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WF)*S3+70{}l>~N`8v?}<% + filter(Expire.Year == 2020) %>% #vast majority of observations fall into year 2020 = 22504/29043 total rows + sample_n(5000, replace = FALSE) %>% #sampling 5000 observations with set seed value + dplyr::select(-HVAC.Plus.Count, -Service.Fee.Saveup.Count, -Expire.Period, -Expire.Year) %>% #dropping unimportant purchase options + now year column as it will be factor with 1 class + dplyr::select(-(Addt.Frig.Count:Purchased.Roof.Count)) %>% #dropping unimportant purchase options + relocate(Renewed.) #move binary response variable to front of df + +#checking new dimension and column names of df +dim(home_warranty_1) +colnames(home_warranty_1) + +#converting appropriate columns into factors +home_warranty_1$Primary.Sales.Channel = as.factor(home_warranty_1$Primary.Sales.Channel) +home_warranty_1$Payment.Method = as.factor(home_warranty_1$Payment.Method) +home_warranty_1$Brochure.Name = as.factor(home_warranty_1$Brochure.Name) +home_warranty_1$Expire.Month = as.factor(home_warranty_1$Expire.Month) +home_warranty_1$Sales.Region = as.factor(home_warranty_1$Sales.Region) +home_warranty_1$State = as.factor(home_warranty_1$State) + +#recode appropriate factor variables into binary +home_warranty_1$Had.Phone.Number. = ifelse(home_warranty_1$Had.Phone.Number. == "Phone Number", 1, 0) +home_warranty_1$Had.Email.Address. = ifelse(home_warranty_1$Had.Email.Address. == "Email Address", 1, 0) +home_warranty_1$Had.Web.Profile. = ifelse(home_warranty_1$Had.Web.Profile. == "Web Profile", 1, 0) +home_warranty_1$Had.Claim. = ifelse(home_warranty_1$Had.Claim. == "Yes", 1, 0) +home_warranty_1$Purchased.Option. = ifelse(home_warranty_1$Purchased.Option. == "Yes", 1, 0) + +#recode step ups to numeric variables +home_warranty_1$Renewal.Discount.Step.Up = suppressWarnings(as.numeric(home_warranty_1$Renewal.Discount.Step.Up)) +home_warranty_1$Renewal.Net.Step.Up = suppressWarnings(as.numeric(home_warranty_1$Renewal.Net.Step.Up)) + +#rename variables for clarity +home_warranty_2 = home_warranty_1 %>% + rename(Renewed = Renewed., Had.Phone = Had.Phone.Number., Had.Email = Had.Email.Address., + Had.Webprofile = Had.Web.Profile., Purchased.Option = Purchased.Option., + Number.Of.Options.Purchased = Option.Purchased, Had.Claim = Had.Claim., Condo = Condo.) + +#check structure of df +str(home_warranty_2) + +#check for class bias in Y variable +table(home_warranty_2$Renewed) + + + +################################################################################################################ +#Checking for correlations in data set +################################################################################################################ + +#look at overall correlation of numeric variables in df +data.correlations = cor(home_warranty_2[sapply(home_warranty_2, is.numeric)]); data.correlations + +#### Contact Info #### +#correlation between a client having contact info on file versus the probability of home warranty renewal success +contact.info.sums = home_warranty_2 %>% + group_by(Renewed) %>% + summarise_each(funs(sum, n()), Had.Phone, Had.Email, Had.Webprofile); contact.info.sums + +#plotting relationship between contact info and home warranty renewal +contact.info.correlation = cor(home_warranty_2[c(1,12,13,14)]) + +col2 = colorRampPalette(c("#67001F", "#B2182B", "#D6604D", "#F4A582", + "#FDDBC7", "#FFFFFF", "#D1E5F0", "#92C5DE", + "#4393C3", "#2166AC", "#053061")) +contact.info.correlation.plot = corrplot(contact.info.correlation, col = col2(200), addCoef.col = "dark grey") +mtext("Correlation Matrix of Contact Info vs Home Warranty Renewal", at = 2.5, line = -2, cex = 1.75) + +#pairs plot +contact.info.plot.pairs = pairs(contact.info.correlation, col = home_warranty_2$Renewed) + +#melting correlation data into df and visualizing with ggplot2 +contact.info.melt = reshape2::melt(contact.info.correlation, varnames = paste0("Contact.Info", 1:2), value.name = "correlation") +ggplot(contact.info.melt, aes(Contact.Info1, Contact.Info2, fill = correlation)) + geom_tile() + ggtitle("Correlation across Contact Info On File for Home Warranty Renewal") + +#### Housing Market Index and Consumer Sentiment Index by Month #### +#group indexes by month and calculate mean +month.indeces.mean = home_warranty_2 %>% + group_by(Expire.Month) %>% + summarise_each(funs(mean, n()), NAHB.Housing.Market.Index, Consumer.Sentiment.Index) + +ggplot(month.indeces.mean) + geom_point(aes(x = Expire.Month, y = NAHB.Housing.Market.Index_mean, colour = "NAHB.Housing.Market.Index_mean")) + + geom_point(aes(x = Expire.Month, y = Consumer.Sentiment.Index_mean, colour = "Consumer.Sentiment.Index_mean")) + + labs(x = "Home Warranty Expiration Month", y = "Indexes", title = "Mean NAHB Housing Market Index + Consumer Sentiment Index by Expiration Month") + theme_dark() +#indexes seem to converge around 75 + + + +################################################################################################################ +#Logistic Regression Model Full +################################################################################################################ + +str(home_warranty_2) + +#subset uninfluencing factors out of data set +final_df = home_warranty_2 %>% + dplyr::select(-c(Warranty.key, Brochure.Name, State, Zip.Code, House.over.5.000.Sq.Ft, + Sales.Region, Sell.Date, Expiration.Date, Base.Price, Option.Price, Had.Claim)) + +str(final_df) +summary(final_df) + +#first logit model using all data points as predictor variables +model_full = glm(Renewed ~ ., data = final_df, family = 'binomial') +summary(model_full) +caret::varImp(model_full) + +summary_full_glm = summary(model_full) +Pseudo_R_Full = list(summary_full_glm$coefficients, round(1 - (summary_full_glm$deviance / summary_full_glm$null.deviance), 2)); Pseudo_R_Full + +#cross validation of model_full +set.seed(4) +cv_model_full = cv.glm(na.omit(final_df), model_full, K = 10) +cv_model_full$delta + +anova(model_full, test = "Chisq") + +#Identify overinfluential observations with Cook's distance values +#Scaled change in fitted values, which is useful for identifying outliers in the X predictor values +plot(model_full, which = 4, id.n = 5) + +#odds ratio + confidence intervals +exp(cbind(OR = coef(model_full), confint(model_full))) + +#Residual deviance: 5847.4 on 4956 degrees of freedom +#AIC: 5921.4 +#Delta: 0.2059676 0.2057791 + +#Evaluation: running the full model, you can clearly the following variables are +#statistically significant towards predicting home warranty renewal success: +### Supreme.in.Base + Had.Email + Had.Webprofile + Expire.Month + Primary.Sales.Channel + Auto.Renew + Discount + Claim.Count + High.Claims + Purchased.Supreme.Count + +### Purchased.Wash.Dryer.Count + Number.Of.Options.Purchased + Renewal.Option.Step.Up + Renewal.Discount.Step.Up + +#NAs can be explained by linear dependence of the predictor variables. Need to remove these to avoid dummy variable trap +#----------------------------------------------------------------------------------------------------------- + + + +################################################################################################################ +#Logistic Regression Using STEPAIC to Fit +#Will drop predictor variables in each model and test AIC, VIF, and Odds Ratio +################################################################################################################ + +model_1 = stepAIC(model_full, direction="both") +summary(model_1) +caret::varImp(model_1) + +sort((vif(model_1)), decreasing = TRUE) #sorting and checking for the highest VIF valued variable + +model_2 = glm(Renewed ~ Supreme.in.Base + Had.Email + Had.Webprofile + + Expire.Month + Primary.Sales.Channel + Auto.Renew + + Discount + Claim.Count + High.Claims + Purchased.Supreme.Count + + Purchased.Wash.Dryer.Count + Number.Of.Options.Purchased + + Renewal.Option.Step.Up + Renewal.Discount.Step.Up, family = "binomial", data = final_df) +summary(model_2) + +set.seed(4) +cv_model_2 = cv.glm(na.omit(final_df), model_2, K = 10) +cv_model_2$delta + +#odds ratio + confidence intervals +exp(cbind(OR = coef(model_2), confint(model_2))) + +anova(model_2, test = "Chisq") + +#----------------------------------------------------------------------------------------------------------- +#Residual deviance: 5873.0 on 4970 degrees of freedom +#AIC: 5919 +#Delta: 0.2057145 0.2056059 + +#Evaluation: by removing beta coefficients with high p values and statistical insignificance, the AIC and the residual delta have decreased +#----------------------------------------------------------------------------------------------------------- + +#model final based off stepped model and removing values with too large of P values from anova test +model_final = glm(Renewed ~ Supreme.in.Base + Had.Email + Had.Phone + Had.Webprofile + + Expire.Month + Primary.Sales.Channel + Auto.Renew + + Discount + Claim.Count + High.Claims + Service.Fee.Buydown.Count + + Purchased.Supreme.Count + Purchased.Wash.Dryer.Count + Renewal.Option.Step.Up + + Renewal.Discount.Step.Up, family = "binomial", data = final_df) +summary(model_final) + +summary_final_glm = summary(model_final) +#A true measure of fit is one based strictly on a comparison of observed to predicted values from the fitted model +#R2 values in logit are always low +Pseudo_R_Final = list(summary_final_glm$coefficients, round(1 - (summary_final_glm$deviance / summary_final_glm$null.deviance), 2)); Pseudo_R_Final + +#cross validation of model_final +set.seed(4) +cv_model_final = cv.glm(na.omit(final_df), model_final, K = 10) +cv_model_final$delta + +#odds ratio + confidence intervals +exp(cbind(OR = coef(model_final), confint(model_final))) + +#Identify overinfluential observations with Cook's distance values +#Scaled change in fitted values, which is useful for identifying outliers in the X predictor values +plot(model_final, which = 4, id.n = 5) + +#showing factors that most influenced our renewal success probability +caret::varImp(model_final) + +#comparing models +anova(model_final, model_1, model_full, test = "Chisq") + +#small observable class bias in renewed residuals +qqnorm(model_final$residuals) +qqline(model_final$residuals, col=2) +hist(model_final$residuals) + +#logistic regression does not assume the residuals are normally distributed nor that the variance is constant. +#However, the deviance residual is useful for determining if individual points are not well fit by the model. +#Here we can fit the standardized deviance residuals to see how many exceed 3 standard deviations. +model_final_mutate = augment(model_final) %>% + mutate(index = 1:n()) + +ggplot(model_final_mutate, aes(index, .std.resid)) + + geom_point(alpha = .5) + + geom_ref_line(h = 3) + ggtitle("Plot of Standard Deviation Distribution of Residuals") + +#No outliers in the residuals (all residual observations within 3 SD) +model_outliers = model_final_mutate %>% + filter(abs(.std.resid) > 3) + + + + +#----------------------------------------------------------------------------------------------------------- +#Residual deviance: 5856.9 on 4969 degrees of freedom +#AIC: 5904.9 +#Delta: 0.2049345 0.2048219 + +#Final Predictor Variables: `Supreme.in.Base`, `Had.Phone`, `Had.Email`, `Had.Webprofile`, `Expire.Month`, `Primary.Sales.Channel` +# `Auto.Renew`, `Discount`, `Claim.Count`, `Service.Fee.Buydown.Count`, `Purchased.Supreme.Count` +# `Purchased.Wash.Dryer.Count`, `Renewal.Option.Step.Up`, `Renewal.Discount.Step.Up` + +#some interpretation: With all other input variables unchanged, every unit of increase in the client filing a claim +#increases the odds of the client renewing their home warranty by a factor of 1.609. +################################################################################################################ +#Model Evaluation +#Due to the fact that accuracy isn't suitable for this situation, we'll have to use another measurement to decide which cutoff value to choose, the ROC curve. +#The ROC curve is a graphical plot that illustrates the diagnostic ability of a binary classifier system as its discrimination threshold is varied. +################################################################################################################ + +#break df into training in test set with train = 80% of data and test = 20% of data +set.seed(100) +#split data into training and test sets +indices = sample.split(final_df$Renewed, SplitRatio = 0.8) +train = final_df[indices,] +test = final_df[!(indices),] + +#predicted probabilities of success for test data +test_pred = predict(model_final, type = "response", newdata = test[,-1]) + +# Let's see the summary +summary(test_pred) + +test$prob = test_pred + +#using the probability cutoff of 50% +test_pred_success = factor(ifelse(test_pred >= 0.50, "Yes", "No")) +test_actual_success = factor(ifelse(test$Renewed == 1,"Yes","No")) + +#at 50% probability cutoff, we achieved 664/1000 correct predictions +table(test_actual_success, test_pred_success) + +#checking for other levels of cut off by calibrating the output of the binary classification model and examining all possible outcomes of predictions +#confusion matrix reveals how confused the model is between the different classes +# +# Prediction Reference +# Yes No +# Yes True Pos False Pos +# +# No False Neg True Neg + +#At 0.40 +test_pred_success_2 = factor(ifelse(test_pred >= 0.40, "Yes", "No")) +test_conf2 = confusionMatrix(test_pred_success_2, test_actual_success, positive = "Yes"); test_conf2 + +#At 0.30 +test_pred_success_3 = factor(ifelse(test_pred >= 0.30, "Yes", "No")) +test_conf3 = confusionMatrix(test_pred_success_3, test_actual_success, positive = "Yes"); test_conf3 + +#At 0.20 +test_pred_success_4 = factor(ifelse(test_pred >= 0.20, "Yes", "No")) +test_conf4 = confusionMatrix(test_pred_success_4, test_actual_success, positive = "Yes"); test_conf4 + +train$prediction = predict(model_final, newdata = train, type = "response") +test$prediction = predict(model_final, newdata = test, type = "response") +test$real = test$Renewed + +#obtaining the predicted value that a client will renew on both training and testing set. +#After that we'll perform a quick evaluation on the training set by plotting the probability (score) estimated by our model with a double density plot. +#a ideal double density plot you want the distribution of scores to be separated, +#with the score of the negative instances to be on the left and the score of the positive instance to be on the right. +ggplot( train, aes(prediction, color = as.factor(Renewed) ) ) + + geom_density( size = 2 ) + + ggtitle( "Training Set's Predicted Score" ) + + scale_color_economist( name = "data", labels = c( "negative", "positive" ) ) +#Our skewed double density plot, however, can actually tell us a very important thing: Accuracy will not be a suitable measurement for this model. +#Since the prediction of a logistic regression model is a probability, in order to use it as a classifier, +#we'll have to choose a cutoff value, or you can say its a threshold value. Where scores above this value will classified as positive, those below as negative. + + +#ROC curve for this model +#Shows you the trade off between the rate at which you can correctly predict something +#with the rate of incorrectly predicting something when choosing different cutoff values. +#This curve is created by plotting the true positive rate (TPR) on the y axis against the false positive rate (FPR) on the x axis +#at various cutoff settings ( between 0 and 1 ). +#ROC analysis provides tools to select possibly optimal models and to discard suboptimal ones. +#AUC: measure ranging from 0 to 1, shows how well the classification model is performing in general = 74.1% +plot.roc(test$real, test$prediction, col = "red", main = "ROC Validation set", + percent = TRUE, print.auc = TRUE) + +# finding the optimal probability cutoff value +perform_fn = function(cutoff) { + predicted_success = factor(ifelse(test_pred >= cutoff, "Yes", "No")) + conf = confusionMatrix(predicted_success, test_actual_success, positive = "Yes") + acc = conf$overall[1] + sens = conf$byClass[1] + spec = conf$byClass[2] + out = t(as.matrix(c(sens, spec, acc))) + colnames(out) = c("sensitivity", "specificity", "accuracy") + return(out) +} + +summary(test_pred) +s = seq(.01,.80,length=1000) +OUT = matrix(0,1000,3) + +conf.matrix = data.frame(cbind(s,OUT)) + +for(i in 1:1000) { + OUT[i,] = perform_fn(s[i]) +} + +#plotting linear convergence of probability cutoff sensitivity, specificity, and accuracy +#allows us to visualize the optimal probability cutoff value +ggplot(conf.matrix) + geom_point(aes(x = s, y = V2, colour = "Sensitivity")) + geom_point(aes(x = s, y = V3, colour = "Specificity")) + + geom_point(aes(x = s, y = V4, colour = "Accuracy")) + labs(x = "Cutoff", y = "Value", title = "Linear Convergence of Probability Prediction Values in Model") + +#exact cuttoff value Where scores above this value will classified as positive, those below as negative. +cutoff = s[which(abs(conf.matrix[,2]-OUT[,3]) < 0.01)] #0.5920220 + +test_cutoff_success = factor(ifelse(test_pred >= 0.61, "Yes", "No")) + +conf_final = confusionMatrix(test_cutoff_success, test_actual_success, positive = "Yes"); conf_final +#Accuracy based upon un-weighted values in binary response class : 0.6802 + +#Using the IV variables in our final model, the final model can classify between Home Warranty Renewal success and failure at a 74.1% probability rate +#Due to the fact that accuracy isn't suitable for this situation, we used the ROC curve: +#we're making a balance between the false positive rate (FPR) and false negative rate (FNR). The objective function for our model, +#where we're trying to minimize the number of mistakes we're making or so called costs. The ROC curve's purpose is used to visualize and quantify the tradeoff +#we're making between the two measures. + +#Using a classification algorithm like logistic regression in this example enabled us to estimate probabilities of Home Warranty renewal in the future. +#As the dataset was unbalanced, meaning there were a lot more positive outcome data than negative, we shouldn't use accuracy as the measurement to evaluate our model's performance. + +################################################################################################################ +#Advanced Machine Learning Algorithms +#We felt most comfortable with our model projections above, but also performed advanced machine learning algorithms to +#test if more accurate models exist +################################################################################################################ + +# advanced machine learning algorithms +# Load CART packages +library(rpart) +# install rpart package +#install.packages("rpart.plot") +library(rpart.plot) + +#Omit NA values +final_df2 = na.omit(final_df) +final_df2 +#break df into training in test set with train = 80% of data and test = 20% of data +set.seed(100) +#split data into training and test sets +indices2 = sample.split(final_df2$Renewed, SplitRatio = 0.8) +train2 = final_df2[indices2,] +test2 = final_df2[!(indices2),] + +train2 +test2 + +#Change Renewed into a factor +train2$RenewedFactor = as.factor(train2$Renewed) +test2$RenewedFactor = as.factor(test2$Renewed) +final_df2$RenewedFactor = as.factor(final_df2$Renewed) + + +#Check that the train and test data are similar +prop.table(table(train2$RenewedFactor)) +prop.table(table(test2$RenewedFactor)) +control = trainControl(method="cv", number=10) +metric = "Accuracy" + +# decision tree +set.seed(7) +fit.dt = train(RenewedFactor ~ Supreme.in.Base + Had.Email + Had.Phone + Had.Webprofile + + Expire.Month + Primary.Sales.Channel + Auto.Renew + + Discount + Claim.Count + High.Claims + Service.Fee.Buydown.Count + + Purchased.Supreme.Count + Purchased.Wash.Dryer.Count + Renewal.Option.Step.Up + + Renewal.Discount.Step.Up, data=train2, na.action=na.omit, method="rpart",metric=metric, trControl=control) +fit.dt +#cp Accuracy Kappa +#0.02973978 0.6990520 0.3746903 + +# CART model +renewedtree = rpart(Renewed ~ Supreme.in.Base + Had.Email + Had.Phone + Had.Webprofile + + Expire.Month + Primary.Sales.Channel + Auto.Renew + + Discount + Claim.Count + High.Claims + Service.Fee.Buydown.Count + + Purchased.Supreme.Count + Purchased.Wash.Dryer.Count + Renewal.Option.Step.Up + + Renewal.Discount.Step.Up, data=final_df2) + +# Plot the tree using prp command defined in rpart.plot package +prp(renewedtree) + +# Random Forest +set.seed(7) +fit.rf = train(RenewedFactor ~ Supreme.in.Base + Had.Email + Had.Phone + Had.Webprofile + + Expire.Month + Primary.Sales.Channel + Auto.Renew + + Discount + Claim.Count + High.Claims + Service.Fee.Buydown.Count + + Purchased.Supreme.Count + Purchased.Wash.Dryer.Count + Renewal.Option.Step.Up + + Renewal.Discount.Step.Up, data=train2, na.action=na.omit, method="rf",metric=metric, trControl=control) +fit.rf +#mtry Accuracy Kappa +#12 0.7821792 0.5494473 + +#library(randomForest) +fit = randomForest(RenewedFactor ~ Supreme.in.Base + Had.Email + Had.Phone + Had.Webprofile + + Expire.Month + Primary.Sales.Channel + Auto.Renew + + Discount + Claim.Count + High.Claims + Service.Fee.Buydown.Count + + Purchased.Supreme.Count + Purchased.Wash.Dryer.Count + Renewal.Option.Step.Up + + Renewal.Discount.Step.Up, na.action=na.omit, data=final_df2) + +fit +importance(fit) # importance of each predictor +#Rank Variables in term of Importance: Renewal Discount Step Up, Renewal Option Step Up, Discount, Expire Month, Claim Count, +#Auto Renew, Had Email, Purchase Supreme Count, Primary Sales Channel, High Claims, Had Web Profile, Service Fee Buydown Count, +#Supreme in Base, Purchased Washer/Dryer, Had Phone + +# MeanDecreaseGini +#Supreme.in.Base 19.81542 +#Had.Email 85.07460 +#Had.Phone 16.30914 +#Had.Webprofile 29.40951 +#Expire.Month 180.76829 +#Primary.Sales.Channel 34.91059 +#Auto.Renew 87.12413 +#Discount 215.05757 +#Claim.Count 113.14630 +#High.Claims 30.60089 +#Service.Fee.Buydown.Count 27.75447 +#Purchased.Supreme.Count 65.60800 +#Purchased.Wash.Dryer.Count 15.16460 +#Renewal.Option.Step.Up 355.45511 +#Renewal.Discount.Step.Up 460.60145 + + +# kNN +set.seed(7) +fit.knn = train(RenewedFactor ~ Supreme.in.Base + Had.Email + Had.Phone + Had.Webprofile + + Expire.Month + Primary.Sales.Channel + Auto.Renew + + Discount + Claim.Count + High.Claims + Service.Fee.Buydown.Count + + Purchased.Supreme.Count + Purchased.Wash.Dryer.Count + Renewal.Option.Step.Up + + Renewal.Discount.Step.Up, data=train2, na.action=na.omit, method="knn",metric=metric, trControl=control) +fit.knn +# k Accuracy Kappa +#9 0.7253503 0.4392279 + +# SVM +set.seed(7) +fit.svm = train(RenewedFactor ~ Supreme.in.Base + Had.Email + Had.Phone + Had.Webprofile + + Expire.Month + Primary.Sales.Channel + Auto.Renew + + Discount + Claim.Count + High.Claims + Service.Fee.Buydown.Count + + Purchased.Supreme.Count + Purchased.Wash.Dryer.Count + Renewal.Option.Step.Up + + Renewal.Discount.Step.Up, data=train2, na.action=na.omit, method="svmRadial",metric=metric, trControl=control) +fit.svm + +#neural net +set.seed(7) +fit.nn = train(RenewedFactor ~ Supreme.in.Base + Had.Email + Had.Phone + Had.Webprofile + + Expire.Month + Primary.Sales.Channel + Auto.Renew + + Discount + Claim.Count + High.Claims + Service.Fee.Buydown.Count + + Purchased.Supreme.Count + Purchased.Wash.Dryer.Count + Renewal.Option.Step.Up + + Renewal.Discount.Step.Up, data=train2, na.action=na.omit, method="nnet",metric=metric, trControl=control) +fit.nn +# size decay Accuracy Kappa +# 3 1e-01 0.6925332 0.38568029 + +# summarize accuracy of models +results = resamples(list(cart=fit.dt, knn=fit.knn, svm=fit.svm, rf=fit.rf,nn =fit.nn)) +summary(results) +#making prediction +predictionsdt = predict(fit.dt, test2) +confusionMatrix(predictionsdt, test2$RenewedFactor) +#balanced accuracy 67.15% + +predictionsrf = predict(fit.rf, test2) +confusionMatrix(predictionsrf, test2$RenewedFactor) +#balanced accuracy 75.53% + +predictionsknn = predict(fit.knn, test2) +confusionMatrix(predictionsknn, test2$RenewedFactor) +#balanced accuracy 68.88% + +predictionssvm = predict(fit.svm, test2) +confusionMatrix(predictionssvm, test2$RenewedFactor) +#balanced accuracy 66.22% + +predictionsnn = predict(fit.nn, test2) +confusionMatrix(predictionsnn, test2$RenewedFactor) +#Balanced accuracy 74.23% + +#Neural net and random forest built the most accurate models in machine learning and to predict renewal rate. +#Random forest had the highest accuracy at a balanced accuracy of 75.53%. As this improved the model accuracy by a percentage point than with using the ROC +#curve to predict renewal rates we used RF to describe our final model.

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