1.032 4.74e-05 0.01036
## 50 0.051922 0.003897 -7.34e-02 0.061823 0.11147 1.036 3.11e-03 0.02415
## 51 0.006947 -0.002144 -3.22e-03 -0.008430 0.01378 1.031 4.77e-05 0.00960
## 52 0.002587 -0.000426 -5.39e-04 -0.005311 0.00847 1.031 1.80e-05 0.00877
## 53 0.002918 -0.007182 3.52e-03 0.046100 0.05989 1.030 9.00e-04 0.01373
## 54 -0.009371 0.075260 -6.52e-02 0.060691 0.12006 1.047 3.61e-03 0.03257
## 55 0.025701 -0.016919 -8.45e-03 -0.019030 0.03524 1.033 3.12e-04 0.01317
## 56 0.043503 -0.035010 -1.19e-02 -0.023591 0.05241 1.040 6.90e-04 0.02020
## 57 0.032753 -0.014341 -2.89e-02 0.064991 0.09284 1.026 2.16e-03 0.01576
## 58 -0.001282 0.001487 6.71e-04 -0.000953 0.00244 1.041 1.49e-06 0.01828
## 59 0.037587 -0.014584 -2.40e-02 -0.025402 0.04879 1.033 5.98e-04 0.01442
## 60 0.036080 -0.031991 -4.83e-03 -0.023625 0.04873 1.036 5.96e-04 0.01670
## 61 0.036080 -0.031991 -4.83e-03 -0.023625 0.04873 1.036 5.96e-04 0.01670
## 62 0.013580 -0.000264 -9.00e-03 -0.019278 0.03157 1.029 2.50e-04 0.00950
## 63 0.016946 0.006251 -1.91e-02 -0.021888 0.03920 1.031 3.86e-04 0.01148
## 64 -0.005325 0.009425 1.67e-03 -0.008635 0.01773 1.035 7.90e-05 0.01278
## 65 -0.022027 0.025913 2.66e-03 0.058984 0.07884 1.029 1.56e-03 0.01530
## 66 -0.000684 -0.008360 1.31e-02 -0.007342 0.01885 1.044 8.93e-05 0.02113
## 67 0.015433 0.005918 -1.59e-02 -0.023551 0.04037 1.029 4.09e-04 0.01036
## 68 -0.001456 0.000116 1.83e-03 0.000671 0.00202 1.134 1.03e-06 0.09848 *
## 69 0.012677 -0.018327 1.16e-02 -0.020699 0.03838 1.032 3.70e-04 0.01202
## 70 -0.001604 -0.007385 1.61e-02 -0.013177 0.02745 1.035 1.89e-04 0.01389
## 71 0.028519 -0.005513 -3.24e-02 0.078038 0.10801 1.020 2.92e-03 0.01504
## 72 -0.060930 0.060220 1.92e-02 0.056342 0.09562 1.043 2.29e-03 0.02691
## 73 0.016566 0.005626 -2.79e-02 0.078029 0.10526 1.020 2.77e-03 0.01454
## 74 0.073992 -0.061639 -1.76e-02 -0.041043 0.09078 1.034 2.07e-03 0.01991
## 75 0.046789 -0.090122 3.06e-02 0.078708 0.13879 1.029 4.82e-03 0.02383
## 76 0.001018 0.001581 -3.36e-03 0.000698 -0.00372 1.108 3.47e-06 0.07758 *
## 77 -0.003156 0.008058 8.08e-03 -0.025213 0.04339 1.027 4.73e-04 0.00950
## 78 -0.074166 0.102635 -6.94e-03 0.079096 0.14103 1.038 4.98e-03 0.02915
## 79 0.038146 -0.039390 -1.03e-02 0.091207 0.12751 1.014 4.06e-03 0.01526
## 80 -0.015551 -0.007759 3.55e-02 -0.013077 0.04230 1.052 4.50e-04 0.02960
## 81 0.019521 -0.011798 2.25e-03 -0.034769 0.05622 1.024 7.93e-04 0.00910
## 82 -0.033092 0.029875 2.13e-02 -0.014575 0.04852 1.050 5.91e-04 0.02805
## 83 -0.004887 0.066567 -4.42e-02 -0.037340 0.09633 1.035 2.33e-03 0.02141
## 84 0.038290 -0.031119 -5.99e-04 -0.040591 0.07027 1.023 1.24e-03 0.01092
## 85 0.026824 -0.001898 -1.35e-02 -0.044081 0.07089 1.019 1.26e-03 0.00906
## 86 0.082283 -0.100465 -6.15e-03 0.109260 0.17929 1.009 8.01e-03 0.02025
## 87 0.092041 -0.047433 -4.84e-02 -0.058737 0.11480 1.018 3.30e-03 0.01509
## 88 0.019599 -0.004264 -8.47e-04 -0.044758 0.07143 1.018 1.28e-03 0.00873
## 89 -0.064624 0.064423 3.10e-02 -0.019614 0.08650 1.066 1.88e-03 0.04442 *
## 90 0.035433 -0.014691 -9.06e-03 -0.050207 0.08090 1.016 1.64e-03 0.00920
## 91 0.009511 0.005537 2.85e-03 -0.044888 0.07278 1.018 1.33e-03 0.00877
## 92 0.031008 -0.029104 1.12e-02 -0.048814 0.08240 1.017 1.70e-03 0.01000
## 93 -0.086386 -0.071313 1.89e-01 0.068857 0.20944 1.111 1.10e-02 0.08891 *
## 94 0.043599 0.061232 -1.21e-01 0.125890 0.20889 1.001 1.09e-02 0.02163
## 95 0.067162 -0.129363 4.39e-02 0.112978 0.19923 1.011 9.89e-03 0.02383
## 96 -0.027422 0.058908 -3.07e-03 -0.042475 0.09335 1.024 2.18e-03 0.01461
## 97 -0.042269 0.045184 2.80e-02 -0.035391 0.08495 1.029 1.81e-03 0.01637
## 98 0.008837 -0.075828 6.65e-02 0.107804 0.16723 1.011 6.98e-03 0.01956
## 99 0.008837 -0.075828 6.65e-02 0.107804 0.16723 1.011 6.98e-03 0.01956
## 100 -0.038956 0.073442 -1.33e-03 -0.044602 0.10679 1.025 2.86e-03 0.01690
## 101 0.049793 0.018367 -5.60e-02 -0.064314 0.11517 1.008 3.31e-03 0.01148
## 102 -0.054707 -0.091639 1.68e-01 0.107823 0.22371 1.033 1.25e-02 0.03761
## 103 0.052589 0.019398 -5.92e-02 -0.067926 0.12164 1.006 3.69e-03 0.01148
## 104 0.063304 0.003529 -5.68e-02 -0.069110 0.12118 1.005 3.67e-03 0.01119
## 105 0.075283 -0.048369 -2.00e-02 -0.068213 0.11857 1.006 3.51e-03 0.01124
## 106 -0.067362 -0.011019 1.13e-01 -0.020458 0.12038 1.105 3.64e-03 0.07845 *
## 107 -0.011579 0.111754 -6.94e-02 -0.063029 0.16071 1.016 6.45e-03 0.02078
## 108 -0.020948 -0.032951 8.68e-02 -0.050225 0.12223 1.023 3.74e-03 0.01830
## 109 0.093598 -0.109185 -1.23e-02 0.144900 0.22415 0.982 1.24e-02 0.01821
## 110 0.029686 -0.123475 1.16e-01 -0.059848 0.18276 1.033 8.35e-03 0.03203
## 111 -0.105328 0.073457 8.57e-02 -0.037327 0.14338 1.046 5.15e-03 0.03526
## 112 0.111409 -0.093142 -1.68e-02 -0.081089 0.15712 1.000 6.15e-03 0.01445
## 113 -0.087346 0.128702 -1.63e-02 0.143828 0.21991 0.993 1.20e-02 0.02058
## 114 -0.054928 0.172276 -7.09e-02 -0.067064 0.21094 1.020 1.11e-02 0.02942
## 115 -0.052847 -0.088045 1.62e-01 0.137513 0.24377 1.003 1.48e-02 0.02703
## 116 -0.030166 0.075455 -4.69e-03 -0.066912 0.13552 1.003 4.58e-03 0.01268
## 117 0.134454 -0.181968 4.56e-02 -0.085393 0.22222 1.010 1.23e-02 0.02669
## 118 -0.024255 0.081651 -1.72e-02 -0.070913 0.14366 1.000 5.14e-03 0.01285
## 119 0.030939 0.036721 -4.17e-02 -0.080163 0.13785 0.992 4.73e-03 0.01009
## 120 0.231828 -0.146254 -1.13e-01 -0.108003 0.25545 0.988 1.62e-02 0.02386
## 121 0.013578 -0.073539 9.15e-02 -0.070948 0.15795 1.006 6.22e-03 0.01645
## 122 -0.056540 0.029014 7.95e-02 -0.067236 0.14685 1.003 5.38e-03 0.01407
## 123 0.101715 -0.041890 -5.03e-02 -0.094223 0.16122 0.982 6.45e-03 0.01087
## 124 0.055357 -0.029380 -1.59e-03 -0.090776 0.14623 0.981 5.31e-03 0.00908
## 125 0.012045 0.034957 -9.52e-03 -0.089653 0.14954 0.979 5.55e-03 0.00920
## 126 -0.049778 0.176766 -7.24e-02 -0.088243 0.23476 0.990 1.37e-02 0.02164
## 127 -0.182450 0.187668 8.53e-02 -0.063046 0.25364 1.026 1.60e-02 0.03847
## 128 0.104783 -0.114372 -2.18e-02 0.194016 0.28457 0.937 1.98e-02 0.01657
## 129 0.085992 0.033284 -8.63e-02 -0.136218 0.23171 0.923 1.31e-02 0.01017 *
## 130 -0.467133 0.886277 -2.12e-01 -0.138582 0.92825 0.969 2.08e-01 0.10239 *
## 131 0.100923 -0.225752 9.84e-02 -0.280839 -0.42335 0.860 4.29e-02 0.01941 *
## 132 0.085082 -0.237517 4.88e-02 0.167885 -0.36904 0.856 3.26e-02 0.01485 *
## 133 0.550740 -0.382401 -3.41e-01 -0.300249 -0.66120 0.901 1.05e-01 0.04998 *
## 134 -0.105771 -0.078565 1.58e-01 0.141173 -0.27577 0.921 1.86e-02 0.01362 *
## 135 -0.152417 -0.085864 2.36e-01 0.126070 -0.30701 0.957 2.32e-02 0.02246
## 136 0.090241 -0.094673 -8.48e-02 0.123956 -0.25360 0.928 1.57e-02 0.01252 *
## 137 -0.142788 -0.016688 1.56e-01 0.117826 -0.23712 0.960 1.39e-02 0.01532
## 138 -0.037928 -0.017934 1.63e-02 0.112378 -0.18140 0.952 8.11e-03 0.00883
## 139 -0.026246 -0.014458 -2.38e-03 0.110671 -0.17903 0.954 7.90e-03 0.00876
## 140 0.060283 0.070044 -1.53e-01 -0.150447 -0.24651 0.990 1.51e-02 0.02313
## 141 0.063565 -0.185748 1.07e-01 -0.126488 -0.25503 1.019 1.62e-02 0.03528
## 142 -0.092777 0.040222 8.24e-02 -0.087442 -0.15540 1.023 6.04e-03 0.02291
## 143 -0.047586 -0.045950 6.75e-02 0.093510 -0.16642 0.979 6.87e-03 0.01097
## 144 -0.140326 0.164572 -2.60e-02 0.098783 -0.22145 0.988 1.22e-02 0.01943
## 145 -0.036264 -0.045829 9.58e-02 -0.091189 -0.15626 1.023 6.10e-03 0.02293
## 146 0.007898 0.066654 -7.94e-02 -0.119530 -0.18024 1.004 8.09e-03 0.01881
## 147 0.123679 0.131362 -3.57e-01 0.109653 -0.41116 0.976 4.16e-02 0.04000
## 148 0.067532 -0.004288 -8.58e-02 -0.128192 -0.18213 1.000 8.25e-03 0.01764
## 149 -0.114475 0.029994 8.44e-02 0.084948 -0.15983 0.995 6.36e-03 0.01361
## 150 -0.081550 0.061821 7.82e-03 0.082419 -0.14247 0.993 5.05e-03 0.01096
## 151 -0.083203 -0.048824 1.28e-01 0.074343 -0.17319 1.011 7.48e-03 0.02031
## 152 -0.121957 0.058598 7.00e-02 0.074786 -0.14938 1.008 5.57e-03 0.01590
## 153 -0.050694 0.041300 2.51e-02 -0.074476 -0.11263 1.024 3.18e-03 0.01733
## 154 0.010371 -0.045462 3.31e-02 -0.087049 -0.12266 1.019 3.76e-03 0.01648
## 155 -0.006811 -0.006992 -2.23e-02 0.080805 -0.13380 0.988 4.45e-03 0.00901
## 156 -0.044599 0.074257 -1.71e-02 -0.077388 -0.12678 1.026 4.02e-03 0.02060
## 157 -0.032670 0.032067 1.05e-02 -0.075027 -0.10518 1.022 2.77e-03 0.01531
## 158 -0.004790 0.011792 -5.78e-03 -0.075687 -0.09832 1.021 2.42e-03 0.01373
## 159 0.012951 -0.064130 1.41e-02 0.071820 -0.13484 0.998 4.53e-03 0.01124
## 160 -0.049192 0.010276 5.51e-02 -0.042646 -0.08294 1.045 1.73e-03 0.02714
## 161 -0.049939 0.047000 1.82e-02 -0.053493 -0.09048 1.035 2.05e-03 0.02107
## 162 -0.046242 -0.034348 6.90e-02 0.061719 -0.12056 1.013 3.63e-03 0.01362
## 163 -0.083984 0.038660 4.48e-02 0.062254 -0.11411 1.013 3.26e-03 0.01291
## 164 -0.050499 0.096242 -6.35e-02 0.068717 -0.15188 1.011 5.76e-03 0.01732
## 165 -0.037728 0.032553 1.68e-02 -0.045774 -0.07338 1.036 1.35e-03 0.01916
## 166 -0.022606 0.023343 6.09e-03 -0.054051 -0.07556 1.029 1.43e-03 0.01526
## 167 -0.077130 0.018050 6.04e-02 0.054580 -0.10576 1.020 2.80e-03 0.01456
## 168 -0.042910 -0.044662 7.95e-02 0.052420 -0.11796 1.024 3.48e-03 0.01825
## 169 0.018113 -0.067271 4.53e-02 -0.050072 -0.09819 1.050 2.42e-03 0.03281
## 170 -0.102218 0.087736 2.39e-02 0.051937 -0.12228 1.032 3.75e-03 0.02305
## 171 0.082342 0.023222 -1.34e-01 -0.089965 -0.17281 1.038 7.47e-03 0.03387
## 172 -0.017584 0.019131 3.73e-03 -0.043844 -0.06115 1.032 9.39e-04 0.01522
## 173 -0.010912 -0.010887 2.58e-02 -0.039107 -0.05759 1.036 8.33e-04 0.01718
## 174 -0.094828 0.088156 1.39e-02 0.050814 -0.11896 1.032 3.55e-03 0.02248
## 175 -0.035305 0.001090 2.21e-02 0.051879 -0.08449 1.015 1.79e-03 0.00937
## 176 0.056630 -0.062753 -1.08e-02 -0.064548 -0.10307 1.036 2.66e-03 0.02322
## 177 -0.002967 0.007304 -3.58e-03 -0.046881 -0.06090 1.030 9.31e-04 0.01373
## 178 -0.026683 0.032579 1.99e-03 -0.035431 -0.05814 1.039 8.49e-04 0.02025
## 179 -0.010440 -0.003407 1.75e-02 -0.035190 -0.04920 1.034 6.08e-04 0.01546
## 180 -0.071217 0.064466 7.85e-03 0.047298 -0.09754 1.027 2.38e-03 0.01664
## 181 0.038059 -0.026938 -5.13e-02 0.056751 -0.11528 1.011 3.32e-03 0.01242
## 182 -0.060970 0.025029 3.69e-02 0.042447 -0.08018 1.026 1.61e-03 0.01387
## 183 0.100468 -0.013488 -1.20e-01 -0.082427 -0.15924 1.044 6.35e-03 0.03558
## 184 -0.023533 0.022202 8.50e-03 -0.016324 -0.03421 1.053 2.94e-04 0.03060
## 185 -0.001162 -0.025846 2.82e-02 -0.027386 -0.04991 1.048 6.26e-04 0.02702
## 186 -0.080557 0.063407 2.75e-02 0.035229 -0.08978 1.045 2.02e-03 0.02820
## 187 -0.010177 -0.003157 1.69e-02 -0.017779 -0.02902 1.042 2.12e-04 0.02040
## 188 -0.049444 0.076085 -3.45e-02 0.048636 -0.10883 1.027 2.97e-03 0.01838
## 189 -0.005695 0.010896 -3.65e-03 -0.034829 -0.04647 1.033 5.42e-04 0.01432Distinction between outliers and influential data points
考慮這個點是outliers 還是influential
範例 它同時做了很多假設
Global test of model assumptions
the gvlmapackage, performs a global validation of linear model assumptions as well separate evaluations of skewness, kurtosis, and heteroscedasticity install.packages(“gvlma”)
library(gvlma)
gvmodel<-gvlma(fit)
summary(gvmodel)##
## Call:
## lm(formula = BWT ~ AGE + LWT + SMOKE)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2069.89 -433.18 13.67 516.45 1813.75
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2362.720 300.687 7.858 3.11e-13 ***
## AGE 7.093 9.925 0.715 0.4757
## LWT 4.019 1.720 2.337 0.0205 *
## SMOKE -267.213 105.802 -2.526 0.0124 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 708.8 on 185 degrees of freedom
## Multiple R-squared: 0.06988, Adjusted R-squared: 0.05479
## F-statistic: 4.633 on 3 and 185 DF, p-value: 0.003781
##
##
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance = 0.05
##
## Call:
## gvlma(x = fit)
##
## Value p-value Decision
## Global Stat 31.5604 2.353e-06 Assumptions NOT satisfied!
## Skewness 3.7646 5.235e-02 Assumptions acceptable.
## Kurtosis 0.2277 6.332e-01 Assumptions acceptable.
## Link Function 0.1574 6.916e-01 Assumptions acceptable.
## Heteroscedasticity 27.4107 1.645e-07 Assumptions NOT satisfied!Variable Selection
Stepwise Regression
install.packages(“MASS”)
library(MASS)
y =c(202,186,187,180,156,169,174,172,153,199,193,174,198,183,178)
x1 = c(18,23,25,35,65,54,34,56,72,19,23,42,18,39,37)
x2 = c(56,45,67,89,65,76,55,66,77,63,53,49,76,62,53)
x3 = c(6,5,7,9,5,6,5,6,7,3,3,9,6,2,3)
fit <-lm(y~x1+x2+x3)
step <-stepAIC(fit, direction="both") # direction = c("both", "backward", "forward")## Start: AIC=48.81
## y ~ x1 + x2 + x3
##
## Df Sum of Sq RSS AIC
## - x3 1 26.45 254.35 48.460
## <none> 227.89 48.812
## - x2 1 34.09 261.99 48.904
## - x1 1 2504.38 2732.27 84.073
##
## Step: AIC=48.46
## y ~ x1 + x2
##
## Df Sum of Sq RSS AIC
## - x2 1 18.08 272.43 47.490
## <none> 254.35 48.460
## + x3 1 26.45 227.89 48.812
## - x1 1 2582.36 2836.71 82.635
##
## Step: AIC=47.49
## y ~ x1
##
## Df Sum of Sq RSS AIC
## <none> 272.43 47.490
## + x2 1 18.08 254.35 48.460
## + x3 1 10.45 261.99 48.904
## - x1 1 2724.50 2996.93 81.459# -的 back +的for
step$anova # display results## Stepwise Model Path
## Analysis of Deviance Table
##
## Initial Model:
## y ~ x1 + x2 + x3
##
## Final Model:
## y ~ x1
##
##
## Step Df Deviance Resid. Df Resid. Dev AIC
## 1 11 227.8941 48.81246
## 2 - x3 1 26.45498 12 254.3491 48.45986
## 3 - x2 1 18.08209 13 272.4312 47.49004