Instructions

This is the R portion of your final exam.

Follow the instructions carefully and write your R code in the provided chunks. You will be graded on the correctness of your code, the quality of your analysis, and your interpretation of the results.

Submission: Please make sure the RMD is knittable and submit the RMD file along with the generated HTML report.

Troubleshooting: If you find errors in your code that prevent the RMD file from knitting, please comment them out (add # before the code). I will give you partial credit based on your logic.

Good luck!

Part I: Logistic Regression

0. Background

Context: You have been hired by a retail consulting firm to analyze the sales performance of a company selling child car seats. The company wants to identify the key drivers of high sales performance to optimize their marketing and store layout strategies.

They have provided you with a dataset (store_sales.csv) containing data from 400 different store locations. Your goal is to build classification models to predict whether a store will have “High Sales” (Yes) or not.

Data Dictionary:

  • High_Sales (Target): Factor with levels Yes and No. Indicates if the store sold more than 8,000 units.
  • CompPrice: Price charged by the nearest competitor at each location.
  • Income: Community income level (in thousands of dollars).
  • Advertising: Local advertising budget for the company at each location.
  • Population: Population size of the region (in thousands).
  • Price: Price charged for the car seats at each site.
  • ShelveLoc: A factor indicating the quality of the shelving location for the car seats at the site (Good, Bad, or Medium).
  • Age: Average age of the local population.
  • Education: Education level at each location.
  • Urban: Factor (Yes/No) indicating if the store is in an urban location.
  • US: Factor (Yes/No) indicating if the store is in the US.

1. Data Preparation (0.5 point)

  1. Load the data from the file store_sales.csv and name it store_sales.
  2. Split the data into training (70%) and test (30%) sets. Use set.seed(2025) to ensure reproducibility.
# a) Load data
# Your code here
getwd()
## [1] "C:/Users/benfa/Downloads"
store_sales <- read.csv("store_sales.csv")
str(store_sales)
## 'data.frame':    400 obs. of  11 variables:
##  $ CompPrice  : int  138 111 113 117 141 124 115 136 132 132 ...
##  $ Income     : int  73 48 35 100 64 113 105 81 110 113 ...
##  $ Advertising: int  11 16 10 4 3 13 0 15 0 0 ...
##  $ Population : int  276 260 269 466 340 501 45 425 108 131 ...
##  $ Price      : int  120 83 80 97 128 72 108 120 124 124 ...
##  $ ShelveLoc  : chr  "Bad" "Good" "Medium" "Medium" ...
##  $ Age        : int  42 65 59 55 38 78 71 67 76 76 ...
##  $ Education  : int  17 10 12 14 13 16 15 10 10 17 ...
##  $ Urban      : chr  "Yes" "Yes" "Yes" "Yes" ...
##  $ US         : chr  "Yes" "Yes" "Yes" "Yes" ...
##  $ High_Sales : int  1 1 1 0 0 1 0 1 0 0 ...
# b) Split data into training and test sets
set.seed(2025)
# Your code here
sample_index_ss <- sample(1:nrow(store_sales), 
                       round(.7 * nrow(store_sales)))
store_sales_train <- store_sales[sample_index_ss, ]
store_sales_test <- store_sales[- sample_index_ss, ]

2. Logistic Regression (5 points)

  1. Fit a logistic regression model to predict High_Sales using all other variables as predictors. Please use the training dataset.
# Your code here
store_sales_glm <- glm(High_Sales ~ .,
                       data = store_sales,
                       family = "binomial")
  1. Use the summary() function to examine your fitted model. What is the estimated coefficient for Price? Is it statistically significant? Please interpret the number using the odds ratio?
# Your code here
summary(store_sales_glm)
## 
## Call:
## glm(formula = High_Sales ~ ., family = "binomial", data = store_sales)
## 
## Coefficients:
##                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept)     -5.0889857  2.4067745  -2.114   0.0345 *  
## CompPrice        0.1724750  0.0233456   7.388 1.49e-13 ***
## Income           0.0341248  0.0079002   4.319 1.56e-05 ***
## Advertising      0.2957492  0.0512506   5.771 7.90e-09 ***
## Population      -0.0009173  0.0014190  -0.646   0.5180    
## Price           -0.1674933  0.0196266  -8.534  < 2e-16 ***
## ShelveLocGood    8.2408876  1.0328293   7.979 1.48e-15 ***
## ShelveLocMedium  3.5970462  0.6520385   5.517 3.46e-08 ***
## Age             -0.0793793  0.0142195  -5.582 2.37e-08 ***
## Education       -0.0576359  0.0763170  -0.755   0.4501    
## UrbanYes        -0.3827861  0.4392739  -0.871   0.3835    
## USYes           -0.6986095  0.5949922  -1.174   0.2403    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 541.49  on 399  degrees of freedom
## Residual deviance: 181.48  on 388  degrees of freedom
## AIC: 205.48
## 
## Number of Fisher Scoring iterations: 7
exp(-.1674933) - 1
## [1] -0.1542177

Comments: yes it is significant beacsue the p value of is below .05

  1. Generate predicted probabilities on the testing dataset. Then, obtain the predicted classes using 0.6 as the cutoff value (threshold).
# Your code here
pred_prob_ss_test_glm <- predict(store_sales_glm, 
                              newdata = store_sales_test,
                              type = "response")
head(pred_prob_ss_test_glm)
##          1          3          7          9         11         17 
## 0.21575375 0.88564177 0.04360418 0.07951665 0.70645231 0.44478259
pred_class_ss_test_glm <- as.numeric(pred_prob_ss_test_glm > .6)
  1. Create a confusion matrix using the testing dataset and report Misclassification Rate (MR).
# Your code here
confusion_mat_ss_test_glm <- table(actual = store_sales_test$High_Sales,
      pred = pred_class_ss_test_glm)

confusion_mat_ss_test_glm
##       pred
## actual  0  1
##      0 63  3
##      1 14 40
1 - sum(diag(confusion_mat_ss_test_glm))/sum(confusion_mat_ss_test_glm)
## [1] 0.1416667

Comments: this 14.46% of predictions are incorret

  1. Draw an ROC curve and calculate the AUC (Area Under Curve) for this logistic regression model on the testing dataset. Do you think the prediction performance is acceptable?
# Your code here
library(pROC)
## Type 'citation("pROC")' for a citation.
## 
## Attaching package: 'pROC'
## The following objects are masked from 'package:stats':
## 
##     cov, smooth, var
roc_store_sales_test_glm <- roc(store_sales_test$High_Sales,
               pred_prob_ss_test_glm)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
plot(roc_store_sales_test_glm)

auc(roc_store_sales_test_glm)
## Area under the curve: 0.9512

Comments: An AUC of .9512 means we have a very high discriminatory curve

Part II: Regression Tree

0. Background

You have been hired by a health insurance company to improve their pricing strategy. They want to understand which factors contribute most to high individual medical costs.

Data Dictionary:

  • charges (Target): Individual medical costs billed by health insurance.
  • age: Age of primary beneficiary.
  • sex: Insurance contractor gender (female, male).
  • bmi: Body mass index (providing an understanding of body weights that are relatively high or low relative to height).
  • children: Number of children covered by health insurance / Number of dependents.
  • smoker: Smoking status (yes, no).
  • region: The beneficiary’s residential area in the US (northeast, southeast, southwest, northwest).

1. Data Preparation (0.5 point)

  1. Load the data from the file insurance.csv and name it insurance.
  2. Split the data into training (70%) and test (30%) sets. Use set.seed(2025) to ensure reproducibility. Hint: use round() function to retain only the integer part of a number.
# Your code here
getwd()
## [1] "C:/Users/benfa/Downloads"
insurance <- read.csv("insurance.csv")
str(insurance)
## 'data.frame':    1338 obs. of  7 variables:
##  $ age     : int  19 18 28 33 32 31 46 37 37 60 ...
##  $ sex     : chr  "female" "male" "male" "male" ...
##  $ bmi     : num  27.9 33.8 33 22.7 28.9 ...
##  $ children: int  0 1 3 0 0 0 1 3 2 0 ...
##  $ smoker  : chr  "yes" "no" "no" "no" ...
##  $ region  : chr  "southwest" "southeast" "southeast" "northwest" ...
##  $ charges : num  16885 1726 4449 21984 3867 ...
# b) Split data into training and test sets
set.seed(2025)
# Your code here
training_index_insurnace <- sample(1 : nrow(insurance), round(0.7 * nrow(insurance)))
insurance_training <- insurance[training_index_insurnace, ] 
insurance_testing <- insurance[-training_index_insurnace, ] 
dim(insurance_training)
## [1] 937   7
dim(insurance_testing)
## [1] 401   7
insurance$sex    <- as.factor(insurance$sex)
insurance$smoker <- as.factor(insurance$smoker)
insurance$region <- as.factor(insurance$region)

2. Regression Tree (4 points)

  1. Fit a regression tree based on the training data, using the charges as response variable, and all other variables as predictors. Then visualize the tree using rpart.plot.
# Your code here
library(rpart)
## Warning: package 'rpart' was built under R version 4.5.2
library(rpart.plot)
## Warning: package 'rpart.plot' was built under R version 4.5.2
insurance_tree <- rpart(charges ~ .,
                        data = insurance_training,
                        method = "anova")

rpart.plot(insurance_tree)

  1. Pruning: Fit a large regression tree with cp = 0.001, and then use plotcp() function to view the complexity parameter plot. Based on this plot, what value of cp you would you choose to prune the tree, and why?
# Your code here
insurance_tree_big <- rpart(
  charges ~ ., 
  data = insurance_training,
  method  = "anova",
  control = rpart.control(cp = 0.001))

plotcp(insurance_tree_big)

Comments: from this chart we can conclude that the proper cp value is .012

  1. Refit the regression tree using the cp selected in question (b). Then obtain the predictions on the testing data.
# Your code here
insurance_tree_pruned <- rpart(charges ~ .,
                               data = insurance_training,
                               method = "anova",
                               control = rpart.control(cp = .012))

pred_test_insurance <- predict(insurance_tree_pruned, new_data = insurance_testing)

head(pred_test_insurance)
##       909       460       932       279       187      1290 
## 12157.543  5318.788  5318.788 12157.543  5318.788 12157.543
  1. Obtain the out-of-sample MSE (Mean Squared Error) for both the initial tree model in (a) and the pruned tree model in (c). Which model is preferred for this data, and why?
# Your code here
pred_test_a <- predict(insurance_tree,
                       newdata = insurance_testing)

pred_test_b <- predict(insurance_tree_pruned,
                       newdata = insurance_testing)

MSE_a <- mean((insurance_testing$charges - pred_test_a)^2)
MSE_b <- mean((insurance_testing$charges - pred_test_b)^2)

MSE_a
## [1] 30205107
MSE_b
## [1] 31288947

Comments: since the initial tree mse_a is lower than mse_b, mse_a is preferred. It is a less complex tree

End of Exam. Please double-check that your RMD file knits successfully. Submit both the RMD and the generated HTML report.

Reminder: If a specific chunk causes an error, comment it out to allow the file to knit. Failure to submit an HTML report may result in a point deduction.