Among those 14 potential explanatory variables,non-dummy variables are:
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1 Among those 14 potential explanatory variables,non-dummy variables are: Size: 2nd column in the dataset Land: 14th column in the dataset Bed.Rooms: 5th column in the dataset Fireplace: 7th column in the dataset Full.Bath: 8th column in the dataset Half.Bath: 9th column in the dataset Basement..Total.: 10th column in the dataset Finished.Bsmt: 11th column in the dataset there are 8 non-dummy explanatory variables 1. First step standardize all non-dummy variables via scale function in R. 2. There are 17 columns in the original dataset. A new data frame with 15 columns, which means get rid of two columns, Bsmt.Full.Bath (12th column) and Bsmt.Half.Bath (13th column) in the original dataset 3. OLS output: > summary(db_outols) Call: lm(formula = Y ~ X) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) * Size Garage Mutiple.Car Bed.Rooms Central.Air Fireplace e-05 *** Full.Bath Half.Bath * Basement..Total ** Finished.Bsmt Land e-05 *** Style..2.Story Zone..Town.Center Bsmt.Bath * --- Signif. codes: 0 *** ** 0.01 * Residual standard error: on 78 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: 21.1 on 14 and 78 DF, p-value: < 2.2e-16 From OLS output, the highlight predictor variables have significant coefficient.
2 Lasso > coef(db_outlasso, s = "lambda.1se") 15 x 1 sparse Matrix of class "dgcmatrix" 1 (Intercept) Size Garage. Mutiple.Car. Bed.Rooms. Central.Air Fireplace Full.Bath. Half.Bath. Basement..Total.. Finished.Bsmt. Land Style..2.Story.. Zone..Town.Center.. Bsmt.Bath. There are four predictor variables via LASSO procedure: size, central air, fire place, land Ridge > coef(db_outridge, s = "lambda.1se") 15 x 1 sparse Matrix of class "dgcmatrix" 1 (Intercept) Size Garage Mutiple.Car Bed.Rooms Central.Air Fireplace Full.Bath Half.Bath Basement..Total Finished.Bsmt Land Style..2.Story Zone..Town.Center Bsmt.Bath The first four predictors with largest coefficients are: central air, size, garage, basement bath Elastic Net with \alpha = 0.5 > coef(db_outenet, s = "lambda.1se") 15 x 1 sparse Matrix of class "dgcmatrix" 1 (Intercept) Size Garage. Mutiple.Car. Bed.Rooms. Central.Air Fireplace Full.Bath. Half.Bath. Basement..Total.. Finished.Bsmt. Land Style..2.Story..
3 Zone..Town.Center.. Bsmt.Bath. There are four predictor variables via LASSO procedure: size, central air, fire place, land Ps: OLS will give more relatively complexity model. The four predictors that be considered in the following analysis are: size, central air, fire place, Bsmt.Bath The highest correlation are between lasso and Elastic Net Y_OLS Y_ridge Y_lasso Y_enet Y_knn Y_loess1 Y_loesscv Y_rf Y_nnet Y_avnnet Here is the R code:
4 rm(list = ls()) ## read data db = read.csv("f:././././isu_course/stat342/hw8/328 Final 03 Data.csv",stringsAsFactors = FALSE) ## print out the columns names of the data set print(colnames(db)) ## Among those 14 potential explanatory variables,non-dummy variables are: ## Size: 2nd column in the dataset ## Land: 14th column in the dataset ## Bed.Rooms: 5th column in the dataset ## Fireplace: 7th column in the dataset ## Full.Bath: 8th column in the dataset ## Half.Bath: 9th column in the dataset ## Basement..Total.: 10th column in the dataset ## Finished.Bsmt: 11th column in the dataset ## there are 8 non-dummy explanatory variables ## standardize all those eight explanatory variables using scale function in R db_standardized = db db_standardized$size = scale(db$size) db_standardized$land = scale(db$land) db_standardized$bed.rooms = scale(db$bed.rooms) db_standardized$fireplace = scale(db$fireplace) db_standardized$full.bath = scale(db$full.bath) db_standardized$half.bath = scale(db$half.bath) db_standardized$basement..total. = scale(db$basement..total.) db_standardized$finished.bsmt = scale(db$finished.bsmt) db_standardized$price = scale(db$price)
5 ## there are 17 columns in the original dataset ## a new data frame with 15 columns, which means get rid of two columns, Bsmt.Full.Bath (12th column) and Bsmt.Half.Bath (13th column) in the original dataset db_standardized_15 = as.data.frame(db_standardized[,c(-12,-13)]) Y = db_standardized_15$price X = db_standardized_15[,c(-1)] X = as.matrix(x) ## OLS db_outols = lm(y~x) summary(db_outols) coef(db_outols) # lasso fit library(glmnet) db_outlasso = cv.glmnet(x,y,alpha=1) summary(db_outlasso) x11() plot(db_outlasso) ## get the coefficeinet for lasso regression coef(db_outlasso, s = "lambda.1se") #Next a ridge fit db_outridge = cv.glmnet(x,y,alpha=0) summary(db_outridge) x11() plot(db_outridge)
6 ## get the coefficeinet for ridge fit regression coef(db_outridge, s = "lambda.1se") #Then an alpha=.5 elastic net fit db_outenet = cv.glmnet(x,y,alpha=.5) summary(db_outenet) x11() plot(db_outenet) ## get the coefficeinet for elastic net fit coef(db_outenet, s = "lambda.1se") library(fnn) ## choose k with largest R2-Predict value. ## ps: P2-Predict here represents predicted R-square. So larger is better ## only chose size, central air, fire place, garage four variables #x_new = X[,c("Size", "Central.Air", "Fireplace", "Garage")] x_new = X[,c("Size", "Central.Air", "Fireplace", "Bsmt.Bath")] db_outknn = knn.reg(x_new,test=null,y,k=4) print(db_outknn) #db_outknn$pred #Now try random forest fitting ## use default value library(randomforest) db_outrf = randomforest(y~x_new[,1]+x_new[,2]+x_new[,3]+x_new[,4],type="regression")
7 ##predict(db_outrf) ## N-W kernel regression library(regpro) nwregr = function(x){ ## input each point, apply N-W kernel regression ## return predicted value for that point y_pred = kernesti.regr(x,x_new,y,h = 3) return(y_pred) } db_outnw = rep(0,nrow(x_new)) for(i in 1:nrow(X)){ db_outnw = nwregr(x_new[i,]) } #Now some local regression smoothing db_outloess1 = loess(y~x_new,as.data.frame(cbind(x_new,y)),control=loess.control("direct"),family="gaussian",degree=2,span= 0.75,normalize=FALSE) #Now cross-validate local regression smmothing library(bisoreg) db_loesscv = loess.wrapper(x_new, Y, span.vals = seq(.25, 1, by = 0.5), folds = 5)
8 #Now some neural nets and averages of neural nets require(nnet) db_outnnet = nnet(x,y,size=1,decay=.001,linout=true,maxit=1000) var(residuals(db_outnnet)) fitted.values(db_outnnet) require(caret) db_outavnnet = avnnet(x,y,repeats=8,size=1,decay=.001,linout=true,maxit=1000) Y_OLS = predict(db_outols,as.data.frame(x)) Y_ridge = predict(db_outridge,x,s="lambda.1se") Y_lasso = predict(db_outlasso,x,s="lambda.1se") Y_Enet = predict(db_outenet,x,s="lambda.1se") Y_knn = db_outknn$pred Y_loess1 = predict(db_outloess1) Y_loesscv = predict(db_loesscv) Y_rf = predict(db_outrf) Y_nw = db_outnw Y_nnet = fitted.values(db_outnnet) Y_avnnet = predict(db_outavnnet) Ypreds = as.data.frame(cbind(y_ols,y_ridge,y_lasso,y_enet,y_knn,y_loess1,y_loesscv,y_rf,y_nnet,y_avnnet)) colnames(ypreds)<-c("y_ols","y_ridge","y_lasso","y_enet","y_knn","y_loess1","y_loesscv","y_rf","y_nnet","y_avnnet") x11() pairs(ypreds,pch = 20) cor(ypreds)
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