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We will apply pca on wine dataset
Applying PCA on relevant predictors
Analyzing components of the output
Creating biplot
Calculating proportion of variance
Creating scree plot and cumulative plots
Building model using PC1 to PC4
We will apply pca on wine dataset
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wine = read.csv ("https://storage.googleapis. com/dimensionless/ Analytics/wine.csv") |
Applying PCA on relevant predictors
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pca<-prcomp(wine[,3:7],scale=TRUE) |
Analyzing components of the output
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#Std Dev pca$sdev |
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## [1] 1.45691795 1.16557440 0.99526725 0.72328569 0.07160523 |
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# Loadings pca$rotation |
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## PC1 PC2 PC3 PC4 PC5 ## WinterRain 0.09395915 0.7384046 -0.1256430 -0.65563602 0.01689675 ## AGST -0.32836427 -0.3806578 0.6264975 -0.59544647 0.01486508 ## HarvestRain 0.03679770 -0.5244412 -0.7238807 -0.44675373 -0.00390888 ## Age -0.66342357 0.1258942 -0.1914225 0.10156506 0.70502609 ## FrancePop 0.66472828 -0.1377328 0.1762640 -0.07536942 0.70881341 |
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# Principal Components pca$x |
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## PC1 PC2 PC3 PC4 PC5 ## [1,] -2.66441523 0.01812071 -0.19940771 -0.26187403 0.017848626 ## [2,] -2.31090775 1.27230388 0.17749206 0.09070174 -0.006316369 ## [3,] -2.31872688 -0.42425903 0.34077385 0.31372038 -0.067315308 ## [4,] -1.55060520 -0.23588712 -0.23518124 1.69094289 -0.101731306 ## [5,] -1.35803408 -0.06913418 -0.82614968 0.15237445 -0.073508609 ## [6,] -1.77313036 -1.24596188 0.30308288 -0.33015372 -0.062254812 ## [7,] -0.83734190 0.14770821 -1.90545030 -1.40861601 -0.059226672 ## [8,] -1.17507833 1.74417439 1.38340778 -1.06038701 -0.003711288 ## [9,] -0.49978424 1.43298732 0.48615479 0.39280758 0.049944991 ## [10,] -0.01341322 0.49601115 -0.91321708 0.70204963 0.066036711 ## [11,] -0.75505205 -1.14907041 1.34584178 0.68608150 0.093179804 ## [12,] 0.56223704 -0.19991293 -2.22360713 0.32097131 0.062303660 ## [13,] 0.22813081 1.59605527 0.45968547 -0.71903876 0.121180565 ## [14,] 0.47318950 0.92227025 0.01377674 -0.14755601 0.084300103 ## [15,] 0.65743468 -0.89650446 -1.56747979 -0.66837607 0.043747752 ## [16,] 0.60397262 -0.98362933 -0.69683131 -0.53748100 0.042134220 ## [17,] 0.67149628 0.27205617 0.92090308 0.03475269 0.053849458 ## [18,] 0.76315093 -0.37837929 0.90694860 0.13667046 0.053372925 ## [19,] 1.81242805 0.18510809 -1.13339807 1.48444569 0.007580131 ## [20,] 0.83436088 -1.66846501 1.33756198 0.62859729 0.028001330 ## [21,] 1.52887804 -0.59071652 -0.11300095 -0.06358380 0.010558586 ## [22,] 1.33939957 -0.90295396 0.65594023 -0.56734753 -0.015034228 ## [23,] 1.05051137 -2.71675250 0.74697721 -0.89482443 -0.075496028 ## [24,] 2.38846524 1.80061406 0.03888058 -0.12744556 -0.110346034 ## [25,] 2.34283421 1.57421714 0.69629625 0.15256833 -0.159098209 |
Creating biplot
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biplot(pca,scale=0) |
Calculating proportion of variance|
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pr.var<-pca$sdev^2 pve<-pr.var/sum(pr.var) |
Creating scree plot and cumulative plots
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plot(pve, xlab ="Principal Component", ylab ="Proportion of Variance Explained", ylim=c(0 ,1) ,type="b") |
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plot(cumsum (pve), xlab ="Principal Component", ylab =" Cumulative Proportion of Variance Explained ", ylim=c(0 ,1), type="b") |
Building model using PC1 to PC4
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predictor<-pca$x[,1:4] wine<-cbind(wine,predictor) model<-lm(Price~PC1+PC2+PC3+PC4,data=wine) summary(model) |
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## ## Call: ## lm(formula = Price ~ PC1 + PC2 + PC3 + PC4, data = wine) ## ## Residuals: ## Min 1Q Median 3Q Max ## -0.46899 -0.24789 -0.00215 0.20607 0.52709 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 7.06722 0.05889 120.016 < 2e-16 *** ## PC1 -0.25487 0.04125 -6.178 4.91e-06 *** ## PC2 0.12730 0.05156 2.469 0.0227 * ## PC3 0.41744 0.06039 6.913 1.03e-06 *** ## PC4 -0.18647 0.08309 -2.244 0.0363 * ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 0.2944 on 20 degrees of freedom ## Multiple R-squared: 0.8292, Adjusted R-squared: 0.795 ## F-statistic: 24.27 on 4 and 20 DF, p-value: 1.964e-07 |
Making Predictions
We cannot convert test data into principal components, by applying pca. Instead we have to apply same transformations on test data as we did for train data
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wineTest = read.csv("https://storage.googleapis.com/dimensionless/Analytics/wine_test.csv") wineTest |
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## Year Price WinterRain AGST HarvestRain Age FrancePop ## 1 1979 6.9541 717 16.1667 122 4 54835.83 ## 2 1980 6.4979 578 16.0000 74 3 55110.24 |
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pca_test<-predict(pca,wineTest[,3:7]) class(pca_test) |
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## [1] "matrix" |
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pca_test |
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## PC1 PC2 PC3 PC4 PC5 ## [1,] 2.303725 0.5946824 0.4101509 -0.3722356 -0.2074747 ## [2,] 2.398317 0.2242893 0.8925278 0.7329912 -0.2649691 |
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# Converting to data frame pca_test<-as.data.frame(pca_test) pca_test |
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## PC1 PC2 PC3 PC4 PC5 ## 1 2.303725 0.5946824 0.4101509 -0.3722356 -0.2074747 ## 2 2.398317 0.2242893 0.8925278 0.7329912 -0.2649691 |
Making predictions
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pred_pca<-predict(object = model, newdata=pca_test) pred_pca |
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## 1 2 ## 6.796398 6.720412 |
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wineTest$Price |
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## [1] 6.9541 6.4979 |