다음 자료는 토양으로부터 증발되는 수분의 양이 토양의 온도, 대기온도와
어떠한 관계가 있는지를 알아보고자 수집한 것이다.
MAXST: 토양 내
최고온도
MINST: 토양 내 최저온도
AVST: 토양 내 평균온도
MAXAT: 최고기온
MINAT: 최저기온
AVAT: 평균기온
EVAP:
증발되는 수분의 양
DAY = c(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30)
MAXST = c(84,84,79,81,84,74,73,75,84,86,88,90,88,88,81,79,84,84,84,77,87,89,89,93,93)
MINST = c(65,65,66,67,68,66,66,67,68,72,73,74,72,72,69,68,69,70,70,67,67,69,72,72,74)
AVST = c(147,149,142,147,167,131,131,134,161,169,178,187,171,171,154,149,160,160,168,147,166,171,180,186,188)
MAXAT = c(85,86,83,83,88,77,78,84,89,91,91,94,94,92,87,83,87,87,88,83,92,92,94,92,93)
MINAT = c(59,61,64,65,69,67,69,68,71,76,76,76,75,70,68,68,66,68,70,66,67,72,72,73,72)
AVAT = c(151,159,152,158,180,147,159,159,195,206,208,211,211,201,167,162,173,177,169,170,196,199,204,201,206)
EVAP = c(30,34,33,26,41,4,5,20,31,38,43,47,45,45,11,10,30,29,23,16,37,50,36,54,44)
dataF = data.frame(DAY, MAXST, AVST, MAXAT, MINAT, AVAT, EVAP)
str(DAY)## num [1:25] 6 7 8 9 10 11 12 13 14 15 ...str(AVST)## num [1:25] 147 149 142 147 167 131 131 134 161 169 ...str(dataF)## 'data.frame': 25 obs. of 7 variables:
## $ DAY : num 6 7 8 9 10 11 12 13 14 15 ...
## $ MAXST: num 84 84 79 81 84 74 73 75 84 86 ...
## $ AVST : num 147 149 142 147 167 131 131 134 161 169 ...
## $ MAXAT: num 85 86 83 83 88 77 78 84 89 91 ...
## $ MINAT: num 59 61 64 65 69 67 69 68 71 76 ...
## $ AVAT : num 151 159 152 158 180 147 159 159 195 206 ...
## $ EVAP : num 30 34 33 26 41 4 5 20 31 38 ...#install.packages("corrplot")
library(corrplot)## Warning: package 'corrplot' was built under R version 4.1.3
## corrplot 0.92 loadedplot(dataF)
matrixVal = matrix(dataF)
str(matrixVal)## List of 7
## $ : num [1:25] 6 7 8 9 10 11 12 13 14 15 ...
## $ : num [1:25] 84 84 79 81 84 74 73 75 84 86 ...
## $ : num [1:25] 147 149 142 147 167 131 131 134 161 169 ...
## $ : num [1:25] 85 86 83 83 88 77 78 84 89 91 ...
## $ : num [1:25] 59 61 64 65 69 67 69 68 71 76 ...
## $ : num [1:25] 151 159 152 158 180 147 159 159 195 206 ...
## $ : num [1:25] 30 34 33 26 41 4 5 20 31 38 ...
## - attr(*, "dim")= int [1:2] 7 1cor(dataF) ## DAY MAXST AVST MAXAT MINAT AVAT EVAP
## DAY 1.0000000 0.5119643 0.6057847 0.5357711 0.4468035 0.5497730 0.2753970
## MAXST 0.5119643 1.0000000 0.9486608 0.9268580 0.5048854 0.8250186 0.8933048
## AVST 0.6057847 0.9486608 1.0000000 0.9282693 0.6834957 0.8928071 0.8173403
## MAXAT 0.5357711 0.9268580 0.9282693 1.0000000 0.6256655 0.9094757 0.8509974
## MINAT 0.4468035 0.5048854 0.6834957 0.6256655 1.0000000 0.8307017 0.4544024
## AVAT 0.5497730 0.8250186 0.8928071 0.9094757 0.8307017 1.0000000 0.7675541
## EVAP 0.2753970 0.8933048 0.8173403 0.8509974 0.4544024 0.7675541 1.0000000corrplot(cor(dataF), method="number")
head(dataF)## DAY MAXST AVST MAXAT MINAT AVAT EVAP
## 1 6 84 147 85 59 151 30
## 2 7 84 149 86 61 159 34
## 3 8 79 142 83 64 152 33
## 4 9 81 147 83 65 158 26
## 5 10 84 167 88 69 180 41
## 6 11 74 131 77 67 147 4data.lm = lm(EVAP~DAY+MAXST+AVST+MAXAT+MINAT+AVAT, data=dataF)
summary(data.lm)##
## Call:
## lm(formula = EVAP ~ DAY + MAXST + AVST + MAXAT + MINAT + AVAT,
## data = dataF)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.9404 -3.5317 -0.9769 1.6295 11.0227
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -184.9217 75.7520 -2.441 0.0252 *
## DAY -0.4731 0.2195 -2.156 0.0449 *
## MAXST 2.5123 1.0853 2.315 0.0326 *
## AVST -0.2582 0.3787 -0.682 0.5041
## MAXAT 0.3312 0.9557 0.347 0.7329
## MINAT -0.1203 0.7669 -0.157 0.8771
## AVAT 0.1913 0.2329 0.821 0.4222
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.996 on 18 degrees of freedom
## Multiple R-squared: 0.864, Adjusted R-squared: 0.8187
## F-statistic: 19.06 on 6 and 18 DF, p-value: 6.733e-07anova(data.lm)## Analysis of Variance Table
##
## Response: EVAP
## Df Sum Sq Mean Sq F value Pr(>F)
## DAY 1 360.9 360.9 10.0400 0.005317 **
## MAXST 1 3650.2 3650.2 101.5351 7.942e-09 ***
## AVST 1 0.0 0.0 0.0004 0.984404
## MAXAT 1 59.9 59.9 1.6668 0.213018
## MINAT 1 16.6 16.6 0.4604 0.506051
## AVAT 1 24.3 24.3 0.6747 0.422162
## Residuals 18 647.1 36.0
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#install.packages("fmsb")
library(fmsb)## Warning: package 'fmsb' was built under R version 4.1.3VIF(lm(DAY~MAXST+AVST+MAXAT+MINAT+AVAT, data=dataF))## [1] 1.74147VIF(lm(MAXST~AVST+MAXAT+MINAT+AVAT+DAY, data=dataF))## [1] 23.84687VIF(lm(AVST~MAXAT+MINAT+AVAT+DAY+MAXST, data=dataF))## [1] 27.78584VIF(lm(MAXAT~MINAT+AVAT+DAY+MAXST+AVST, data=dataF))## [1] 14.4067VIF(lm(MINAT~AVAT+DAY+MAXST+AVST+MAXAT, data=dataF))## [1] 7.633176Y = c(10.006, 9.737, 15.087, 8.422, 8.625, 16.289, 5.958, 9.313, 12.960, 5.541, 8.756, 10.937)
X1=c(8,8,8,0,0,0,2,2,2,0,0,0)
X2=c(1,1,1,0,0,0,7,7,7,0,0,0)
X3=c(1,1,1,9,9,9,0,0,0,0,0,0)
X4=c(1,0,0,1,1,1,1,1,1,10,10,10)
X5=c(0.541, 0.130, 2.116, -2.397, -0.046, 0.365, 1.996, 0.228, 1.380, -0.798, 0.257, 0.440)
X6=c(-0.099, 0.070, 0.115, 0.252, 0.017, 1.504, -0.865, -0.055, 0.502, -0.399, 0.101, 0.432)
dataF = data.frame(X1,X2,X3,X4,X5,X6,Y)
cor(dataF[,-7])## X1 X2 X3 X4 X5 X6
## X1 1.00000000 0.05230658 -0.3433818 -0.49761095 0.4172974 -0.19209942
## X2 0.05230658 1.00000000 -0.4315953 -0.37069641 0.4845495 -0.31673965
## X3 -0.34338179 -0.43159531 1.0000000 -0.35512135 -0.5051579 0.49437941
## X4 -0.49761095 -0.37069641 -0.3551214 1.00000000 -0.2145543 -0.08690551
## X5 0.41729739 0.48454950 -0.5051579 -0.21455429 1.0000000 -0.12295400
## X6 -0.19209942 -0.31673965 0.4943794 -0.08690551 -0.1229540 1.00000000head(dataF)## X1 X2 X3 X4 X5 X6 Y
## 1 8 1 1 1 0.541 -0.099 10.006
## 2 8 1 1 0 0.130 0.070 9.737
## 3 8 1 1 0 2.116 0.115 15.087
## 4 0 0 9 1 -2.397 0.252 8.422
## 5 0 0 9 1 -0.046 0.017 8.625
## 6 0 0 9 1 0.365 1.504 16.289data.lm = lm(Y~X1+X2+X3+X4+X5, data=dataF)
summary(data.lm)##
## Call:
## lm(formula = Y ~ X1 + X2 + X3 + X4 + X5, data = dataF)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.8104 -1.1245 0.1114 1.6036 3.3694
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 22.5823 41.7129 0.541 0.608
## X1 -1.1835 3.9822 -0.297 0.776
## X2 -1.6352 4.2127 -0.388 0.711
## X3 -0.9861 4.1922 -0.235 0.822
## X4 -1.4113 4.1674 -0.339 0.746
## X5 1.7090 1.1253 1.519 0.180
##
## Residual standard error: 3.36 on 6 degrees of freedom
## Multiple R-squared: 0.4236, Adjusted R-squared: -0.0568
## F-statistic: 0.8818 on 5 and 6 DF, p-value: 0.5452anova(data.lm)## Analysis of Variance Table
##
## Response: Y
## Df Sum Sq Mean Sq F value Pr(>F)
## X1 1 7.461 7.4614 0.6608 0.4473
## X2 1 1.477 1.4772 0.1308 0.7300
## X3 1 10.940 10.9404 0.9689 0.3630
## X4 1 3.859 3.8592 0.3418 0.5801
## X5 1 26.046 26.0463 2.3066 0.1796
## Residuals 6 67.752 11.2921#install.packages("fmsb")
library(fmsb)
VIF(lm(X1~X2+X3+X4+X5, data=dataF))## [1] 181.1577VIF(lm(X2~X3+X4+X5+X1, data=dataF))## [1] 160.3068VIF(lm(X3~X4+X5+X1+X2, data=dataF))## [1] 266.1398VIF(lm(X4~X5+X1+X2+X3, data=dataF))## [1] 296.7028VIF(lm(X5~X1+X2+X3+X4, data=dataF))## [1] 1.797182교통사고의 원인을 알아보기 위해서 1973년 미국 미네소타주의 도로 39개
구간에서 자동차 주행거리 100만 마일당 사고의 횟수를 반응변수로 하고,
사고의 원인이 될 수 있는 것으로 예상되는 13개의 설명변수를 얻은 자료이다
Y: 100만 마일의 자동차 주행거리당 사고의 횟수
X1: 구간의
길이(miles) X2: 일 평균 통과 자동차수(천 대) X3: 트럭의 비율 X4:
제한속도(mile/hour) X5: 차선의 폭(feet) X6: 갓길의 폭(feet) X7: 1마일당
고속도로 진입로의 수 X8: 1마일당 신호등이 있는 교차로의 수 X9: 1마일당
진입로의 수 X10: 차선의 수 X11: 1: 연방고속도로, 0: 기타 X12: 1:
principal arterial highway, 0: 기타 X13: 1: major arterial highway, 0:
기타
Y = c(4.58,2.86,3.02,2.29,1.61,6.87,3.85,6.12,3.29,5.88,4.20,4.61,4.80,3.85,2.69,1.99,2.01,4.22,2.76,2.55,1.89,2.34,2.83,1.81,9.23,8.60,8.21,2.93,7.48,2.57,5.77,2.90,2.97,1.84,3.78,2.76,4.27,3.05,4.12)
X1 = c(4.99,16.11,9.75,10.65,20.01,5.97,8.57,5.24,15.79,8.26,7.03,13.28,5.40,2.96,11.75,8.86,9.78,5.49,8.63,20.31,40.09,11.81,11.39,22.00,3.58,3.23,7.73,14.41,11.54,11.10,22.09,9.39,19.49,21.01,27.16,14.03,20.63,20.06,12.91)
X2 = c(69,73,49,61,28,30,46,25,43,23,23,20,18,21,27,22,19,9,12,12,15,8,5,5,23,13,7,10,12,9,4,5,4,5,2,3,1,3,1)
X3 = c(8,8,10,13,12,6,8,9,12,7,6,9,14,8,7,9,9,11,8,7,13,8,9,15,6,6,8,10,7,8,8,10,13,12,10,8,11,11,10)
X4 = c(55,60,60,65,70,55,55,55,50,50,60,50,50,60,55,60,60,50,55,60,55,60,50,60,40,45,55,55,45,60,45,55,55,55,55,50,55,60,55)
X5 = c(12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,12,12,12,12,12,12,12,12,12,12,12,11,13,12,10,12,12,11,12,12)
X6 = c(10,10,10,10,10,10,8,10,4,5,10,2,8,10,10,10,10,6,6,10,8,10,8,7,2,2,8,6,3,7,3,1,4,8,3,4,4,8,3)
X7 = c(1.20,1.43,1.54,0.94,0.65,0.34,0.47,0.38,0.95,0.12,0.29,0.15,0,0.34,0.26,0.68,0.20,0.18,0.14,0.05,0.05,0,0,0,0.56,0.31,0.13,0,0.09,0,0,0,0,0,0.04,0.07,0,0,0)
X8 = c(0,0,0,0,0,1.84,0.70,0.38,1.39,1.21,1.85,1.21,0.56,0,0.60,0,0.10,0.18,0,0.99,0.12,0,0.09,0,2.51,0.93,0.52,0.07,0.09,0,0.14,0,0,0.10,0.04,0,0,0,0)
X9 = c(4.60,4.40,4.70,3.80,2.20,24.80,11.00,18.50,7.50,8.20,5.40,11.20,15.20,5.40,7.90,3.20,11.00,8.90,12.40,7.80,9.60,4.30,11.10,6.80,53.00,17.30,27.30,18.00,30.20,10.30,18.20,12.30,7.10,14.00,11.30,16.30,9.60,9.00,10.40)
X10 = c(8,4,4,6,4,4,4,4,4,4,4,4,2,4,4,4,4,2,2,4,4,2,2,2,4,2,2,2,2,2,2,2,2,2,2,2,2,2,2)
X11 = c(1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)
X12 = c(0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)
X13 = c(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0)
str(X7)## num [1:39] 1.2 1.43 1.54 0.94 0.65 0.34 0.47 0.38 0.95 0.12 ...dataF = data.frame(Y,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13)start.lm = lm(Y~1, data=dataF)
full.lm = lm(Y~ . , data=dataF)
step(start.lm, scope=list(lower=start.lm, upper=full.lm), direction="forward")## Start: AIC=54.51
## Y ~ 1
##
## Df Sum of Sq RSS AIC
## + X9 1 84.767 65.119 23.994
## + X4 1 69.508 80.378 32.204
## + X8 1 47.759 102.127 41.543
## + X3 1 39.372 110.514 44.622
## + X1 1 32.449 117.437 46.991
## + X6 1 22.438 127.449 50.182
## + X13 1 17.108 132.778 51.780
## <none> 149.886 54.506
## + X11 1 6.460 143.426 54.788
## + X12 1 3.911 145.975 55.475
## + X10 1 0.163 149.723 56.464
## + X2 1 0.122 149.764 56.474
## + X7 1 0.092 149.794 56.482
## + X5 1 0.005 149.881 56.505
##
## Step: AIC=23.99
## Y ~ X9
##
## Df Sum of Sq RSS AIC
## + X1 1 12.9806 52.139 17.323
## + X3 1 10.0532 55.066 19.454
## + X4 1 7.9430 57.176 20.920
## + X8 1 7.1603 57.959 21.451
## <none> 65.119 23.994
## + X2 1 3.0871 62.032 24.099
## + X7 1 2.4664 62.653 24.488
## + X10 1 2.4108 62.708 24.522
## + X6 1 0.8293 64.290 25.494
## + X13 1 0.4750 64.644 25.708
## + X11 1 0.4259 64.693 25.738
## + X5 1 0.1013 65.018 25.933
## + X12 1 0.0148 65.104 25.985
##
## Step: AIC=17.32
## Y ~ X9 + X1
##
## Df Sum of Sq RSS AIC
## + X4 1 7.2920 44.847 13.448
## + X8 1 3.4703 48.668 16.637
## + X6 1 3.2651 48.873 16.801
## + X3 1 2.9834 49.155 17.025
## <none> 52.139 17.323
## + X5 1 0.8546 51.284 18.679
## + X12 1 0.4613 51.677 18.977
## + X10 1 0.3814 51.757 19.037
## + X2 1 0.3062 51.832 19.094
## + X7 1 0.2262 51.912 19.154
## + X13 1 0.1771 51.962 19.191
## + X11 1 0.0457 52.093 19.289
##
## Step: AIC=13.45
## Y ~ X9 + X1 + X4
##
## Df Sum of Sq RSS AIC
## + X8 1 2.51322 42.333 13.198
## + X3 1 2.40652 42.440 13.297
## <none> 44.847 13.448
## + X11 1 1.47651 43.370 14.142
## + X10 1 1.30168 43.545 14.299
## + X12 1 1.21471 43.632 14.377
## + X2 1 0.93309 43.913 14.628
## + X7 1 0.87112 43.975 14.683
## + X5 1 0.38786 44.459 15.109
## + X6 1 0.01982 44.827 15.431
## + X13 1 0.00346 44.843 15.445
##
## Step: AIC=13.2
## Y ~ X9 + X1 + X4 + X8
##
## Df Sum of Sq RSS AIC
## + X12 1 4.1181 38.215 11.207
## <none> 42.333 13.198
## + X11 1 1.8859 40.447 13.421
## + X3 1 1.4051 40.928 13.882
## + X13 1 0.6230 41.710 14.620
## + X7 1 0.4833 41.850 14.751
## + X5 1 0.3969 41.936 14.831
## + X2 1 0.3231 42.010 14.900
## + X10 1 0.2948 42.039 14.926
## + X6 1 0.1400 42.193 15.069
##
## Step: AIC=11.21
## Y ~ X9 + X1 + X4 + X8 + X12
##
## Df Sum of Sq RSS AIC
## <none> 38.215 11.207
## + X3 1 1.05617 37.159 12.114
## + X6 1 0.40683 37.808 12.790
## + X13 1 0.40513 37.810 12.792
## + X10 1 0.13528 38.080 13.069
## + X11 1 0.10984 38.105 13.095
## + X5 1 0.05020 38.165 13.156
## + X2 1 0.00796 38.207 13.199
## + X7 1 0.00252 38.213 13.205
##
## Call:
## lm(formula = Y ~ X9 + X1 + X4 + X8 + X12, data = dataF)
##
## Coefficients:
## (Intercept) X9 X1 X4 X8 X12
## 9.94408 0.06428 -0.07405 -0.10510 0.79736 -0.77443step(full.lm, data=dataF, direction="backward")## Start: AIC=24.76
## Y ~ X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9 + X10 + X11 +
## X12 + X13
##
## Df Sum of Sq RSS AIC
## - X6 1 0.0109 35.905 22.775
## - X10 1 0.0127 35.906 22.777
## - X2 1 0.0203 35.914 22.785
## - X5 1 0.0719 35.966 22.841
## - X11 1 0.1420 36.036 22.917
## - X7 1 0.1973 36.091 22.977
## - X13 1 0.4530 36.347 23.252
## - X3 1 1.0941 36.988 23.934
## - X12 1 1.1976 37.091 24.043
## <none> 35.894 24.763
## - X8 1 2.6508 38.544 25.542
## - X4 1 3.2969 39.191 26.190
## - X9 1 3.5130 39.407 26.405
## - X1 1 5.4061 41.300 28.235
##
## Step: AIC=22.77
## Y ~ X1 + X2 + X3 + X4 + X5 + X7 + X8 + X9 + X10 + X11 + X12 +
## X13
##
## Df Sum of Sq RSS AIC
## - X10 1 0.0123 35.917 20.788
## - X2 1 0.0160 35.921 20.792
## - X11 1 0.1578 36.062 20.946
## - X5 1 0.1755 36.080 20.965
## - X7 1 0.1989 36.103 20.990
## - X13 1 0.4848 36.389 21.298
## - X3 1 1.3528 37.257 22.217
## - X12 1 1.4020 37.307 22.269
## <none> 35.905 22.775
## - X8 1 3.0823 38.987 23.987
## - X9 1 5.1901 41.095 26.040
## - X1 1 5.6461 41.551 26.471
## - X4 1 7.6597 43.564 28.316
##
## Step: AIC=20.79
## Y ~ X1 + X2 + X3 + X4 + X5 + X7 + X8 + X9 + X11 + X12 + X13
##
## Df Sum of Sq RSS AIC
## - X2 1 0.0068 35.924 18.796
## - X11 1 0.1741 36.091 18.977
## - X5 1 0.1856 36.102 18.989
## - X7 1 0.2200 36.137 19.026
## - X13 1 0.4973 36.414 19.324
## - X12 1 1.3897 37.307 20.269
## - X3 1 1.4436 37.360 20.325
## <none> 35.917 20.788
## - X8 1 3.3097 39.227 22.226
## - X9 1 5.2062 41.123 24.067
## - X1 1 5.6613 41.578 24.497
## - X4 1 7.6961 43.613 26.360
##
## Step: AIC=18.8
## Y ~ X1 + X3 + X4 + X5 + X7 + X8 + X9 + X11 + X12 + X13
##
## Df Sum of Sq RSS AIC
## - X11 1 0.1755 36.099 16.986
## - X5 1 0.1832 36.107 16.994
## - X7 1 0.4396 36.363 17.270
## - X13 1 0.5000 36.424 17.335
## - X3 1 1.4372 37.361 18.325
## - X12 1 1.5503 37.474 18.443
## <none> 35.924 18.796
## - X8 1 3.3734 39.297 20.296
## - X9 1 5.2294 41.153 22.096
## - X1 1 5.6571 41.581 22.499
## - X4 1 7.7285 43.652 24.395
##
## Step: AIC=16.99
## Y ~ X1 + X3 + X4 + X5 + X7 + X8 + X9 + X12 + X13
##
## Df Sum of Sq RSS AIC
## - X5 1 0.1860 36.285 15.186
## - X7 1 0.2754 36.375 15.282
## - X13 1 0.9744 37.074 16.024
## - X3 1 1.3763 37.476 16.445
## <none> 36.099 16.986
## - X8 1 3.2337 39.333 18.331
## - X12 1 3.5259 39.625 18.620
## - X9 1 5.1980 41.297 20.232
## - X1 1 5.6122 41.711 20.621
## - X4 1 7.6380 43.737 22.471
##
## Step: AIC=15.19
## Y ~ X1 + X3 + X4 + X7 + X8 + X9 + X12 + X13
##
## Df Sum of Sq RSS AIC
## - X7 1 0.2611 36.546 13.466
## - X13 1 0.8738 37.159 14.114
## - X3 1 1.2995 37.585 14.558
## <none> 36.285 15.186
## - X8 1 3.4668 39.752 16.745
## - X12 1 3.5885 39.874 16.864
## - X9 1 5.0490 41.334 18.267
## - X1 1 5.4363 41.722 18.631
## - X4 1 7.9013 44.187 20.869
##
## Step: AIC=13.47
## Y ~ X1 + X3 + X4 + X8 + X9 + X12 + X13
##
## Df Sum of Sq RSS AIC
## - X13 1 0.6127 37.159 12.114
## - X3 1 1.2638 37.810 12.792
## <none> 36.546 13.466
## - X8 1 3.2074 39.754 14.746
## - X12 1 4.0057 40.552 15.522
## - X1 1 5.1775 41.724 16.633
## - X9 1 5.5731 42.119 17.001
## - X4 1 7.7925 44.339 19.004
##
## Step: AIC=12.11
## Y ~ X1 + X3 + X4 + X8 + X9 + X12
##
## Df Sum of Sq RSS AIC
## - X3 1 1.0562 38.215 11.207
## <none> 37.159 12.114
## - X12 1 3.7692 40.928 13.882
## - X8 1 3.9001 41.059 14.007
## - X9 1 4.9675 42.127 15.008
## - X1 1 6.4378 43.597 16.346
## - X4 1 7.1968 44.356 17.019
##
## Step: AIC=11.21
## Y ~ X1 + X4 + X8 + X9 + X12
##
## Df Sum of Sq RSS AIC
## <none> 38.215 11.207
## - X12 1 4.1181 42.333 13.198
## - X9 1 5.2241 43.439 14.204
## - X8 1 5.4166 43.632 14.377
## - X4 1 7.4907 45.706 16.188
## - X1 1 10.5678 48.783 18.729
##
## Call:
## lm(formula = Y ~ X1 + X4 + X8 + X9 + X12, data = dataF)
##
## Coefficients:
## (Intercept) X1 X4 X8 X9 X12
## 9.94408 -0.07405 -0.10510 0.79736 0.06428 -0.77443step(start.lm, scope=list(upper=full.lm), data=dataF, direction="both")## Start: AIC=54.51
## Y ~ 1
##
## Df Sum of Sq RSS AIC
## + X9 1 84.767 65.119 23.994
## + X4 1 69.508 80.378 32.204
## + X8 1 47.759 102.127 41.543
## + X3 1 39.372 110.514 44.622
## + X1 1 32.449 117.437 46.991
## + X6 1 22.438 127.449 50.182
## + X13 1 17.108 132.778 51.780
## <none> 149.886 54.506
## + X11 1 6.460 143.426 54.788
## + X12 1 3.911 145.975 55.475
## + X10 1 0.163 149.723 56.464
## + X2 1 0.122 149.764 56.474
## + X7 1 0.092 149.794 56.482
## + X5 1 0.005 149.881 56.505
##
## Step: AIC=23.99
## Y ~ X9
##
## Df Sum of Sq RSS AIC
## + X1 1 12.981 52.139 17.323
## + X3 1 10.053 55.066 19.454
## + X4 1 7.943 57.176 20.920
## + X8 1 7.160 57.959 21.451
## <none> 65.119 23.994
## + X2 1 3.087 62.032 24.099
## + X7 1 2.466 62.653 24.488
## + X10 1 2.411 62.708 24.522
## + X6 1 0.829 64.290 25.494
## + X13 1 0.475 64.644 25.708
## + X11 1 0.426 64.693 25.738
## + X5 1 0.101 65.018 25.933
## + X12 1 0.015 65.104 25.985
## - X9 1 84.767 149.886 54.506
##
## Step: AIC=17.32
## Y ~ X9 + X1
##
## Df Sum of Sq RSS AIC
## + X4 1 7.292 44.847 13.448
## + X8 1 3.470 48.668 16.637
## + X6 1 3.265 48.873 16.801
## + X3 1 2.983 49.155 17.025
## <none> 52.139 17.323
## + X5 1 0.855 51.284 18.679
## + X12 1 0.461 51.677 18.977
## + X10 1 0.381 51.757 19.037
## + X2 1 0.306 51.832 19.094
## + X7 1 0.226 51.912 19.154
## + X13 1 0.177 51.962 19.191
## + X11 1 0.046 52.093 19.289
## - X1 1 12.981 65.119 23.994
## - X9 1 65.298 117.437 46.991
##
## Step: AIC=13.45
## Y ~ X9 + X1 + X4
##
## Df Sum of Sq RSS AIC
## + X8 1 2.5132 42.333 13.198
## + X3 1 2.4065 42.440 13.297
## <none> 44.847 13.448
## + X11 1 1.4765 43.370 14.142
## + X10 1 1.3017 43.545 14.299
## + X12 1 1.2147 43.632 14.377
## + X2 1 0.9331 43.913 14.628
## + X7 1 0.8711 43.975 14.683
## + X5 1 0.3879 44.459 15.109
## + X6 1 0.0198 44.827 15.431
## + X13 1 0.0035 44.843 15.445
## - X4 1 7.2920 52.139 17.323
## - X1 1 12.3296 57.176 20.920
## - X9 1 17.7442 62.591 24.449
##
## Step: AIC=13.2
## Y ~ X9 + X1 + X4 + X8
##
## Df Sum of Sq RSS AIC
## + X12 1 4.1181 38.215 11.207
## <none> 42.333 13.198
## + X11 1 1.8859 40.447 13.421
## - X8 1 2.5132 44.847 13.448
## + X3 1 1.4051 40.928 13.882
## + X13 1 0.6230 41.710 14.620
## + X7 1 0.4833 41.850 14.751
## + X5 1 0.3969 41.936 14.831
## + X2 1 0.3231 42.010 14.900
## + X10 1 0.2948 42.039 14.926
## + X6 1 0.1400 42.193 15.069
## - X4 1 6.3349 48.668 16.637
## - X1 1 9.1881 51.521 18.859
## - X9 1 12.5355 54.869 21.314
##
## Step: AIC=11.21
## Y ~ X9 + X1 + X4 + X8 + X12
##
## Df Sum of Sq RSS AIC
## <none> 38.215 11.207
## + X3 1 1.0562 37.159 12.114
## + X6 1 0.4068 37.808 12.790
## + X13 1 0.4051 37.810 12.792
## + X10 1 0.1353 38.080 13.069
## + X11 1 0.1098 38.105 13.095
## + X5 1 0.0502 38.165 13.156
## - X12 1 4.1181 42.333 13.198
## + X2 1 0.0080 38.207 13.199
## + X7 1 0.0025 38.213 13.205
## - X9 1 5.2241 43.439 14.204
## - X8 1 5.4166 43.632 14.377
## - X4 1 7.4907 45.706 16.188
## - X1 1 10.5678 48.783 18.729
##
## Call:
## lm(formula = Y ~ X9 + X1 + X4 + X8 + X12, data = dataF)
##
## Coefficients:
## (Intercept) X9 X1 X4 X8 X12
## 9.94408 0.06428 -0.07405 -0.10510 0.79736 -0.77443#install.packages("leaps")
library(leaps)## Warning: package 'leaps' was built under R version 4.1.3str(Y)## num [1:39] 4.58 2.86 3.02 2.29 1.61 6.87 3.85 6.12 3.29 5.88 ...all.lm=regsubsets(Y~. , data=dataF)
(rs=summary(all.lm))## Subset selection object
## Call: regsubsets.formula(Y ~ ., data = dataF)
## 13 Variables (and intercept)
## Forced in Forced out
## X1 FALSE FALSE
## X2 FALSE FALSE
## X3 FALSE FALSE
## X4 FALSE FALSE
## X5 FALSE FALSE
## X6 FALSE FALSE
## X7 FALSE FALSE
## X8 FALSE FALSE
## X9 FALSE FALSE
## X10 FALSE FALSE
## X11 FALSE FALSE
## X12 FALSE FALSE
## X13 FALSE FALSE
## 1 subsets of each size up to 8
## Selection Algorithm: exhaustive
## X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13
## 1 ( 1 ) " " " " " " " " " " " " " " " " "*" " " " " " " " "
## 2 ( 1 ) "*" " " " " " " " " " " " " " " "*" " " " " " " " "
## 3 ( 1 ) "*" " " " " "*" " " " " " " " " "*" " " " " " " " "
## 4 ( 1 ) "*" " " " " "*" " " " " " " "*" "*" " " " " " " " "
## 5 ( 1 ) "*" " " " " "*" " " " " " " "*" "*" " " " " "*" " "
## 6 ( 1 ) "*" " " "*" "*" " " " " " " "*" "*" " " " " "*" " "
## 7 ( 1 ) "*" " " "*" "*" " " " " " " "*" "*" " " " " "*" "*"
## 8 ( 1 ) "*" " " "*" "*" " " " " "*" "*" "*" " " " " "*" "*"