Question 1 :
술집의 갯수로 부터 사망자수를 예측한ㄴ 단순 회귀 분석 실시
회귀 매개변수들에 부트스트랩 방법을 적용해서 같은 분석하기
setwd("C:/Users/Administrator/Desktop/BIG DATA/R_Book_Regression")
pubs<-read.delim("pubs.dat", header = TRUE)
head(pubs)## pubs mortality
## 1 10 1000
## 2 20 2000
## 3 30 3000
## 4 40 4000
## 5 50 5000
## 6 60 6000## 'data.frame': 8 obs. of 2 variables:
## $ pubs : int 10 20 30 40 50 60 70 500
## $ mortality: int 1000 2000 3000 4000 5000 6000 7000 10000##
## Call:
## lm(formula = mortality ~ pubs, data = pubs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2495.3 -996.3 -223.5 1145.2 2644.3
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3351.955 781.236 4.291 0.00515 **
## pubs 14.339 4.301 3.334 0.01572 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1864 on 6 degrees of freedom
## Multiple R-squared: 0.6495, Adjusted R-squared: 0.591
## F-statistic: 11.12 on 1 and 6 DF, p-value: 0.01572ggplot(pubs, aes(mortality))+
geom_histogram(aes(y=..density..), col="red", fill="white")+
stat_function(fun = dnorm,
args = list(mean = mean(pubs$mortality),
sd = sd(pubs$mortality)))
회귀식이 유의하다고 할 수 있지만 R-squared 가 0.64로 그렇게 설명력이 높지는 않다.
부트스트랩 시도
bootReg <- function(formula, data, indices)
{
d <- data[indices,]
fit <- lm(formula, data=d)
return(coef(fit))
}
bootResults<-boot(statistic = bootReg, formula = mortality ~
pubs, data = pubs, R =2000)
boot.ci(bootResults, type ="bca", index=2)## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 2000 bootstrap replicates
##
## CALL :
## boot.ci(boot.out = bootResults, type = "bca", index = 2)
##
## Intervals :
## Level BCa
## 95% ( 8.44, 100.00 )
## Calculations and Intervals on Original Scale
## Warning : BCa Intervals used Extreme Quantiles
## Some BCa intervals may be unstableQuestion 2
다중회귀 분석 수행, 모형이 수입을 예측하는지에 대한
회귀 모형의 타당성 검증하기
## # A tibble: 231 x 1
## Supermodel$salary $age $years $beauty
## <dbl> <dbl> <dbl> <dbl>
## 1 0.370 16.7 3.15 78.3
## 2 53.7 20.3 5.51 68.6
## 3 1.46 18.2 5.33 75.0
## 4 0.0243 15.4 3.84 65.1
## 5 95.3 24.2 8.53 71.8
## 6 14.6 18.3 4.39 78.1
## 7 8.67 17.7 4.40 72.1
## 8 2.65 17.5 4.11 75.3
## 9 7.55 17.1 3.52 72.0
## 10 1.20 20.1 6.83 71.9
## # ... with 221 more rows회귀식
##
## Call:
## lm(formula = salary ~ age + years + beauty, data = Supermodel)
##
## Residuals:
## Min 1Q Median 3Q Max
## -24.853 -7.950 -4.197 4.605 68.085
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -60.8897 16.4966 -3.691 0.00028 ***
## age 6.2344 1.4112 4.418 1.54e-05 ***
## years -5.5612 2.1222 -2.621 0.00937 **
## beauty -0.1964 0.1524 -1.289 0.19871
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.57 on 227 degrees of freedom
## Multiple R-squared: 0.184, Adjusted R-squared: 0.1733
## F-statistic: 17.07 on 3 and 227 DF, p-value: 4.973e-10검증하기
dwt 더빗왓슨데트스 : 오차의 독립성 가정을 확인한다.
검저통계량이 1보다 작거나 3보다 크면 주의해야한다.
2에 가까울수록 좋은 것. D-W Stastics 값이 2점 대로 좋다.
즉, 오차의 독립성 가정이 만족되었다.
## lag Autocorrelation D-W Statistic p-value
## 1 -0.03061432 2.057416 0.686
## Alternative hypothesis: rho != 0다중 공선성은 예측 변수들 사이에 강한 상관관계가 있는 것 다중 회귀에서만 문제가 된다.
다중 공선성이 발생하면?
b를 못믿는다. y=ax+b
R 의 크기가 제한된다.
변수의 중요도 평가가 어렵다.
그래서 분산팽창인자를 확인한다.
다중공선성 평가하기 VIF 함수사용
만약에 VIF 가 10 보다 크면 문제의 여지가 있다. (Bowerman & O`connell, 1990)
## age years beauty
## 12.652841 12.156757 1.153364## age years beauty
## 0.07903364 0.08225878 0.86702902Supermodel$cooks.distance<-cooks.distance(Supermodel.1)
Supermodel$residuals<-resid(Supermodel.1)
Supermodel$standardized.residuals <- rstandard(Supermodel.1)
Supermodel$studentized.residuals <- rstudent(Supermodel.1)
Supermodel$dfbeta <- dfbeta(Supermodel.1)
Supermodel$dffit <- dffits(Supermodel.1)
Supermodel$leverage <- hatvalues(Supermodel.1)
Supermodel$covariance.ratios <- covratio(Supermodel.1)표준잔차가가 2 이상인것들
## [1] FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [85] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [97] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [181] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [193] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [205] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [217] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [229] FALSE FALSE FALSE잔차가 2 보다 크거나 -2 보다 작은것들을 large residual 로 묶음
Supermodel$large.residual <- Supermodel$standardized.residuals > 2|Supermodel$standardized.residuals < -2
sum(Supermodel$large.residual)## [1] 12## salary age beauty years standardized.residuals
## 1 3.703971e-01 16.66699 78.25149 3.1484550 -6.747754e-01
## 2 5.372479e+01 20.34707 68.56999 5.5068856 2.214829e+00
## 3 1.460159e+00 18.20307 75.04376 5.3307484 -4.665046e-01
## 4 2.433401e-02 15.35626 65.14253 3.8400879 -4.703833e-02
## 5 9.533807e+01 24.17183 71.77039 8.5320504 4.696607e+00
## 6 1.463548e+01 18.26022 78.05224 4.3931585 9.931831e-02
## 7 8.673332e+00 17.69861 72.06817 4.3966331 -1.496188e-01
## 8 2.649274e+00 17.48589 75.32745 4.1107347 -5.380704e-01
## 9 7.547323e+00 17.06954 72.03374 3.5150774 -2.959397e-01
## 10 1.202515e+00 20.07689 71.93139 6.8287270 -7.634754e-01
## 11 1.016436e+01 22.76918 86.20372 7.3210631 -9.214962e-01
## 12 1.987528e+01 21.68824 76.32069 6.1588807 -3.621862e-01
## 13 8.385047e-01 16.72428 65.43778 3.8002693 -5.914733e-01
## 14 1.601111e-01 18.38796 75.13174 4.6607977 -8.884270e-01
## 15 1.489679e+00 17.31925 84.70345 3.8262186 -5.309503e-01
## 16 3.595230e+00 18.38007 76.94420 4.8278267 -5.602202e-01
## 17 6.443246e-01 18.33266 81.37625 4.3977673 -8.491928e-01
## 18 4.646695e+00 12.17059 83.07885 0.4339258 5.890137e-01
## 19 2.973564e+00 18.89094 80.37354 5.0459225 -6.929207e-01
## 20 2.586351e+01 17.80244 87.93203 4.3488346 1.193607e+00
## 21 1.613791e-01 16.23688 76.84810 3.4874074 -3.919766e-01
## 22 7.584990e-01 17.19504 82.29596 3.9458943 -5.136175e-01
## 23 6.419431e+00 18.99114 99.22141 5.2379833 -1.753720e-01
## 24 4.886766e+01 19.11451 73.32626 4.9510269 2.241876e+00
## 25 1.256859e+01 20.53822 82.26454 6.5188997 -1.506090e-01
## 26 1.696610e+01 16.94019 67.84139 3.9598198 5.235251e-01
## 27 4.307648e+00 18.54992 76.27180 4.9985696 -5.278862e-01
## 28 1.234005e+00 16.81235 65.08967 3.6989503 -6.464789e-01
## 29 2.863909e+00 16.78278 73.29196 5.2351901 1.850227e-01
## 30 1.527670e+00 18.39744 77.83912 4.6099508 -7.813705e-01
## 31 1.495334e-01 16.37244 61.63453 3.6214628 -6.106731e-01
## 32 1.776442e+01 23.43212 70.08264 7.2719372 -9.314468e-01
## 33 6.125179e+00 17.39769 92.43000 3.5176862 -2.611130e-01
## 34 9.291888e-02 19.81517 89.02132 6.1378894 -7.623817e-01
## 35 1.910441e+00 16.24275 68.61040 3.3888299 -4.239939e-01
## 36 2.732945e+01 18.07624 81.26469 4.3697672 1.087287e+00
## 37 1.191727e+01 18.05274 78.71101 4.3680489 5.317031e-04
## 38 2.458539e+01 17.32800 65.68004 4.3163601 9.917392e-01
## 39 1.062363e+00 18.65045 89.26983 5.3246681 -5.001983e-01
## 40 4.359976e+00 18.13858 77.02018 4.5798330 -4.978784e-01
## 41 5.102516e+01 19.46200 80.00141 5.1872748 2.420635e+00
## 42 5.172850e+00 17.44897 79.12363 4.4924827 -1.515986e-01
## 43 8.549782e+00 18.17740 79.56613 4.1272609 -3.661117e-01
## 44 7.117571e+00 19.97936 68.29500 4.7592273 -1.171002e+00
## 45 2.929431e+01 20.56706 78.79560 5.7632401 6.547716e-01
## 46 7.334332e+00 18.12868 77.36095 4.5930152 -2.794299e-01
## 47 1.937737e+01 17.51028 72.90725 4.3688177 6.684422e-01
## 48 2.186554e+01 19.61866 80.24739 5.1207788 3.228702e-01
## 49 4.824773e+00 20.94525 74.98394 7.2286573 -6.908384e-01
## 50 3.798638e+01 19.11602 75.27881 4.8423508 1.476108e+00
## 51 3.534612e-01 16.68522 60.62331 4.4935306 -4.104158e-01
## 52 4.760367e+00 21.06153 84.42742 6.7612675 -7.950632e-01
## 53 1.125083e+01 15.84034 85.57886 3.0430586 4.934295e-01
## 54 4.347790e-01 19.41528 72.16440 5.8755140 -8.880943e-01
## 55 1.338526e+01 18.50682 77.54678 4.5199397 -5.089540e-02
## 56 1.668403e+01 16.95609 81.15548 3.7181125 5.843726e-01
## 57 2.268144e+01 25.28966 75.42205 9.9321576 -2.862837e-01
## 58 1.817073e-01 19.47374 75.95184 6.2091472 -7.538241e-01
## 59 1.322564e+01 15.20555 70.96073 1.7282407 2.004308e-01
## 60 6.012428e+00 12.41973 58.30106 0.9656664 4.428375e-01
## 61 9.640217e-01 15.55789 76.66398 2.9020477 -2.721436e-01
## 62 2.395939e-03 15.29866 65.03334 3.1279126 -2.991846e-01
## 63 1.066358e+00 13.67640 62.39485 3.0152831 4.021357e-01
## 64 2.600380e-01 17.64202 73.70490 4.2955612 -7.206195e-01
## 65 1.852551e+01 17.69771 78.65391 4.7269553 7.455605e-01
## 66 6.277020e+00 16.56039 74.47669 3.5882699 -1.030187e-01
## 67 9.673410e+00 14.59537 58.12680 2.8099151 4.623650e-01
## 68 6.891057e-01 21.87370 86.24061 7.0668647 -1.287655e+00
## 69 2.263934e+00 17.32623 76.10902 3.9832955 -5.343670e-01
## 70 1.827790e+00 17.90095 76.59170 4.6327485 -5.558398e-01
## 71 1.444184e+00 16.42965 74.32155 3.5317617 -4.033616e-01
## 72 3.585104e+01 17.96876 75.96337 4.7055631 1.775164e+00
## 73 4.333067e+00 15.69231 93.25221 2.2495408 -1.258103e-01
## 74 3.747556e+00 18.00909 77.82820 4.1135545 -6.530975e-01
## 75 5.408553e-01 21.21304 78.86243 6.6432366 -1.269533e+00
## 76 1.645637e-01 16.34446 69.70922 3.7964950 -4.166168e-01
## 77 6.558605e+00 18.40960 76.48040 5.0815477 -2.785075e-01
## 78 2.961231e+01 17.75333 85.31971 4.0778010 1.330674e+00
## 79 1.867287e+01 20.17078 66.50441 6.3587504 1.548335e-01
## 80 3.419027e+00 18.52445 66.46959 5.1367933 -6.608395e-01
## 81 3.797471e+00 17.82809 78.67549 4.2240556 -5.174935e-01
## 82 1.499705e+00 14.42700 73.89189 1.6962632 -2.505344e-01
## 83 4.104912e+01 20.37681 72.85344 5.9793074 1.549867e+00
## 84 7.750085e-01 15.49243 87.70637 2.1601806 -3.970768e-01
## 85 1.451881e+01 18.71816 79.20491 4.9275488 1.148662e-01
## 86 3.091410e+01 18.51927 67.26349 4.6677394 1.073090e+00
## 87 2.749344e+01 18.84635 79.11545 5.1265902 1.027774e+00
## 88 2.343788e+00 15.87149 71.96165 4.0451148 6.324903e-02
## 89 1.709936e+00 14.60694 70.39189 1.7893123 -3.259850e-01
## 90 7.472343e-01 15.15041 71.04004 3.4853191 3.582485e-02
## 91 5.683151e+01 24.41146 80.65103 8.7530406 2.099147e+00
## 92 1.806455e+01 17.44970 69.09284 4.6400518 6.581749e-01
## 93 1.119163e-01 14.91756 82.63138 1.8731523 -3.726514e-01
## 94 3.495623e+01 21.80961 78.17259 5.8919817 5.591060e-01
## 95 3.222634e-01 15.83544 74.16377 2.6746939 -5.579367e-01
## 96 1.279998e+00 14.19641 71.19168 2.9146353 2.679571e-01
## 97 2.854670e+00 18.25138 85.24126 4.2769790 -6.578047e-01
## 98 2.902140e+00 17.54673 75.71688 4.2503008 -4.880330e-01
## 99 2.193244e-01 13.75012 72.26602 2.4876528 2.371109e-01
## 100 4.712755e-01 16.21302 78.03807 3.0555698 -5.103968e-01
## 101 3.429248e-01 22.84161 70.28268 7.6451804 -1.731570e+00
## 102 8.102901e-01 16.50416 64.44491 3.9767454 -4.446824e-01
## 103 1.700289e+00 15.55565 77.42865 2.6951387 -2.896691e-01
## 104 1.136496e+01 19.82012 78.04347 5.4567989 -3.884751e-01
## 105 2.843866e+00 18.16756 80.93552 4.2128927 -7.037468e-01
## 106 1.290359e-01 15.10217 69.40076 2.5488371 -3.684836e-01
## 107 3.660229e+01 17.10333 79.69408 3.4874170 1.787428e+00
## 108 1.168010e+01 19.39829 76.67018 5.2926508 -2.668548e-01
## 109 6.838792e+00 13.17186 62.32155 1.8506930 5.679975e-01
## 110 6.201637e+00 18.33536 76.14232 4.4335630 -5.239411e-01
## 111 2.013968e-01 18.69651 84.16251 5.5076303 -5.764484e-01
## 112 1.541185e+01 18.87722 78.30391 5.8447004 4.498044e-01
## 113 3.699026e+00 17.83574 77.50995 4.3922743 -4.786583e-01
## 114 3.778518e+00 23.06794 69.24792 7.3301306 -1.736244e+00
## 115 1.532099e+01 19.99374 78.69276 5.7672187 -6.281584e-02
## 116 6.479129e+01 18.46839 78.91763 4.2843223 3.440027e+00
## 117 1.898591e+01 18.87963 76.11634 4.8125123 2.673777e-01
## 118 1.947776e-01 15.12283 76.02902 2.7262092 -2.143407e-01
## 119 4.636142e+00 17.48013 80.94036 3.6660961 -4.949428e-01
## 120 1.227366e-03 16.72727 67.81910 4.6290760 -3.006952e-01
## 121 7.409133e-01 15.23149 68.22308 2.2739782 -5.056696e-01
## 122 5.901547e+00 18.50362 76.58008 4.6581656 -5.245742e-01
## 123 1.887512e+00 16.89154 83.87001 3.5094720 -4.522338e-01
## 124 3.115363e+00 14.98476 80.50189 2.2516865 -7.512236e-02
## 125 3.244277e+01 16.12009 76.83557 2.8117236 1.627620e+00
## 126 2.298857e-02 17.35333 67.13023 3.9417151 -8.413250e-01
## 127 6.131880e+01 22.25275 78.92917 7.3971377 2.778123e+00
## 128 2.656742e+01 17.65071 69.21527 4.4060851 1.069087e+00
## 129 2.985039e-03 17.71717 84.21619 4.8061578 -4.363840e-01
## 130 1.382870e+00 19.17259 69.80639 5.5804520 -8.634743e-01
## 131 3.301870e-02 12.66218 78.66492 0.9213049 1.780221e-01
## 132 1.434407e+01 13.97466 65.13150 1.4270135 6.173569e-01
## 133 3.447183e+00 18.91910 73.01478 4.6375428 -9.311087e-01
## 134 1.705852e+01 17.58862 79.56327 3.2804525 1.501856e-01
## 135 8.998003e+01 22.28899 75.93018 7.4198248 4.717284e+00
## 136 1.609030e+00 18.43827 76.80226 4.8779417 -7.045502e-01
## 137 2.097175e-01 21.10098 75.44406 7.5004015 -9.713558e-01
## 138 1.361472e+01 17.90038 79.08983 5.1576680 4.928601e-01
## 139 1.260071e+01 19.72664 76.56762 5.3831745 -3.113944e-01
## 140 1.968269e+01 17.75303 80.83436 4.8134326 8.658146e-01
## 141 1.460631e+01 18.62615 81.00010 4.2461495 -7.648002e-02
## 142 6.927047e+00 17.38349 77.05769 4.4151074 -6.011409e-02
## 143 8.601645e+00 18.55353 78.08138 4.8779599 -2.557592e-01
## 144 3.692791e-01 18.30329 76.70438 4.3464768 -9.378736e-01
## 145 2.033008e+00 20.77335 77.04786 5.9572258 -1.265351e+00
## 146 3.534942e+00 16.04653 83.59070 4.5986950 4.511656e-01
## 147 2.562882e+01 17.87016 79.06292 4.8654060 1.220272e+00
## 148 2.533001e+00 20.77152 83.29602 5.6424055 -1.270319e+00
## 149 1.218998e+01 19.59314 80.84237 5.5838779 -1.476382e-01
## 150 9.753228e+00 18.06380 76.96539 4.8611146 1.197942e-02
## 151 9.623078e+00 18.77308 73.13289 5.5705111 -8.180508e-02
## 152 6.040311e+00 16.66608 70.40607 4.0391461 -4.716809e-02
## 153 2.011362e-04 14.33255 86.81369 2.3605666 1.196122e-01
## 154 9.384136e-01 21.38410 69.37950 7.2049333 -1.236077e+00
## 155 7.486075e+01 24.40682 86.09212 8.4447665 3.319137e+00
## 156 2.147815e+00 16.60794 78.36973 3.9364429 -2.221163e-01
## 157 5.703960e+00 23.35849 75.45728 8.8507310 -1.052237e+00
## 158 8.242705e+00 21.07500 86.73389 6.7492172 -5.339530e-01
## 159 3.327271e+00 17.10945 82.85448 3.7320377 -3.743583e-01
## 160 8.593815e-02 20.57832 70.31464 6.1101444 -1.350621e+00
## 161 1.726230e-03 14.98373 66.82637 3.6068345 4.588376e-02
## 162 2.371026e+01 16.11660 83.31355 2.7639336 1.098562e+00
## 163 8.880482e-01 16.90386 77.76886 3.8997538 -4.576518e-01
## 164 2.474596e+01 18.85150 79.86669 5.3261921 9.241166e-01
## 165 8.764009e-02 16.03111 73.70805 4.2008217 -7.851512e-02
## 166 3.145105e+01 22.77909 65.16828 7.2766448 2.524245e-01
## 167 1.652200e+01 14.33095 73.86493 2.0057640 9.495996e-01
## 168 7.652401e+00 13.93696 70.69104 2.4360868 6.298397e-01
## 169 8.118150e-01 17.68051 71.29599 4.0556736 -8.253091e-01
## 170 5.456552e+01 22.31422 88.01470 6.8333672 2.200115e+00
## 171 3.352353e+01 20.72526 74.89299 6.8025451 1.227291e+00
## 172 5.755568e+00 15.23203 74.66280 2.7573555 1.158316e-01
## 173 4.725182e+00 17.77430 79.39558 4.3504821 -3.724453e-01
## 174 1.741507e+01 21.85924 76.92375 6.7056399 -3.859868e-01
## 175 1.215535e+00 18.21793 80.21448 4.8448848 -6.045315e-01
## 176 1.890198e+01 16.95127 72.97062 3.9086739 7.004345e-01
## 177 1.696870e-01 17.68738 72.95978 4.7951656 -5.662387e-01
## 178 1.078210e+00 13.49755 77.41866 1.9842813 2.819055e-01
## 179 7.943317e+00 17.60066 85.69701 4.1214040 -7.933076e-02
## 180 2.162378e-02 17.04439 59.91218 4.1982648 -7.129140e-01
## 181 1.105746e+00 19.10820 75.12854 5.4484942 -8.314501e-01
## 182 5.912415e-01 16.27438 73.12921 3.6843108 -3.533873e-01
## 183 1.280226e-01 22.43751 80.72994 6.9615557 -1.685094e+00
## 184 8.063805e+00 17.86014 76.13970 4.4556324 -1.831361e-01
## 185 3.264288e+00 17.54843 76.78715 4.2789713 -4.384693e-01
## 186 2.359829e+01 20.71767 76.37824 5.6808370 1.326835e-01
## 187 2.810383e+00 18.23541 79.96413 4.7574493 -5.387807e-01
## 188 4.160569e+00 18.97862 73.39256 5.2144992 -6.785641e-01
## 189 5.792839e+00 18.60422 73.49739 4.9626328 -5.003846e-01
## 190 2.997872e+01 24.02154 89.97008 8.2269043 3.172256e-01
## 191 5.065578e+01 15.27406 66.38544 2.9816968 3.177863e+00
## 192 2.063458e+00 17.94530 67.50855 5.0456642 -5.258992e-01
## 193 1.464615e-03 15.54879 82.92712 1.9463464 -6.240888e-01
## 194 2.743113e+00 21.72690 92.52992 6.4668227 -1.235141e+00
## 195 1.761481e+01 18.71204 87.18586 4.3958752 2.366170e-01
## 196 1.610823e+01 18.86435 69.58605 5.0548423 8.043959e-02
## 197 7.433609e+00 18.78038 79.70986 4.5789779 -5.268749e-01
## 198 7.132073e+01 20.65061 77.57684 5.8345590 3.531357e+00
## 199 1.860040e+01 15.78994 70.61232 3.0145182 8.058387e-01
## 200 3.074632e-01 19.48365 84.61809 5.9959226 -7.151983e-01
## 201 1.216101e+01 18.10050 76.55841 4.2364072 -8.271959e-02
## 202 1.177116e+01 19.37485 72.32531 5.3038151 -3.053608e-01
## 203 2.280426e+01 15.30119 75.66293 2.6848021 1.248114e+00
## 204 1.353928e+01 14.88318 60.41909 2.5463069 5.346318e-01
## 205 3.198209e+00 18.22033 75.09305 5.4420787 -3.108997e-01
## 206 2.525252e+00 17.38850 78.15523 4.1833348 -4.390005e-01
## 207 5.968844e+00 19.18362 68.20927 4.9330119 -8.249514e-01
## 208 4.779746e+00 18.29094 76.80199 4.8234657 -4.441492e-01
## 209 3.676807e-01 15.67899 79.65221 3.7492858 6.535097e-05
## 210 1.812109e+01 18.61331 80.20596 4.8860091 4.054899e-01
## 211 7.223432e+00 18.06912 82.69693 4.7203847 -1.411405e-01
## 212 3.297789e+01 22.54835 76.58926 8.0473610 9.109082e-01
## 213 1.029441e+00 18.72934 85.93521 4.3444736 -9.566741e-01
## 214 2.577141e+01 13.22896 71.12583 1.7354027 1.929692e+00
## 215 1.425157e+01 17.54786 73.20215 4.0317575 1.747302e-01
## 216 2.743312e-01 16.46088 70.06163 3.9185400 -4.075139e-01
## 217 1.015202e-03 13.89716 67.28552 2.7797720 2.036788e-01
## 218 7.327891e+00 20.08475 77.25928 6.3798334 -4.385257e-01
## 219 3.384669e+01 19.47072 76.43607 5.0474820 1.132834e+00
## 220 4.860327e-02 19.03370 77.60311 5.9174273 -6.629274e-01
## 221 5.595154e+00 17.73842 76.60311 4.3089425 -3.506040e-01
## 222 9.578354e-02 18.87020 62.30070 5.9765568 -7.809750e-01
## 223 1.339455e+00 15.96868 70.59462 2.9829930 -4.745438e-01
## 224 4.974499e+00 23.68361 75.72559 7.6529213 -1.701725e+00
## 225 5.213939e+00 18.21792 64.92145 5.3084787 -3.608362e-01
## 226 1.349124e+01 17.28494 75.84810 4.2759842 3.643298e-01
## 227 8.218144e+00 16.81494 63.05563 3.3135122 -3.425363e-01
## 228 4.955020e-01 15.59418 72.35867 3.0622674 -3.168259e-01
## 229 4.349503e-02 20.69407 80.92086 5.4961825 -1.498934e+00
## 230 1.627651e+01 18.52002 79.69074 4.5968314 2.009399e-01
## 231 2.152101e+00 15.91776 73.57108 2.2213600 -6.548673e-01
Question 3
회귀분석과 회귀모형의 신뢰성과 일반화 가능성 평가
## # A tibble: 810 x 1
## gfr$ticknumb $music $day1 $day2 $day3 $change
## <int> <fct> <dbl> <dbl> <dbl> <dbl>
## 1 2111 Metaller 2.65 1.35 1.61 -1.04
## 2 2229 Crusty 0.97 1.41 0.290 -0.68
## 3 2338 No Musical Affiliation 0.84 NA NA NA
## 4 2384 Crusty 3.03 NA NA NA
## 5 2401 No Musical Affiliation 0.88 0.08 NA NA
## 6 2405 Crusty 0.85 NA NA NA
## 7 2467 Indie Kid 1.56 NA NA NA
## 8 2478 Indie Kid 3.02 NA NA NA
## 9 2490 Crusty 2.29 NA NA NA
## 10 2504 No Musical Affiliation 1.11 0.44 0.55 -0.56
## # ... with 800 more rows데이터 클리닝 - Dummay Variable
Question 4
data(father.son)
ggplot(father.son, aes(x= fheight, y=sheight))+
geom_point(col= "indianred2")+
geom_smooth(method = "lm", col ="black") +
labs(x= "Fathers", y = "Sons")
##
## Call:
## lm(formula = sheight ~ fheight, data = father.son)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.8772 -1.5144 -0.0079 1.6285 8.9685
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 33.88660 1.83235 18.49 <2e-16 ***
## fheight 0.51409 0.02705 19.01 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.437 on 1076 degrees of freedom
## Multiple R-squared: 0.2513, Adjusted R-squared: 0.2506
## F-statistic: 361.2 on 1 and 1076 DF, p-value: < 2.2e-16QUestion 5
## Age Gender studentN studentE studentO studentA studentC lectureN lecturE
## 1 NA Female 33 35 26 43 30 -14 NA
## 2 NA Female 18 29 19 31 27 -17 NA
## 3 18 Female 35 29 30 45 26 -30 NA
## 4 18 Female 38 43 17 49 29 -24 NA
## 5 NA Female 30 30 29 56 40 -21 NA
## 6 NA Female 19 31 31 35 22 -22 NA
## 7 19 Female 33 27 33 60 38 -30 NA
## 8 NA Male 30 31 25 60 28 -23 NA
## 9 18 Female 30 23 26 48 27 -25 NA
## 10 18 Male 13 28 34 48 29 -30 NA
## 11 18 Female 37 36 37 45 32 -29 NA
## 12 18 Male 23 25 25 48 34 -13 NA
## 13 18 Male 21 20 24 38 26 -18 NA
## 14 0 Female 30 28 21 41 25 0 NA
## 15 18 Female 8 27 34 55 40 -26 NA
## 16 18 Female 21 28 38 37 27 -30 NA
## 17 18 Female 40 30 23 37 40 -23 NA
## 18 NA Female 28 36 40 45 29 -5 NA
## 19 18 Female 40 24 20 35 21 -29 NA
## 20 17 Female 30 42 16 51 34 -26 NA
## 21 18 Male 31 13 20 47 27 -30 NA
## 22 NA Female 41 30 37 51 34 -26 NA
## 23 18 Female 25 30 19 50 31 -28 NA
## 24 18 Female 37 21 35 45 24 -30 NA
## 25 19 Male 14 36 27 NA 34 -27 NA
## 26 18 Male 17 33 32 53 31 -17 NA
## 27 17 Male 10 38 26 52 39 -22 NA
## 28 18 Female 28 29 25 58 34 -24 NA
## 29 18 Female 19 35 23 46 30 -24 NA
## 30 NA Male 33 31 30 36 28 -24 NA
## 31 18 Male 15 34 37 43 25 -17 NA
## 32 18 Female 20 24 25 57 39 -29 NA
## 33 18 Female 15 34 35 50 34 -24 NA
## 34 18 Male 25 38 20 47 58 0 NA
## 35 NA Male 28 33 30 46 23 -19 NA
## 36 18 Male 26 26 28 NA 25 -1 NA
## 37 18 Female 26 35 30 51 33 -27 NA
## 38 18 Female 16 29 33 49 34 -30 NA
## 39 18 Female 21 38 36 45 29 -22 NA
## 40 18 Female NA NA NA 57 NA NA NA
## 41 18 Female 32 33 27 57 36 -30 NA
## 42 18 Female 24 41 NA 50 32 -24 NA
## 43 19 Female 15 34 37 50 25 -26 NA
## 44 18 Female 15 34 35 50 34 -26 NA
## 45 18 Female 25 38 20 45 58 -24 NA
## 46 19 Male 14 36 27 NA 34 -28 NA
## 47 18 Male 17 33 32 53 31 -27 NA
## 48 17 Male 10 38 26 52 39 -6 NA
## 49 18 Female 28 29 25 58 34 -17 NA
## 50 18 Female 19 35 23 46 30 -22 NA
## 51 NA Male 33 31 30 36 28 -24 NA
## 52 18 Male 41 30 37 43 34 -24 NA
## 53 18 Female 25 27 31 57 30 -24 NA
## 54 18 Female 25 30 19 50 31 -17 NA
## 55 18 Male 37 21 35 47 24 -29 NA
## 56 NA Male 28 33 30 46 23 -24 NA
## 57 18 Male 26 26 28 NA 25 0 NA
## 58 18 Female 24 41 NA 50 32 -1 NA
## 59 21 Female 34 28 36 42 30 -30 NA
## 60 18 Female 25 27 31 55 30 -24 NA
## 61 18 Female 18 26 22 43 29 -6 NA
## 62 18 Female 12 26 29 45 34 -26 NA
## 63 18 Female 20 24 25 55 39 -24 NA
## 64 18 Female 18 26 22 43 29 -30 NA
## 65 18 Female 12 26 29 45 34 -19 NA
## 66 18 Male 26 26 28 NA 25 -1 NA
## 67 19 Female 33 27 33 60 38 -30 NA
## 68 18 Female 8 27 34 55 40 -26 NA
## 69 18 Female 25 30 19 50 31 -17 NA
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## 71 18 Female 25 30 19 50 31 -28 NA
## 72 20 Female 24 31 23 55 40 -30 NA
## 73 18 Female 13 36 26 50 31 -30 NA
## 74 18 Female 30 29 40 59 43 -30 NA
## 75 19 Female 27 21 29 49 27 -22 NA
## 76 23 Female 14 32 21 57 35 -15 NA
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## 78 18 Male 19 27 22 51 32 -17 NA
## 79 18 Male 17 34 31 49 29 -21 NA
## 80 18 Female 26 36 28 41 29 -25 NA
## 81 17 Female 15 38 33 53 38 -24 NA
## 82 19 Male 31 37 30 51 34 -16 NA
## 83 18 Female 30 33 24 36 23 -27 NA
## 84 18 Female 13 32 30 41 41 -23 NA
## 85 19 Female 22 37 28 55 34 -30 NA
## 86 20 Male 19 31 35 45 26 NA NA
## 87 16 Male 35 21 23 56 NA 8 NA
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## 89 18 Female NA NA NA 49 NA -30 NA
## 90 18 Female 20 37 30 41 30 -23 NA
## 91 18 Male 14 24 32 43 24 -17 NA
## 92 18 Female 27 39 24 42 32 -30 NA
## 93 18 Male 20 NA 21 38 21 -11 NA
## 94 18 Female 18 31 23 50 NA -16 NA
## 95 18 Female 16 35 26 49 29 -24 NA
## 96 18 Female 31 37 22 53 32 -30 NA
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## 98 19 Male 15 31 36 45 24 -18 NA
## 99 18 Female 35 31 28 49 30 -25 NA
## 100 19 Female 18 42 35 49 31 -30 NA
## 101 18 Female 18 28 37 51 33 -19 NA
## 102 18 Female 32 27 27 54 24 -5 NA
## 103 18 Female 27 32 21 46 37 -21 NA
## 104 17 Female 21 38 23 49 32 -30 NA
## 105 17 Female 15 32 26 41 25 -20 NA
## 106 19 Male 10 36 23 48 32 -20 NA
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## 108 18 Female 19 29 35 43 31 -26 NA
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## 110 19 Male 5 31 33 43 41 -28 NA
## 111 18 Female 17 33 32 48 33 -30 NA
## 112 18 Female 27 30 32 50 32 -18 NA
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## 114 20 Female 19 35 39 61 39 -24 NA
## 115 18 Female 13 30 25 51 39 -24 NA
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## 117 17 Male 36 23 29 41 23 -24 NA
## 118 19 Female 26 34 38 64 39 -27 NA
## 119 18 Female 14 39 41 57 37 -30 NA
## 120 NA Female 23 27 27 42 33 -30 NA
## 121 NA Female 34 28 34 38 25 -28 NA
## 122 NA Female 23 26 32 50 34 -24 NA
## 123 18 Male 4 35 23 43 27 -13 NA
## 124 26 Female 25 28 33 49 35 -24 NA
## 125 NA Female 20 34 29 60 42 -29 NA
## 126 18 Male 19 27 30 51 23 -24 NA
## 127 18 Female 38 29 46 45 33 -24 NA
## 128 20 Male 6 33 39 34 20 -28 NA
## 129 NA Female 25 36 29 61 39 -29 NA
## 130 19 Male 7 38 33 62 42 -30 NA
## 131 NA Male 26 32 36 44 28 -6 NA
## 132 18 Male 19 36 39 50 33 -17 NA
## 133 17 Male 36 23 29 41 23 -24 NA
## 134 18 Male 20 NA 21 38 21 -11 NA
## 135 18 Female 18 31 23 50 NA -16 NA
## 136 17 Female 30 42 16 51 34 -26 NA
## 137 NA Female 39 31 42 42 23 -20 NA
## 138 19 Female 27 21 29 49 27 -22 NA
## 139 23 Female 14 32 21 57 35 -15 NA
## 140 NA NA NA NA NA NA NA NA
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## 235 NA NA NA NA NA NA NA NA
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## 380 19 Female 34 20 22 53 36 -29 21
## 381 20 Female 36 38 28 56 35 -30 4
## 382 19 Female 16 31 26 43 33 -17 10
## 383 20 Female 14 41 27 33 25 -27 14
## 384 20 Female 19 31 25 44 30 -25 8
## 385 19 Female 20 31 32 32 26 -30 14
## 386 20 Female 27 25 21 33 28 -29 6
## 387 19 Female 29 24 21 43 27 -27 25
## 388 20 Female 29 28 33 41 25 -19 18
## 389 25 Female 37 20 32 40 29 -12 15
## 390 19 Female 27 35 23 49 30 -29 6
## 391 21 Female 25 26 31 45 34 -30 18
## 392 21 Female 15 33 24 34 25 -30 -4
## 393 20 Male 32 20 31 45 25 -9 9
## 394 19 Female 24 30 27 50 30 -28 11
## 395 19 Male 39 33 42 40 13 -27 13
## 396 20 Male 10 32 30 46 35 -19 21
## 397 19 Female 30 27 23 51 37 -30 13
## 398 31 Female 28 25 34 29 30 -10 13
## 399 NA NA NA NA NA NA NA NA
## 400 23 Female 28 28 17 52 21 2 12
## 401 19 Female 24 29 25 36 29 -28 10
## 402 19 Female 30 34 23 45 25 -23 7
## 403 20 Female 28 30 31 41 31 -6 14
## 404 20 Male 26 31 32 44 17 -21 17
## 405 19 Male 24 32 25 46 22 -18 11
## 406 18 Female 36 33 39 44 26 -30 10
## 407 19 Female 28 37 28 47 28 0 2
## 408 19 Female 24 27 26 48 31 -25 12
## 409 18 Female 15 33 23 48 35 -24 5
## 410 19 Female 26 22 32 53 22 -30 7
## 411 19 Male 24 14 26 45 22 1 6
## 412 25 Male 26 29 33 43 23 -15 10
## 413 19 Female 13 33 28 39 29 -8 9
## 414 19 Female 20 33 27 48 34 8 15
## 415 22 Male 17 31 24 44 29 -30 14
## 416 18 Female 28 35 34 39 18 -30 25
## 417 19 Female 25 30 25 36 25 -9 3
## 418 19 Female NA NA NA 54 NA -29 NA
## 419 25 Female 27 25 19 57 35 25 19
## 420 19 Male 21 33 26 54 25 -23 17
## 421 19 Female 24 27 29 49 20 -30 10
## 422 21 Male 12 40 40 63 32 25 28
## 423 19 Female NA NA NA 54 NA 4 6
## 424 21 Male 27 38 24 58 19 -8 16
## 425 20 Male 21 25 27 44 26 13 15
## 426 20 Male 23 31 21 51 29 -25 19
## 427 22 Female 24 26 23 59 24 0 13
## 428 19 Male 18 21 36 44 26 -12 11
## 429 22 Male 40 32 29 73 24 -18 26
## 430 19 Female 10 37 43 62 39 -23 16
## lecturO lecturA lecturC
## 1 3 6 10
## 2 4 19 9
## 3 13 15 25
## 4 2 9 8
## 5 11 21 12
## 6 2 13 8
## 7 10 15 11
## 8 15 15 24
## 9 5 7 18
## 10 10 9 7
## 11 28 25 16
## 12 5 4 NA
## 13 6 13 8
## 14 16 22 21
## 15 17 22 29
## 16 20 20 20
## 17 10 1 6
## 18 24 22 19
## 19 8 21 18
## 20 12 24 21
## 21 -4 9 27
## 22 0 14 16
## 23 17 23 17
## 24 28 8 17
## 25 11 7 14
## 26 6 2 12
## 27 -6 15 8
## 28 6 10 15
## 29 13 18 22
## 30 19 17 14
## 31 11 2 10
## 32 2 26 20
## 33 22 -3 20
## 34 0 6 4
## 35 2 3 17
## 36 5 10 1
## 37 11 20 18
## 38 13 19 11
## 39 15 14 25
## 40 NA NA NA
## 41 9 28 4
## 42 15 4 10
## 43 9 19 15
## 44 0 14 16
## 45 9 2 23
## 46 17 23 17
## 47 11 7 14
## 48 17 18 19
## 49 6 2 12
## 50 -6 15 8
## 51 6 10 15
## 52 13 18 22
## 53 19 17 14
## 54 11 2 10
## 55 2 26 20
## 56 22 -3 20
## 57 0 6 4
## 58 5 10 1
## 59 16 -5 4
## 60 9 2 23
## 61 17 18 19
## 62 9 19 15
## 63 15 4 10
## 64 28 8 17
## 65 2 3 17
## 66 5 10 1
## 67 10 15 11
## 68 17 22 29
## 69 11 2 10
## 70 12 24 21
## 71 17 23 17
## 72 1 -4 23
## 73 7 21 23
## 74 26 25 18
## 75 23 19 21
## 76 0 15 23
## 77 9 20 21
## 78 7 12 15
## 79 11 14 NA
## 80 2 8 -1
## 81 12 13 19
## 82 7 5 5
## 83 9 17 15
## 84 6 11 19
## 85 13 17 26
## 86 -3 NA NA
## 87 8 13 0
## 88 25 19 15
## 89 20 21 30
## 90 2 10 17
## 91 18 10 7
## 92 NA 19 5
## 93 10 10 12
## 94 6 12 8
## 95 5 -1 4
## 96 16 23 24
## 97 6 3 24
## 98 17 1 7
## 99 27 16 28
## 100 19 21 14
## 101 18 5 14
## 102 17 13 11
## 103 1 23 18
## 104 8 1 19
## 105 1 12 5
## 106 17 19 16
## 107 4 -5 8
## 108 21 20 21
## 109 20 22 25
## 110 3 -3 23
## 111 7 -1 22
## 112 9 17 9
## 113 6 17 20
## 114 18 11 20
## 115 1 -14 30
## 116 4 -6 -1
## 117 3 1 15
## 118 24 25 19
## 119 25 -5 28
## 120 16 8 23
## 121 12 6 29
## 122 3 12 -6
## 123 0 4 12
## 124 16 3 16
## 125 20 17 26
## 126 1 NA 9
## 127 14 7 22
## 128 12 -3 8
## 129 19 22 24
## 130 19 12 24
## 131 10 0 13
## 132 15 6 21
## 133 3 1 15
## 134 10 10 12
## 135 6 12 8
## 136 12 24 21
## 137 4 -6 -1
## 138 23 19 21
## 139 0 15 23
## 140 NA NA NA
## 141 -7 10 23
## 142 17 26 25
## 143 -1 1 10
## 144 6 5 18
## 145 8 -2 20
## 146 -4 12 28
## 147 9 9 16
## 148 5 13 16
## 149 14 6 12
## 150 -8 19 27
## 151 -2 1 26
## 152 NA -7 -2
## 153 5 9 16
## 154 7 12 30
## 155 10 -6 15
## 156 12 11 5
## 157 12 14 30
## 158 4 15 16
## 159 3 10 14
## 160 -3 14 21
## 161 1 3 11
## 162 27 12 18
## 163 12 2 15
## 164 4 3 11
## 165 10 2 13
## 166 5 4 16
## 167 18 2 16
## 168 -1 13 23
## 169 3 -1 26
## 170 1 -1 9
## 171 2 -7 12
## 172 15 20 19
## 173 16 18 21
## 174 9 20 23
## 175 3 14 24
## 176 27 -6 15
## 177 19 12 19
## 178 8 4 16
## 179 -5 7 15
## 180 7 12 7
## 181 10 -7 17
## 182 3 -7 24
## 183 10 -1 4
## 184 3 6 15
## 185 7 -3 19
## 186 18 22 9
## 187 2 10 18
## 188 30 26 -8
## 189 -5 1 15
## 190 -5 17 16
## 191 16 9 20
## 192 -4 -2 15
## 193 10 7 20
## 194 20 6 6
## 195 14 -1 22
## 196 6 2 17
## 197 4 3 13
## 198 19 22 27
## 199 11 -2 7
## 200 10 -11 9
## 201 1 -8 18
## 202 6 4 23
## 203 19 13 10
## 204 6 10 24
## 205 4 22 27
## 206 10 1 12
## 207 10 4 10
## 208 15 -6 -5
## 209 6 13 18
## 210 10 7 16
## 211 -1 11 26
## 212 19 26 3
## 213 2 11 NA
## 214 6 19 29
## 215 12 1 17
## 216 1 13 17
## 217 5 11 22
## 218 14 7 15
## 219 18 15 15
## 220 -3 0 25
## 221 10 9 17
## 222 7 15 20
## 223 3 4 21
## 224 24 -3 15
## 225 1 11 16
## 226 12 1 24
## 227 6 17 20
## 228 -7 7 18
## 229 7 2 8
## 230 -1 9 19
## 231 7 18 23
## 232 3 0 14
## 233 25 7 26
## 234 10 3 26
## 235 NA NA NA
## 236 4 17 22
## 237 -1 -4 27
## 238 8 8 23
## 239 5 4 15
## 240 6 1 9
## 241 11 9 19
## 242 9 7 14
## 243 20 18 23
## 244 -9 0 17
## 245 2 -13 6
## 246 9 7 21
## 247 2 -4 10
## 248 -4 7 15
## 249 1 1 12
## 250 4 -19 24
## 251 10 -6 21
## 252 14 2 12
## 253 18 1 -4
## 254 8 -2 13
## 255 4 8 18
## 256 16 -14 25
## 257 5 9 22
## 258 14 15 23
## 259 -5 -10 21
## 260 4 6 6
## 261 8 3 20
## 262 9 2 16
## 263 10 NA NA
## 264 13 -5 12
## 265 11 -5 13
## 266 12 22 26
## 267 -2 -6 15
## 268 -1 -3 14
## 269 14 -4 19
## 270 2 13 20
## 271 0 -14 29
## 272 4 5 4
## 273 9 4 23
## 274 16 9 16
## 275 19 21 24
## 276 NA NA NA
## 277 11 19 27
## 278 8 29 13
## 279 -10 -4 21
## 280 NA NA NA
## 281 6 23 25
## 282 12 19 18
## 283 18 17 18
## 284 10 21 21
## 285 14 11 26
## 286 13 1 13
## 287 20 5 26
## 288 6 22 16
## 289 -3 6 5
## 290 4 1 27
## 291 5 2 21
## 292 -2 13 3
## 293 6 0 15
## 294 3 4 22
## 295 NA NA NA
## 296 -2 7 20
## 297 6 5 11
## 298 9 13 29
## 299 7 0 24
## 300 8 6 16
## 301 -5 -1 15
## 302 6 12 21
## 303 8 -3 16
## 304 3 NA 10
## 305 12 10 9
## 306 9 22 26
## 307 8 15 18
## 308 17 25 30
## 309 -9 25 30
## 310 5 -3 15
## 311 7 21 30
## 312 -10 26 24
## 313 5 2 26
## 314 5 9 23
## 315 -1 1 6
## 316 3 15 16
## 317 14 2 7
## 318 0 14 15
## 319 3 -5 26
## 320 2 2 8
## 321 5 23 17
## 322 20 0 18
## 323 13 16 16
## 324 13 5 -1
## 325 29 29 27
## 326 -3 -3 9
## 327 8 26 22
## 328 1 2 5
## 329 23 22 22
## 330 14 4 17
## 331 8 -4 23
## 332 3 16 26
## 333 11 8 12
## 334 9 -6 17
## 335 1 27 22
## 336 15 15 2
## 337 21 -3 12
## 338 15 15 13
## 339 NA NA NA
## 340 -2 26 17
## 341 6 2 8
## 342 19 20 15
## 343 -15 14 20
## 344 6 15 28
## 345 5 9 14
## 346 8 13 3
## 347 15 7 16
## 348 16 -12 20
## 349 23 8 18
## 350 13 22 20
## 351 13 19 26
## 352 8 7 30
## 353 7 -9 9
## 354 15 -6 20
## 355 9 -7 2
## 356 5 -2 19
## 357 17 0 20
## 358 24 14 29
## 359 1 -15 20
## 360 13 9 30
## 361 0 4 17
## 362 -9 3 27
## 363 -9 1 7
## 364 20 1 23
## 365 20 -3 -2
## 366 3 -6 18
## 367 3 7 20
## 368 7 -21 18
## 369 26 22 23
## 370 3 -1 4
## 371 16 23 21
## 372 8 -3 2
## 373 5 9 13
## 374 -3 9 13
## 375 6 22 21
## 376 -3 20 23
## 377 -3 3 18
## 378 7 14 16
## 379 6 12 17
## 380 8 12 10
## 381 9 16 23
## 382 19 17 27
## 383 2 13 21
## 384 7 10 8
## 385 17 11 16
## 386 2 19 26
## 387 13 18 10
## 388 11 15 15
## 389 7 -4 15
## 390 2 NA 18
## 391 6 6 16
## 392 1 -3 17
## 393 8 4 10
## 394 5 6 22
## 395 18 16 12
## 396 22 20 22
## 397 2 12 14
## 398 13 4 23
## 399 NA NA NA
## 400 12 6 3
## 401 18 11 5
## 402 7 5 10
## 403 19 8 18
## 404 18 18 23
## 405 8 10 12
## 406 -3 5 4
## 407 -4 0 0
## 408 11 12 5
## 409 8 10 12
## 410 15 14 16
## 411 2 2 0
## 412 6 4 6
## 413 0 5 6
## 414 16 15 16
## 415 -3 22 25
## 416 20 9 21
## 417 1 -5 -7
## 418 23 15 26
## 419 25 26 27
## 420 16 4 20
## 421 -7 17 9
## 422 27 28 28
## 423 2 2 1
## 424 14 7 9
## 425 3 16 4
## 426 17 18 24
## 427 8 12 22
## 428 1 7 8
## 429 16 19 27
## 430 20 -4 22personalityMatrix<-as.matrix(PersonalityData[, c("studentN", "studentE", "studentO",
"studentA", "studentC", "lectureN", "lecturE", "lecturO", "lecturA", "lecturC")])
rcorr(personalityMatrix)## studentN studentE studentO studentA studentC lectureN lecturE lecturO
## studentN 1.00 -0.34 -0.06 0.01 -0.20 0.01 -0.08 -0.02
## studentE -0.34 1.00 0.07 0.08 0.19 -0.10 0.15 0.07
## studentO -0.06 0.07 1.00 -0.04 -0.09 -0.10 0.04 0.20
## studentA 0.01 0.08 -0.04 1.00 0.52 -0.02 0.05 0.11
## studentC -0.20 0.19 -0.09 0.52 1.00 -0.14 0.10 0.03
## lectureN 0.01 -0.10 -0.10 -0.02 -0.14 1.00 0.00 0.04
## lecturE -0.08 0.15 0.04 0.05 0.10 0.00 1.00 0.49
## lecturO -0.02 0.07 0.20 0.11 0.03 0.04 0.49 1.00
## lecturA 0.10 0.00 -0.16 0.16 0.13 0.04 0.12 0.24
## lecturC 0.00 -0.01 -0.03 0.20 0.22 -0.26 0.10 0.12
## lecturA lecturC
## studentN 0.10 0.00
## studentE 0.00 -0.01
## studentO -0.16 -0.03
## studentA 0.16 0.20
## studentC 0.13 0.22
## lectureN 0.04 -0.26
## lecturE 0.12 0.10
## lecturO 0.24 0.12
## lecturA 1.00 0.24
## lecturC 0.24 1.00
##
## n
## studentN studentE studentO studentA studentC lectureN lecturE lecturO
## studentN 420 418 418 408 416 413 281 416
## studentE 418 418 416 406 414 411 281 414
## studentO 418 416 418 406 414 411 281 414
## studentA 408 406 406 413 404 406 276 408
## studentC 416 414 414 404 416 409 280 412
## lectureN 413 411 411 406 409 417 279 415
## lecturE 281 281 281 276 280 279 283 282
## lecturO 416 414 414 408 412 415 282 420
## lecturA 413 411 411 405 409 414 280 415
## lecturC 413 411 411 405 409 414 281 415
## lecturA lecturC
## studentN 413 413
## studentE 411 411
## studentO 411 411
## studentA 405 405
## studentC 409 409
## lectureN 414 414
## lecturE 280 281
## lecturO 415 415
## lecturA 417 414
## lecturC 414 417
##
## P
## studentN studentE studentO studentA studentC lectureN lecturE lecturO
## studentN 0.0000 0.2586 0.8961 0.0000 0.8945 0.1756 0.7123
## studentE 0.0000 0.1599 0.1056 0.0001 0.0448 0.0102 0.1654
## studentO 0.2586 0.1599 0.4613 0.0655 0.0406 0.4989 0.0000
## studentA 0.8961 0.1056 0.4613 0.0000 0.6671 0.4118 0.0315
## studentC 0.0000 0.0001 0.0655 0.0000 0.0046 0.0900 0.5823
## lectureN 0.8945 0.0448 0.0406 0.6671 0.0046 0.9745 0.4561
## lecturE 0.1756 0.0102 0.4989 0.4118 0.0900 0.9745 0.0000
## lecturO 0.7123 0.1654 0.0000 0.0315 0.5823 0.4561 0.0000
## lecturA 0.0410 0.9315 0.0009 0.0009 0.0072 0.3612 0.0491 0.0000
## lecturC 0.9560 0.8442 0.4942 0.0000 0.0000 0.0000 0.0925 0.0144
## lecturA lecturC
## studentN 0.0410 0.9560
## studentE 0.9315 0.8442
## studentO 0.0009 0.4942
## studentA 0.0009 0.0000
## studentC 0.0072 0.0000
## lectureN 0.3612 0.0000
## lecturE 0.0491 0.0925
## lecturO 0.0000 0.0144
## lecturA 0.0000
## lecturC 0.0000dropVars<-names(PersonalityData) %in% c("lecturE","lecturO", "lecturA","lecturC")
neuroticLecturer<-PersonalityData[!dropVars]
neuroticLecturer## Age Gender studentN studentE studentO studentA studentC lectureN
## 1 NA Female 33 35 26 43 30 -14
## 2 NA Female 18 29 19 31 27 -17
## 3 18 Female 35 29 30 45 26 -30
## 4 18 Female 38 43 17 49 29 -24
## 5 NA Female 30 30 29 56 40 -21
## 6 NA Female 19 31 31 35 22 -22
## 7 19 Female 33 27 33 60 38 -30
## 8 NA Male 30 31 25 60 28 -23
## 9 18 Female 30 23 26 48 27 -25
## 10 18 Male 13 28 34 48 29 -30
## 11 18 Female 37 36 37 45 32 -29
## 12 18 Male 23 25 25 48 34 -13
## 13 18 Male 21 20 24 38 26 -18
## 14 0 Female 30 28 21 41 25 0
## 15 18 Female 8 27 34 55 40 -26
## 16 18 Female 21 28 38 37 27 -30
## 17 18 Female 40 30 23 37 40 -23
## 18 NA Female 28 36 40 45 29 -5
## 19 18 Female 40 24 20 35 21 -29
## 20 17 Female 30 42 16 51 34 -26
## 21 18 Male 31 13 20 47 27 -30
## 22 NA Female 41 30 37 51 34 -26
## 23 18 Female 25 30 19 50 31 -28
## 24 18 Female 37 21 35 45 24 -30
## 25 19 Male 14 36 27 NA 34 -27
## 26 18 Male 17 33 32 53 31 -17
## 27 17 Male 10 38 26 52 39 -22
## 28 18 Female 28 29 25 58 34 -24
## 29 18 Female 19 35 23 46 30 -24
## 30 NA Male 33 31 30 36 28 -24
## 31 18 Male 15 34 37 43 25 -17
## 32 18 Female 20 24 25 57 39 -29
## 33 18 Female 15 34 35 50 34 -24
## 34 18 Male 25 38 20 47 58 0
## 35 NA Male 28 33 30 46 23 -19
## 36 18 Male 26 26 28 NA 25 -1
## 37 18 Female 26 35 30 51 33 -27
## 38 18 Female 16 29 33 49 34 -30
## 39 18 Female 21 38 36 45 29 -22
## 40 18 Female NA NA NA 57 NA NA
## 41 18 Female 32 33 27 57 36 -30
## 42 18 Female 24 41 NA 50 32 -24
## 43 19 Female 15 34 37 50 25 -26
## 44 18 Female 15 34 35 50 34 -26
## 45 18 Female 25 38 20 45 58 -24
## 46 19 Male 14 36 27 NA 34 -28
## 47 18 Male 17 33 32 53 31 -27
## 48 17 Male 10 38 26 52 39 -6
## 49 18 Female 28 29 25 58 34 -17
## 50 18 Female 19 35 23 46 30 -22
## 51 NA Male 33 31 30 36 28 -24
## 52 18 Male 41 30 37 43 34 -24
## 53 18 Female 25 27 31 57 30 -24
## 54 18 Female 25 30 19 50 31 -17
## 55 18 Male 37 21 35 47 24 -29
## 56 NA Male 28 33 30 46 23 -24
## 57 18 Male 26 26 28 NA 25 0
## 58 18 Female 24 41 NA 50 32 -1
## 59 21 Female 34 28 36 42 30 -30
## 60 18 Female 25 27 31 55 30 -24
## 61 18 Female 18 26 22 43 29 -6
## 62 18 Female 12 26 29 45 34 -26
## 63 18 Female 20 24 25 55 39 -24
## 64 18 Female 18 26 22 43 29 -30
## 65 18 Female 12 26 29 45 34 -19
## 66 18 Male 26 26 28 NA 25 -1
## 67 19 Female 33 27 33 60 38 -30
## 68 18 Female 8 27 34 55 40 -26
## 69 18 Female 25 30 19 50 31 -17
## 70 17 Female 30 42 16 51 34 -26
## 71 18 Female 25 30 19 50 31 -28
## 72 20 Female 24 31 23 55 40 -30
## 73 18 Female 13 36 26 50 31 -30
## 74 18 Female 30 29 40 59 43 -30
## 75 19 Female 27 21 29 49 27 -22
## 76 23 Female 14 32 21 57 35 -15
## 77 NA Female 17 33 28 41 33 -20
## 78 18 Male 19 27 22 51 32 -17
## 79 18 Male 17 34 31 49 29 -21
## 80 18 Female 26 36 28 41 29 -25
## 81 17 Female 15 38 33 53 38 -24
## 82 19 Male 31 37 30 51 34 -16
## 83 18 Female 30 33 24 36 23 -27
## 84 18 Female 13 32 30 41 41 -23
## 85 19 Female 22 37 28 55 34 -30
## 86 20 Male 19 31 35 45 26 NA
## 87 16 Male 35 21 23 56 NA 8
## 88 18 Male 10 38 40 50 32 -29
## 89 18 Female NA NA NA 49 NA -30
## 90 18 Female 20 37 30 41 30 -23
## 91 18 Male 14 24 32 43 24 -17
## 92 18 Female 27 39 24 42 32 -30
## 93 18 Male 20 NA 21 38 21 -11
## 94 18 Female 18 31 23 50 NA -16
## 95 18 Female 16 35 26 49 29 -24
## 96 18 Female 31 37 22 53 32 -30
## 97 17 Female 36 35 31 54 36 -30
## 98 19 Male 15 31 36 45 24 -18
## 99 18 Female 35 31 28 49 30 -25
## 100 19 Female 18 42 35 49 31 -30
## 101 18 Female 18 28 37 51 33 -19
## 102 18 Female 32 27 27 54 24 -5
## 103 18 Female 27 32 21 46 37 -21
## 104 17 Female 21 38 23 49 32 -30
## 105 17 Female 15 32 26 41 25 -20
## 106 19 Male 10 36 23 48 32 -20
## 107 18 Male 8 30 22 45 26 -25
## 108 18 Female 19 29 35 43 31 -26
## 109 18 Female 25 28 25 38 28 -11
## 110 19 Male 5 31 33 43 41 -28
## 111 18 Female 17 33 32 48 33 -30
## 112 18 Female 27 30 32 50 32 -18
## 113 18 Female 16 34 31 46 34 -13
## 114 20 Female 19 35 39 61 39 -24
## 115 18 Female 13 30 25 51 39 -24
## 116 NA Female 39 31 42 42 23 -20
## 117 17 Male 36 23 29 41 23 -24
## 118 19 Female 26 34 38 64 39 -27
## 119 18 Female 14 39 41 57 37 -30
## 120 NA Female 23 27 27 42 33 -30
## 121 NA Female 34 28 34 38 25 -28
## 122 NA Female 23 26 32 50 34 -24
## 123 18 Male 4 35 23 43 27 -13
## 124 26 Female 25 28 33 49 35 -24
## 125 NA Female 20 34 29 60 42 -29
## 126 18 Male 19 27 30 51 23 -24
## 127 18 Female 38 29 46 45 33 -24
## 128 20 Male 6 33 39 34 20 -28
## 129 NA Female 25 36 29 61 39 -29
## 130 19 Male 7 38 33 62 42 -30
## 131 NA Male 26 32 36 44 28 -6
## 132 18 Male 19 36 39 50 33 -17
## 133 17 Male 36 23 29 41 23 -24
## 134 18 Male 20 NA 21 38 21 -11
## 135 18 Female 18 31 23 50 NA -16
## 136 17 Female 30 42 16 51 34 -26
## 137 NA Female 39 31 42 42 23 -20
## 138 19 Female 27 21 29 49 27 -22
## 139 23 Female 14 32 21 57 35 -15
## 140 NA NA NA NA NA NA NA
## 141 18 Female 28 19 21 48 35 -29
## 142 19 Female 20 28 32 46 28 -10
## 143 18 Female 34 22 28 25 7 -6
## 144 24 Female 20 32 32 44 27 -18
## 145 18 Female 29 17 31 52 27 -25
## 146 18 Female 32 29 26 47 33 -29
## 147 18 Male 0 41 32 50 45 -30
## 148 18 Female 21 25 25 45 33 -17
## 149 22 Female 26 33 32 37 27 -3
## 150 17 Female 19 33 27 34 35 -23
## 151 19 Female 20 17 36 54 38 -27
## 152 19 Male 26 35 29 46 18 -27
## 153 19 Female 37 17 35 47 18 -16
## 154 18 Female 30 34 31 44 32 -20
## 155 20 Female 19 36 28 50 36 -19
## 156 18 Female 28 27 37 32 26 -22
## 157 19 Female 34 29 30 47 23 -23
## 158 19 Male 13 29 27 47 26 -4
## 159 19 Female 35 20 23 46 28 -30
## 160 18 Female 15 31 23 51 32 -21
## 161 18 Female 14 23 31 54 33 -14
## 162 19 Female 32 32 42 36 16 -29
## 163 19 Male 10 39 37 44 34 -30
## 164 18 Female 23 34 26 45 34 -15
## 165 18 Female 26 28 35 50 36 -17
## 166 19 Female 24 25 22 63 32 -18
## 167 18 Female 23 31 22 58 41 -27
## 168 19 Female 34 26 31 58 28 -27
## 169 18 Female 13 35 37 37 24 -30
## 170 18 Female 28 5 28 27 24 -26
## 171 18 Female 20 42 24 46 31 -29
## 172 19 Female 21 37 33 57 43 -30
## 173 18 Female 25 24 19 54 39 -24
## 174 18 Female 14 32 24 50 36 -17
## 175 19 Female 27 23 27 55 26 -28
## 176 24 Male 40 19 37 59 41 -19
## 177 20 Male 24 29 35 34 24 -21
## 178 18 Female 27 26 34 47 30 -25
## 179 18 Female 25 28 33 43 35 -21
## 180 19 Male 24 29 24 52 32 -15
## 181 18 Female 14 36 23 51 28 -30
## 182 18 Female 22 33 31 50 41 -20
## 183 18 Female 23 41 14 50 37 -25
## 184 19 Female 43 33 30 43 17 -11
## 185 19 Female 35 28 36 50 30 -21
## 186 18 Female 34 30 40 52 23 -20
## 187 17 Female 37 33 36 42 21 -23
## 188 18 Male 24 29 44 43 24 -21
## 189 18 Female 19 36 26 NA 25 -30
## 190 19 Female 39 24 21 44 36 -22
## 191 18 Female 28 36 30 50 39 -30
## 192 23 Male 24 23 37 47 15 NA
## 193 18 Female 18 43 29 57 34 -20
## 194 18 Male 2 39 40 33 20 -18
## 195 20 Female 14 30 41 51 27 -20
## 196 18 Female 22 30 34 51 36 -30
## 197 19 Female 29 27 32 38 26 -19
## 198 20 Female 28 34 22 47 31 -21
## 199 18 Female 15 29 31 54 33 -16
## 200 20 Female 32 25 37 43 17 -30
## 201 18 Female 29 29 29 41 31 -14
## 202 19 Male 16 30 29 38 31 -27
## 203 20 Male 30 9 36 35 22 5
## 204 21 Male 2 35 29 53 42 -27
## 205 19 Female 33 21 15 50 29 -29
## 206 29 Female 19 31 30 47 36 -23
## 207 18 Female 22 26 30 48 28 -10
## 208 20 Male 29 20 39 37 21 -20
## 209 19 Female 37 18 32 47 31 -30
## 210 19 Female 20 26 22 49 32 -26
## 211 19 Female 21 31 32 51 39 -27
## 212 18 Male 25 32 37 44 30 -27
## 213 19 Female 35 11 32 58 44 -26
## 214 19 Female 40 21 29 50 26 -30
## 215 18 Female 33 26 30 40 26 -26
## 216 19 Female 41 26 26 56 31 -24
## 217 18 Female 20 40 31 58 41 -30
## 218 18 Female 11 32 28 45 36 -18
## 219 18 Female 21 27 35 46 28 -13
## 220 18 Female 29 31 28 53 29 -24
## 221 19 Female 42 34 33 44 30 -25
## 222 18 Male 8 32 36 49 28 -24
## 223 20 Male 29 23 41 39 20 -21
## 224 19 Female 39 21 41 45 33 -21
## 225 17 Female 24 33 32 49 30 -29
## 226 18 Female 24 33 27 50 37 -28
## 227 20 Female 19 20 14 39 30 -25
## 228 24 Male 22 38 40 45 23 -30
## 229 18 Female 33 29 27 35 21 -20
## 230 18 Male 2 34 38 44 28 -30
## 231 18 Female 23 35 22 47 31 -30
## 232 19 Female 13 33 34 37 27 -19
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## 430 19 Female 10 37 43 62 39 -23LecturerN.1 <- lm(lectureN ~ Age + Gender, data= neuroticLecturer)
LecturerN.2 <- lm(lectureN ~ Age + Gender + studentN + studentE + studentO + studentA
+ studentC, data= neuroticLecturer)
anova(LecturerN.1, LecturerN.2)## Analysis of Variance Table
##
## Model 1: lectureN ~ Age + Gender
## Model 2: lectureN ~ Age + Gender + studentN + studentE + studentO + studentA +
## studentC
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 370 28483
## 2 365 27429 5 1054.3 2.806 0.01677 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Age Gender studentN studentE studentO studentA studentC
## 1.004731 1.153441 1.312781 1.171989 1.026678 1.390897 1.549902## lag Autocorrelation D-W Statistic p-value
## 1 0.01733968 1.963358 0.724
## Alternative hypothesis: rho != 0Question 6
## total_bill tip sex smoker day time size
## 1 16.99 1.01 Female No Sun Dinner 2
## 2 10.34 1.66 Male No Sun Dinner 3
## 3 21.01 3.50 Male No Sun Dinner 3
## 4 23.68 3.31 Male No Sun Dinner 2
## 5 24.59 3.61 Female No Sun Dinner 4
## 6 25.29 4.71 Male No Sun Dinner 4## Df Sum Sq Mean Sq F value Pr(>F)
## day 4 2203.0 550.8 290.1 <2e-16 ***
## Residuals 240 455.7 1.9
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1tips %>%
group_by(day) %>%
mutate (tip.mean = mean(tip), tip.sd = sd(tip),
Length = NROW(tip),
tfrac = qt(p=0.90, df=Length -1),
Lower = tip.mean - tfrac *tip.sd/sqrt(Length),
Upper = tip.mean + tfrac *tip.sd/sqrt(Length)) -> tipsByDay
ggplot(tipsByDay, aes(x=tip.mean , y=day)) +geom_point()+
geom_errorbar(aes(xmin = Lower, xmax = Upper), height =0.3)
##
## Call:
## lm(formula = tip ~ day - 1, data = tips)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.2451 -0.9931 -0.2347 0.5382 7.0069
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## dayFri 2.7347 0.3161 8.651 7.46e-16 ***
## daySat 2.9931 0.1477 20.261 < 2e-16 ***
## daySun 3.2551 0.1581 20.594 < 2e-16 ***
## dayThur 2.7715 0.1750 15.837 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.378 on 240 degrees of freedom
## Multiple R-squared: 0.8286, Adjusted R-squared: 0.8257
## F-statistic: 290.1 on 4 and 240 DF, p-value: < 2.2e-16## total_bill tip sex smoker day time size
## 1 16.99 1.01 Female No Sun Dinner 2
## 2 10.34 1.66 Male No Sun Dinner 3
## 3 21.01 3.50 Male No Sun Dinner 3
## 4 23.68 3.31 Male No Sun Dinner 2
## 5 24.59 3.61 Female No Sun Dinner 4
## 6 25.29 4.71 Male No Sun Dinner 4tipsLM_1 <- lm(tip ~ total_bill, data=tips)
tipsLM_2 <- lm(tip ~ total_bill + size,data=tips)
anova(tipsLM_1, tipsLM_2) # 두번쨰 회귀식이 유의하다. ## Analysis of Variance Table
##
## Model 1: tip ~ total_bill
## Model 2: tip ~ total_bill + size
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 242 252.79
## 2 241 247.55 1 5.2349 5.0963 0.02487 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## total_bill size
## 1.557586 1.557586## lag Autocorrelation D-W Statistic p-value
## 1 -0.05550935 2.100257 0.404
## Alternative hypothesis: rho != 0
QUestion 7 - 평방피트당 가격
housing <- read.table("http://www.jaredlander.com/data/housing.csv",
sep = ",", header = TRUE,
stringsAsFactors = FALSE)
head(housing,2)## Neighborhood Building.Classification Total.Units Year.Built Gross.SqFt
## 1 FINANCIAL R9-CONDOMINIUM 42 1920 36500
## 2 FINANCIAL R4-CONDOMINIUM 78 1985 126420
## Estimated.Gross.Income Gross.Income.per.SqFt Estimated.Expense
## 1 1332615 36.51 342005
## 2 6633257 52.47 1762295
## Expense.per.SqFt Net.Operating.Income Full.Market.Value Market.Value.per.SqFt
## 1 9.37 990610 7300000 200.00
## 2 13.94 4870962 30690000 242.76
## Boro
## 1 Manhattan
## 2 Manhattan
ggplot(housing, aes(x= Market.Value.per.SqFt, fill=Boro))+
geom_histogram(binwidth = 10)+
facet_wrap(~Boro)
Scatter Plots
ggplot(housing, aes(x= Gross.SqFt, y = Market.Value.per.SqFt)) +geom_point() -> pa
ggplot(housing, aes(x= Total.Units, y = Market.Value.per.SqFt)) +geom_point() -> pb
ggplot(housing[housing$Total.Units < 1000,], aes(x= Gross.SqFt, y = Market.Value.per.SqFt))+
geom_point() -> pc
ggplot(housing[housing$Total.Units < 1000,], aes(x= Total.Units, y = Market.Value.per.SqFt))+
geom_point() -> pd
gridExtra::grid.arrange(pa,pb,pc,pd)
## [1] 6##
## Call:
## lm(formula = Market.Value.per.SqFt ~ Total.Units + Gross.SqFt +
## Boro, data = housing)
##
## Residuals:
## Min 1Q Median 3Q Max
## -164.418 -22.692 1.416 26.972 261.122
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.329e+01 5.330e+00 8.122 6.97e-16 ***
## Total.Units -1.881e-01 2.210e-02 -8.511 < 2e-16 ***
## Gross.SqFt 2.103e-04 2.087e-05 10.079 < 2e-16 ***
## BoroBrooklyn 3.456e+01 5.535e+00 6.244 4.95e-10 ***
## BoroManhattan 1.310e+02 5.385e+00 24.327 < 2e-16 ***
## BoroQueens 3.299e+01 5.663e+00 5.827 6.35e-09 ***
## BoroStaten Island -3.630e+00 9.993e+00 -0.363 0.716
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 43.35 on 2619 degrees of freedom
## Multiple R-squared: 0.6009, Adjusted R-squared: 0.6
## F-statistic: 657.2 on 6 and 2619 DF, p-value: < 2.2e-16## (Intercept) Total.Units Gross.SqFt BoroBrooklyn
## 4.329086e+01 -1.881151e-01 2.103228e-04 3.456215e+01
## BoroManhattan BoroQueens BoroStaten Island
## 1.309924e+02 3.299367e+01 -3.630251e+00## lag Autocorrelation D-W Statistic p-value
## 1 0.4522773 1.095255 0
## Alternative hypothesis: rho != 0## GVIF Df GVIF^(1/(2*Df))
## Total.Units 12.45772 1 3.529549
## Gross.SqFt 12.61644 1 3.551963
## Boro 1.09499 4 1.011408신뢰구간이 0을 포함하지 않으면 통계적으로 유의한것 이다.
다중회귀의 특성은 상호작용을 확인해야한다. 상호작용을 포함하려면 * /상호작용만 보려면 :
house2 <- lm(Market.Value.per.SqFt ~ Total.Units * Gross.SqFt +Boro , data=housing)
house3 <- lm(Market.Value.per.SqFt ~ Total.Units : Gross.SqFt +Boro , data=housing)
house2$coefficients## (Intercept) Total.Units Gross.SqFt
## 4.445184e+01 -1.478411e-01 2.077865e-04
## BoroBrooklyn BoroManhattan BoroQueens
## 3.231499e+01 1.270989e+02 2.979932e+01
## BoroStaten Island Total.Units:Gross.SqFt
## -7.542656e+00 -2.255854e-08## (Intercept) BoroBrooklyn BoroManhattan
## 4.768918e+01 3.220106e+01 1.328734e+02
## BoroQueens BoroStaten Island Total.Units:Gross.SqFt
## 2.976284e+01 -5.834055e+00 7.309022e-10
정규화시켜보기
house.b <- lm(Market.Value.per.SqFt ~ scale(Total.Units) + scale(Gross.SqFt) +Boro , data=housing)
coefplot(house.b)
Question 8 - Logistic Regression
displayModel.1 <- glm(display ~ fb, data = displayData, family = binomial())
displayModel.2 <- update(displayModel.1, .~. + age + fb:age)
summary(displayModel.1)##
## Call:
## glm(formula = display ~ fb, family = binomial(), data = displayData)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.8078 -0.6809 0.6589 0.6589 1.7751
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.3437 0.4584 -2.931 0.00338 **
## fbYes 2.7608 0.6045 4.567 4.95e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 96.124 on 69 degrees of freedom
## Residual deviance: 70.042 on 68 degrees of freedom
## AIC: 74.042
##
## Number of Fisher Scoring iterations: 4# 얼마나 더 잘 예측한 것 인가에대해서 Chi-squre 검정을 실행
modelChi <- displayModel.1$null.deviance - displayModel.1$deviance # 잔차계산
chidf <- displayModel.1$df.null - displayModel.1$df.residual #자유도
chisq.prob <- 1 - pchisq(modelChi, chidf) #확률계산
modelChi## [1] 26.08266## [1] 1## [1] 3.271081e-07모형이 추가됨으로써, 26.08, p= 3.23-e7 < a: 0.05
모형이 결과를 예측하지 못한다. (귀무가설) - 기각 가능
## Analysis of Deviance Table
##
## Model 1: display ~ fb
## Model 2: display ~ fb + age + fb:age
## Resid. Df Resid. Dev Df Deviance
## 1 68 70.042
## 2 66 67.634 2 2.4077## (Intercept) fbYes
## 0.2608696 15.8125000## 2.5 % 97.5 %
## (Intercept) 0.0963625 0.6012293
## fbYes 5.1415334 56.1604505##
## Call:
## glm(formula = display ~ fb + age + fb:age, family = binomial(),
## data = displayData)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.0339 -0.6236 0.4875 0.6909 1.9968
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.94817 1.59648 -1.847 0.0648 .
## fbYes 2.85775 2.10523 1.357 0.1746
## age 0.04404 0.04060 1.085 0.2781
## fbYes:age -0.01669 0.04757 -0.351 0.7256
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 96.124 on 69 degrees of freedom
## Residual deviance: 67.634 on 66 degrees of freedom
## AIC: 75.634
##
## Number of Fisher Scoring iterations: 4모델 비교하기
modelChi <- displayModel.1$deviance - displayModel.2$deviance # 잔차계산
chidf <- displayModel.1$df.residuals - displayModel.2$df.residuals #자유도
chisq.prob <- 1 - pchisq(modelChi, chidf)
modelChi## [1] 2.407671## numeric(0)