Project 2 - Machine Learning
Angel Alain Sosa Rodriguez
Feubrary 21 2017
Description of the Project
The following project is a work for the subject Machine Learning in which it will be solve a series of problems. All excercises have been made by Angel Sosa.
In order to avoid some rstudio erros, I’m loading first all libraries needed.
library(ISLR)
library(fmsb)
library(car)
library(stats)
library(leaps)
library(earth)## Loading required package: plotmo## Loading required package: plotrix## Loading required package: TeachingDemoslibrary(class)
library(caret)## Loading required package: lattice## Loading required package: ggplot2Problem #1
I’m using data hitters. Althought could mean a lost of data, I remove all records in which Salary data is missing. Also I’m doing a training and testing data due to my linear model will need it.
data(Hitters)
hitters <- Hitters[, -c(14,15,20)]
hitters <- hitters[!is.na(hitters$Salary),]
hitters$logSalary <- log(hitters$Salary)
hitters <- hitters[,-c(17)]
set.seed(12345)
trainindex <- createDataPartition(hitters$logSalary,p = 0.7, list = FALSE, times = 1)
hitterstrain <- hitters[trainindex,]
hitterstest <- hitters[-trainindex,]The data hitterstrain will be used in the following excercise because based on theory: training data is a set of data used to discover potentially predictive relationships, while test data is used for evaluating the dicoveries relationships hold.
Problem #2
From hitterstrain I’m building a traditional linear model in which P-values are important.
(a)
LM1 <- lm(formula = hitterstrain$logSalary ~ ., data = hitterstrain)
summary(LM1)##
## Call:
## lm(formula = hitterstrain$logSalary ~ ., data = hitterstrain)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.27147 -0.44874 0.01607 0.40936 2.79909
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.677e+00 1.959e-01 23.872 <2e-16 ***
## AtBat -3.931e-03 1.523e-03 -2.582 0.0107 *
## Hits 1.445e-02 5.813e-03 2.485 0.0139 *
## HmRun 9.406e-03 1.480e-02 0.636 0.5258
## Runs -3.868e-03 6.987e-03 -0.554 0.5805
## RBI 3.493e-03 6.463e-03 0.540 0.5896
## Walks 1.066e-02 4.492e-03 2.373 0.0188 *
## Years 4.177e-02 3.128e-02 1.335 0.1836
## CAtBat -2.807e-05 3.299e-04 -0.085 0.9323
## CHits 1.097e-03 1.745e-03 0.629 0.5302
## CHmRun 5.071e-04 3.912e-03 0.130 0.8970
## CRuns 8.409e-04 1.764e-03 0.477 0.6343
## CRBI -1.265e-03 1.822e-03 -0.694 0.4886
## CWalks -9.993e-04 8.293e-04 -1.205 0.2299
## PutOuts 4.154e-04 1.765e-04 2.355 0.0197 *
## Assists 1.052e-03 5.131e-04 2.051 0.0418 *
## Errors -1.647e-02 1.017e-02 -1.619 0.1074
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6188 on 168 degrees of freedom
## Multiple R-squared: 0.5713, Adjusted R-squared: 0.5305
## F-statistic: 13.99 on 16 and 168 DF, p-value: < 2.2e-16(b)
In this case I’m going to remove all P-values greater than 0.05, twice. First I’m locating which data has this condition to exclude them from my new linear model.
data.frame(summary(LM1)$coef[summary(LM1)$coef[,4] <= .05, 4])## summary.LM1..coef.summary.LM1..coef...4.....0.05..4.
## (Intercept) 7.224670e-56
## AtBat 1.069067e-02
## Hits 1.392653e-02
## Walks 1.878951e-02
## PutOuts 1.970092e-02
## Assists 4.184723e-02LM1 <- lm(formula = hitterstrain$logSalary ~ AtBat+Hits+Walks+PutOuts+Assists, data = hitterstrain)
summary(LM1)##
## Call:
## lm(formula = hitterstrain$logSalary ~ AtBat + Hits + Walks +
## PutOuts + Assists, data = hitterstrain)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.5468 -0.5977 0.1007 0.5593 2.6496
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.048e+00 1.799e-01 28.069 < 2e-16 ***
## AtBat -4.240e-03 1.648e-03 -2.573 0.010895 *
## Hits 1.892e-02 5.039e-03 3.753 0.000236 ***
## Walks 1.191e-02 3.544e-03 3.361 0.000950 ***
## PutOuts 1.423e-04 2.081e-04 0.684 0.495085
## Assists 8.827e-05 4.392e-04 0.201 0.840930
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7804 on 179 degrees of freedom
## Multiple R-squared: 0.2734, Adjusted R-squared: 0.2531
## F-statistic: 13.47 on 5 and 179 DF, p-value: 3.739e-11(c)
I repeat the process.
data.frame(summary(LM1)$coef[summary(LM1)$coef[,4] <= .05, 4])## summary.LM1..coef.summary.LM1..coef...4.....0.05..4.
## (Intercept) 1.815111e-67
## AtBat 1.089491e-02
## Hits 2.355260e-04
## Walks 9.503303e-04LM1 <- lm(formula = hitterstrain$logSalary ~ AtBat+Hits+Walks, data = hitterstrain)
summary(LM1)##
## Call:
## lm(formula = hitterstrain$logSalary ~ AtBat + Hits + Walks, data = hitterstrain)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.4733 -0.6045 0.1040 0.5608 2.6699
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.057128 0.177881 28.430 < 2e-16 ***
## AtBat -0.004171 0.001563 -2.669 0.008294 **
## Hits 0.018981 0.004913 3.863 0.000156 ***
## Walks 0.012176 0.003425 3.555 0.000482 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7771 on 181 degrees of freedom
## Multiple R-squared: 0.2715, Adjusted R-squared: 0.2594
## F-statistic: 22.48 on 3 and 181 DF, p-value: 2.028e-12(d)
In order to avoid collinearity in my results is proper to check the variance inflation factors. Then I will remove those factors who contribute for collinearity.
vif(LM1)## AtBat Hits Walks
## 16.374806 15.387746 1.551907LM1 <- lm(formula = hitterstrain$logSalary ~ Hits+Walks, data = hitterstrain)
summary(LM1)##
## Call:
## lm(formula = hitterstrain$logSalary ~ Hits + Walks, data = hitterstrain)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.5822 -0.6320 0.1774 0.5589 2.8355
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.820657 0.156824 30.739 < 2e-16 ***
## Hits 0.006499 0.001533 4.239 3.56e-05 ***
## Walks 0.009822 0.003365 2.919 0.00395 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7901 on 182 degrees of freedom
## Multiple R-squared: 0.2428, Adjusted R-squared: 0.2345
## F-statistic: 29.18 on 2 and 182 DF, p-value: 1.02e-11Due to 16 is greater than 15, I decide to remove Atbats from the linear model. it makes the vif has collinearity.
(e)
In this part we can see if “are there patterns in the residuals?”" by plotting predicted vs observed logSalary. I’m also generating an R-square from testing hitters data (hitterstest).
plot(LM1$fitted.values, LM1$residuals)
abline(0,0)
plot(LM1$fitted.values, hitterstrain$logSalary, asp=1)
abline(0,1)
predicted <- predict(LM1, newdata=hitterstrain)
LM1_R2_train <- cor(predicted, hitterstrain$logSalary)^2
LM1_R2_train## [1] 0.2427942vif(LM1)## Hits Walks
## 1.44903 1.44903Also our new values for vif are more correct.
(f)
Finally by making an R-square for training hitters data (hitterstrain) we can see the difference between LM1’s predictive capacity and R-square predicting capacity. We can observe that are almost the same.
predicted <- predict(LM1, newdata=hitterstest)
LM1_R2 <- cor(predicted, hitterstest$logSalary)^2
LM1_R2## [1] 0.2522379Problem #3
I’m building 2 more linear models with training hitters data. This time those models will be build by forward/backward stepwise regrssion. First I’m making the “arguments” null and full who will help to define the way I’m doing my Linear model.
leaps=regsubsets(hitterstrain$logSalary~., data=hitterstrain, nbest = 10)
null=lm(hitterstrain$logSalary~1, data=hitterstrain)
full=lm(hitterstrain$logSalary~., data=hitterstrain)(a)
By using null in my step function I’m specifying if my model is “forward” or “Backward”. In this case LM2 will be “forward”.
LM2 <- step(null, scope = list(lower=null, upper=full),direction = "forward")## Start: AIC=-36.75
## hitterstrain$logSalary ~ 1
##
## Df Sum of Sq RSS AIC
## + CHits 1 62.279 87.758 -133.968
## + CRuns 1 61.152 88.885 -131.607
## + CAtBat 1 58.656 91.381 -126.484
## + CRBI 1 52.014 98.023 -113.503
## + CWalks 1 45.190 104.848 -101.052
## + Years 1 42.795 107.243 -96.873
## + CHmRun 1 35.394 114.643 -84.528
## + Hits 1 31.109 118.929 -77.739
## + RBI 1 28.142 121.895 -73.181
## + Runs 1 25.595 124.442 -69.355
## + AtBat 1 25.314 124.723 -68.938
## + Walks 1 25.209 124.828 -68.782
## + HmRun 1 16.054 133.983 -55.689
## + PutOuts 1 6.397 143.640 -42.813
## <none> 150.037 -36.752
## + Assists 1 0.680 149.357 -35.593
## + Errors 1 0.009 150.028 -34.763
##
## Step: AIC=-133.97
## hitterstrain$logSalary ~ CHits
##
## Df Sum of Sq RSS AIC
## + Hits 1 13.7220 74.036 -163.42
## + Runs 1 11.9989 75.759 -159.17
## + AtBat 1 10.6337 77.124 -155.86
## + RBI 1 9.2378 78.520 -152.54
## + Walks 1 7.9072 79.851 -149.44
## + PutOuts 1 6.5531 81.205 -146.32
## + HmRun 1 4.2733 83.485 -141.20
## + CAtBat 1 3.3886 84.370 -139.25
## + Years 1 1.6035 86.155 -135.38
## + CRBI 1 1.1586 86.599 -134.43
## + Assists 1 1.0612 86.697 -134.22
## <none> 87.758 -133.97
## + CHmRun 1 0.8151 86.943 -133.69
## + CWalks 1 0.5362 87.222 -133.10
## + Errors 1 0.1170 87.641 -132.21
## + CRuns 1 0.0740 87.684 -132.12
##
## Step: AIC=-163.42
## hitterstrain$logSalary ~ CHits + Hits
##
## Df Sum of Sq RSS AIC
## + PutOuts 1 2.30371 71.732 -167.27
## + AtBat 1 1.41545 72.621 -165.00
## + Walks 1 1.06455 72.972 -164.10
## <none> 74.036 -163.42
## + Errors 1 0.57543 73.461 -162.87
## + Years 1 0.42476 73.611 -162.49
## + CHmRun 1 0.35216 73.684 -162.31
## + CRBI 1 0.34062 73.696 -162.28
## + CAtBat 1 0.27880 73.757 -162.12
## + RBI 1 0.06229 73.974 -161.58
## + HmRun 1 0.05493 73.981 -161.56
## + Runs 1 0.05245 73.984 -161.56
## + CWalks 1 0.01684 74.019 -161.47
## + Assists 1 0.01205 74.024 -161.45
## + CRuns 1 0.00068 74.035 -161.43
##
## Step: AIC=-167.27
## hitterstrain$logSalary ~ CHits + Hits + PutOuts
##
## Df Sum of Sq RSS AIC
## + AtBat 1 1.45545 70.277 -169.06
## <none> 71.732 -167.27
## + CRBI 1 0.69234 71.040 -167.07
## + Walks 1 0.58028 71.152 -166.77
## + Years 1 0.56417 71.168 -166.73
## + CHmRun 1 0.53506 71.197 -166.66
## + Errors 1 0.51310 71.219 -166.60
## + CAtBat 1 0.12139 71.611 -165.59
## + Runs 1 0.08114 71.651 -165.48
## + Assists 1 0.02542 71.707 -165.34
## + CRuns 1 0.01330 71.719 -165.31
## + HmRun 1 0.00192 71.731 -165.28
## + RBI 1 0.00161 71.731 -165.28
## + CWalks 1 0.00103 71.731 -165.27
##
## Step: AIC=-169.06
## hitterstrain$logSalary ~ CHits + Hits + PutOuts + AtBat
##
## Df Sum of Sq RSS AIC
## + Walks 1 1.28214 68.995 -170.47
## <none> 70.277 -169.06
## + CRBI 1 0.57984 69.697 -168.60
## + Years 1 0.54125 69.736 -168.49
## + CHmRun 1 0.32888 69.948 -167.93
## + Assists 1 0.24828 70.029 -167.72
## + Runs 1 0.24429 70.033 -167.71
## + Errors 1 0.18449 70.093 -167.55
## + CRuns 1 0.11788 70.159 -167.37
## + RBI 1 0.06921 70.208 -167.25
## + HmRun 1 0.04273 70.234 -167.18
## + CWalks 1 0.02884 70.248 -167.14
## + CAtBat 1 0.01971 70.257 -167.12
##
## Step: AIC=-170.47
## hitterstrain$logSalary ~ CHits + Hits + PutOuts + AtBat + Walks
##
## Df Sum of Sq RSS AIC
## + CRBI 1 0.97209 68.023 -171.09
## <none> 68.995 -170.47
## + CHmRun 1 0.66399 68.331 -170.26
## + Years 1 0.63599 68.359 -170.18
## + CWalks 1 0.58012 68.415 -170.03
## + Assists 1 0.46264 68.532 -169.72
## + Errors 1 0.06954 68.925 -168.66
## + CRuns 1 0.04122 68.954 -168.58
## + RBI 1 0.02362 68.971 -168.53
## + HmRun 1 0.01653 68.978 -168.51
## + Runs 1 0.00882 68.986 -168.49
## + CAtBat 1 0.00169 68.993 -168.47
##
## Step: AIC=-171.1
## hitterstrain$logSalary ~ CHits + Hits + PutOuts + AtBat + Walks +
## CRBI
##
## Df Sum of Sq RSS AIC
## + RBI 1 0.78089 67.242 -171.23
## <none> 68.023 -171.09
## + Years 1 0.54402 67.479 -170.58
## + HmRun 1 0.51320 67.510 -170.50
## + CWalks 1 0.32193 67.701 -169.97
## + Assists 1 0.22721 67.796 -169.71
## + Errors 1 0.12014 67.903 -169.42
## + CHmRun 1 0.04982 67.973 -169.23
## + CAtBat 1 0.02030 68.002 -169.15
## + CRuns 1 0.00374 68.019 -169.10
## + Runs 1 0.00359 68.019 -169.10
##
## Step: AIC=-171.23
## hitterstrain$logSalary ~ CHits + Hits + PutOuts + AtBat + Walks +
## CRBI + RBI
##
## Df Sum of Sq RSS AIC
## <none> 67.242 -171.23
## + Years 1 0.48548 66.756 -170.57
## + Assists 1 0.33082 66.911 -170.14
## + CWalks 1 0.21262 67.029 -169.82
## + Errors 1 0.15537 67.086 -169.66
## + CHmRun 1 0.07190 67.170 -169.43
## + CAtBat 1 0.02184 67.220 -169.29
## + Runs 1 0.01944 67.222 -169.28
## + HmRun 1 0.01869 67.223 -169.28
## + CRuns 1 0.00038 67.241 -169.23predicted <- predict(LM2, newdata=hitterstest)
LM2_R2 <- cor(predicted, hitterstest$logSalary)^2
LM2_R2## [1] 0.4212This is the R-square of testing data for LM2 which one is almost the same than LM2 R-square.
(b)
Now by full I’m building a backward stepwise regression linear model.
LM3 <- step(full, scope = list(lower=null, upper=full),direction = "backward")## Start: AIC=-161.44
## hitterstrain$logSalary ~ AtBat + Hits + HmRun + Runs + RBI +
## Walks + Years + CAtBat + CHits + CHmRun + CRuns + CRBI +
## CWalks + PutOuts + Assists + Errors
##
## Df Sum of Sq RSS AIC
## - CAtBat 1 0.00277 64.326 -163.43
## - CHmRun 1 0.00643 64.330 -163.42
## - CRuns 1 0.08696 64.410 -163.19
## - RBI 1 0.11183 64.435 -163.12
## - Runs 1 0.11738 64.441 -163.10
## - CHits 1 0.15150 64.475 -163.00
## - HmRun 1 0.15473 64.478 -163.00
## - CRBI 1 0.18447 64.508 -162.91
## - CWalks 1 0.55591 64.879 -161.85
## - Years 1 0.68277 65.006 -161.49
## <none> 64.323 -161.44
## - Errors 1 1.00330 65.327 -160.58
## - Assists 1 1.61018 65.934 -158.87
## - PutOuts 1 2.12262 66.446 -157.43
## - Walks 1 2.15548 66.479 -157.34
## - Hits 1 2.36473 66.688 -156.76
## - AtBat 1 2.55156 66.875 -156.24
##
## Step: AIC=-163.43
## hitterstrain$logSalary ~ AtBat + Hits + HmRun + Runs + RBI +
## Walks + Years + CHits + CHmRun + CRuns + CRBI + CWalks +
## PutOuts + Assists + Errors
##
## Df Sum of Sq RSS AIC
## - CHmRun 1 0.00447 64.331 -165.42
## - RBI 1 0.10978 64.436 -165.12
## - CRuns 1 0.11018 64.436 -165.12
## - Runs 1 0.12591 64.452 -165.07
## - HmRun 1 0.15858 64.485 -164.98
## - CRBI 1 0.18660 64.513 -164.90
## - CHits 1 0.30816 64.634 -164.55
## <none> 64.326 -163.43
## - CWalks 1 0.76838 65.094 -163.24
## - Years 1 0.78033 65.106 -163.20
## - Errors 1 1.00053 65.327 -162.58
## - Assists 1 1.62479 65.951 -160.82
## - PutOuts 1 2.16701 66.493 -159.30
## - Walks 1 2.27754 66.604 -159.00
## - Hits 1 2.94702 67.273 -157.15
## - AtBat 1 3.11340 67.440 -156.69
##
## Step: AIC=-165.42
## hitterstrain$logSalary ~ AtBat + Hits + HmRun + Runs + RBI +
## Walks + Years + CHits + CRuns + CRBI + CWalks + PutOuts +
## Assists + Errors
##
## Df Sum of Sq RSS AIC
## - RBI 1 0.10979 64.440 -167.10
## - Runs 1 0.15513 64.486 -166.97
## - CRuns 1 0.21506 64.546 -166.80
## - HmRun 1 0.24283 64.573 -166.72
## - CHits 1 0.62192 64.953 -165.64
## <none> 64.331 -165.42
## - Years 1 0.78668 65.117 -165.17
## - CWalks 1 0.87782 65.208 -164.91
## - CRBI 1 0.98899 65.320 -164.60
## - Errors 1 0.99788 65.328 -164.57
## - Assists 1 1.62108 65.952 -162.81
## - PutOuts 1 2.17446 66.505 -161.27
## - Walks 1 2.33502 66.666 -160.82
## - Hits 1 3.01160 67.342 -158.96
## - AtBat 1 3.16207 67.493 -158.54
##
## Step: AIC=-167.1
## hitterstrain$logSalary ~ AtBat + Hits + HmRun + Runs + Walks +
## Years + CHits + CRuns + CRBI + CWalks + PutOuts + Assists +
## Errors
##
## Df Sum of Sq RSS AIC
## - CRuns 1 0.1849 64.625 -168.57
## - Runs 1 0.2007 64.641 -168.53
## - CHits 1 0.6080 65.048 -167.37
## <none> 64.440 -167.10
## - Years 1 0.8357 65.276 -166.72
## - CRBI 1 0.8806 65.321 -166.59
## - Errors 1 0.9422 65.383 -166.42
## - CWalks 1 0.9896 65.430 -166.28
## - HmRun 1 1.1478 65.588 -165.84
## - Assists 1 1.6562 66.097 -164.41
## - PutOuts 1 2.1321 66.573 -163.08
## - Walks 1 2.7494 67.190 -161.37
## - AtBat 1 3.1033 67.544 -160.40
## - Hits 1 3.7342 68.175 -158.68
##
## Step: AIC=-168.57
## hitterstrain$logSalary ~ AtBat + Hits + HmRun + Runs + Walks +
## Years + CHits + CRBI + CWalks + PutOuts + Assists + Errors
##
## Df Sum of Sq RSS AIC
## - Runs 1 0.0761 64.701 -170.36
## - Years 1 0.6994 65.325 -168.58
## <none> 64.625 -168.57
## - CWalks 1 0.8078 65.433 -168.28
## - CRBI 1 0.8574 65.483 -168.13
## - Errors 1 1.0301 65.655 -167.65
## - HmRun 1 1.1341 65.759 -167.35
## - Assists 1 1.6612 66.287 -165.88
## - PutOuts 1 1.9977 66.623 -164.94
## - Walks 1 2.6085 67.234 -163.25
## - AtBat 1 2.9512 67.576 -162.31
## - Hits 1 3.6306 68.256 -160.46
## - CHits 1 4.4185 69.044 -158.34
##
## Step: AIC=-170.36
## hitterstrain$logSalary ~ AtBat + Hits + HmRun + Walks + Years +
## CHits + CRBI + CWalks + PutOuts + Assists + Errors
##
## Df Sum of Sq RSS AIC
## <none> 64.701 -170.36
## - Years 1 0.7623 65.464 -170.19
## - CRBI 1 0.7913 65.493 -170.11
## - CWalks 1 0.8654 65.567 -169.90
## - Errors 1 0.9766 65.678 -169.59
## - HmRun 1 1.0704 65.772 -169.32
## - Assists 1 1.6525 66.354 -167.69
## - PutOuts 1 2.2163 66.918 -166.12
## - Walks 1 2.6465 67.348 -164.94
## - AtBat 1 2.9875 67.689 -164.00
## - Hits 1 4.0416 68.743 -161.15
## - CHits 1 4.3473 69.049 -160.33predicted <- predict(LM3, newdata=hitterstest)
LM3_R2 <- cor(predicted, hitterstest$logSalary)^2
LM3_R2## [1] 0.4549475This is the R-square of testing data for LM3 which one is different than LM3 R-square.
Problem #4
Now I’m going to build three kind of linear models (Using 10-fold cros-validation): LM, KNN, and MARS. To simplify my code I will be using the function train, just changing “method”.
(a)
Using hitterstrain and method=“lm”, I able to build a new linear model “LM4”.
LM4 <- train(logSalary~., data=hitterstrain, method="lm",trControl=trainControl(method = "cv", number = 10))
summary(LM4)##
## Call:
## lm(formula = .outcome ~ ., data = dat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.27147 -0.44874 0.01607 0.40936 2.79909
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.677e+00 1.959e-01 23.872 <2e-16 ***
## AtBat -3.931e-03 1.523e-03 -2.582 0.0107 *
## Hits 1.445e-02 5.813e-03 2.485 0.0139 *
## HmRun 9.406e-03 1.480e-02 0.636 0.5258
## Runs -3.868e-03 6.987e-03 -0.554 0.5805
## RBI 3.493e-03 6.463e-03 0.540 0.5896
## Walks 1.066e-02 4.492e-03 2.373 0.0188 *
## Years 4.177e-02 3.128e-02 1.335 0.1836
## CAtBat -2.807e-05 3.299e-04 -0.085 0.9323
## CHits 1.097e-03 1.745e-03 0.629 0.5302
## CHmRun 5.071e-04 3.912e-03 0.130 0.8970
## CRuns 8.409e-04 1.764e-03 0.477 0.6343
## CRBI -1.265e-03 1.822e-03 -0.694 0.4886
## CWalks -9.993e-04 8.293e-04 -1.205 0.2299
## PutOuts 4.154e-04 1.765e-04 2.355 0.0197 *
## Assists 1.052e-03 5.131e-04 2.051 0.0418 *
## Errors -1.647e-02 1.017e-02 -1.619 0.1074
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6188 on 168 degrees of freedom
## Multiple R-squared: 0.5713, Adjusted R-squared: 0.5305
## F-statistic: 13.99 on 16 and 168 DF, p-value: < 2.2e-16predicted <- predict(LM4, newdata=hitterstest)
LM4_R2 <- cor(predicted, hitterstest$logSalary)^2
LM4_R2## [1] 0.4518025To evaluate the predictive capacity I’m computing its R-square for the testing data. For LM4 is a difference of almost 0.1
(b)
Applying same function it’s just necessary to change method=“lm” to method=“knn”.
kNN1 <- train(logSalary~., data=hitterstrain, method="knn",trControl=trainControl(method = "cv", number = 10))
summary(kNN1)## Length Class Mode
## learn 2 -none- list
## k 1 -none- numeric
## theDots 0 -none- list
## xNames 16 -none- character
## problemType 1 -none- character
## tuneValue 1 data.frame list
## obsLevels 1 -none- logicalpredicted <- predict(kNN1, newdata=hitterstest)
kNN1_R2 <- cor(predicted, hitterstest$logSalary)^2
kNN1_R2## [1] 0.6818339To evaluate the predictive capacity I’m computing its R-square for the testing data.
(c)
Finally to generate a linear model with MARS method, I will type “earth” in method, using the same function.
MARS1 <- train(logSalary~., data=hitterstrain, method="earth",trControl=trainControl(method = "cv", number = 10))
summary(MARS1)## Call: earth(x=matrix[185,16], y=c(6.163,6.174,6...), keepxy=TRUE,
## degree=1, nprune=10)
##
## coefficients
## (Intercept) 5.7916571
## h(47-Hits) 0.0326996
## h(1-HmRun) 0.7370106
## h(Walks-15) 0.1475733
## h(20-Walks) 0.1028559
## h(Walks-20) -0.1410792
## h(Years-7) -0.1268858
## h(CAtBat-1089) -0.0004544
## h(476-CHits) -0.0055201
## h(CHits-476) 0.0024829
##
## Selected 10 of 22 terms, and 6 of 16 predictors
## Termination condition: RSq changed by less than 0.001 at 22 terms
## Importance: CHits, Years, Hits, Walks, HmRun, CAtBat, AtBat-unused, ...
## Number of terms at each degree of interaction: 1 9 (additive model)
## GCV 0.1567149 RSS 23.3429 GRSq 0.8088497 RSq 0.8444194predicted <- predict(MARS1, newdata=hitterstest)
MARS1_R2 <- cor(predicted, hitterstest$logSalary)^2
MARS1_R2## [,1]
## y 0.6125382To evaluate the predictive capacity I’m computing its R-square for the testing data. For MARS1 has a difference of 0.2
Problem #5
As follow, It shows the R-square of LM1, LM2, LM3, LM4. We can see at first sight the differences between those results from linear models.
LM1_R2## [1] 0.2522379LM2_R2## [1] 0.4212LM3_R2## [1] 0.4549475LM4_R2## [1] 0.4518025Which model do you think is the best?
By looking at the results I can say that LM1 is better than others models because the predictive capacity between training and testing data is almost the same, it just has a difference of 0.01, while for others models is greater or equal to 0.1. And with that it isn’t generate a variance in our results. I will show this results justifying my answer. Also I belive it happened what it happens because of the times I build LM1, removing values to make it more efficient
summary(LM1)##
## Call:
## lm(formula = hitterstrain$logSalary ~ Hits + Walks, data = hitterstrain)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.5822 -0.6320 0.1774 0.5589 2.8355
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.820657 0.156824 30.739 < 2e-16 ***
## Hits 0.006499 0.001533 4.239 3.56e-05 ***
## Walks 0.009822 0.003365 2.919 0.00395 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7901 on 182 degrees of freedom
## Multiple R-squared: 0.2428, Adjusted R-squared: 0.2345
## F-statistic: 29.18 on 2 and 182 DF, p-value: 1.02e-11LM1_R2## [1] 0.2522379