Housekeeping

Introduction

The purpose of this exercise is to give you additional practice working with multiple linear regression. We will continue with the Kaggle beer consumption dataset (https://www.kaggle.com/dongeorge/beer-consumption-sao-paulo/). You will demonstrate the impacts of some variables on beer consumption in a given region and the consumption forecast for certain scenarios. The data (sample) were collected in Sao Paulo, Brazil, in a university area, where there are some parties with groups of students from 18 to 28 years of age (average).

Kaggle is a great online community of data scientists. To learn more about Kaggle, follow this link: https://www.kaggle.com/getting-started/44916.

The data

This is the same data from the last in-class exercise. so you should already have it saved locally. Just in case you do not, follow the instructions below.

Download the data (named consumo_cerveja.csv) from Sakai and save it locally to the same directory as your R markdown file. To find the data file on Sakai, go to Resources \(\rightarrow\) Datasets \(\rightarrow\) In-Class Analyses. Once you have downloaded the data file into the SAME folder as your R markdown file, load and clean the data by using the following R code.

⊕It is always a good idea to take a look at the first few rows of the raw file to see what the data looks like before loading the data. In this raw ‘consumo_cerveja’ file, you will notice that commas are actually used both as decimals and to separate the columns. Thus, you need to let R know by specifying the sep and dec options as in the code below.

beer <- read.csv("data/consumo_cerveja.csv",
                 stringsAsFactors = FALSE, sep = ",",
                 dec=",",nrows=365)
# rename the variables
beer$date <- beer$Data
beer$temp_median_c <- beer$Temperatura.Media..C.
beer$temp_min_c <- beer$Temperatura.Minima..C.
beer$temp_max_c <- beer$Temperatura.Maxima..C.
beer$precip_mm <- beer$Precipitacao..mm.
beer$weekend <- factor(beer$Final.de.Semana)
beer$beer_cons_liters <- as.numeric(beer$Consumo.de.cerveja..litros.)
beer <- beer[ , 8:ncol(beer)]

After renaming the variables using the code above, your data will be saved in the object beer, and the relevant variables plus their meanings are given in the table below:

Exercises

Continue with the rain variable from last time. Again, In R, remember to treat the variable as a factor variable and not a discrete variable. Fit the same model as last time. That is, fit a linear model for log(beer_cons_liters) using weekend, rain, and temp_median_c as your predictors.

1. Write a code for doing \(k\)-fold cross validation. Refer back to the class notes for details on \(k\)-fold cross validation. Let \(k=10\) and use average RMSE as the metric for quantifying predictive error. What is the average RMSE for your regression model?

   If you were able to complete this question last time, just write your answer down again.

   Hint: if you are not sure how to begin writing your code for doing the cross validation, you should consider writing a “for loop”. A “for loop” is actually not the most efficient way to get this done but it will work just fine here. If you don’t know how to write a “for loop”, use the skeleton code below as a guide for writing your own “for loop” for this question.

   # Suppose your data is stored in the object "Data"
   # First set a seed to ensure your results are reproducible
   set.seed(...) # use whatever number you want
   # Now randomly re-shuffle the data
   Data <- Data[sample(nrow(Data)),]
   # Define the number of folds you want
   K <- ...
   # Define a matrix to save your results into
   RSME <- matrix(0,nrow=K,ncol=1)
   # Split the row indexes into k equal parts
   kth_fold <- cut(seq(1,nrow(Data)),breaks=K,labels=FALSE)
   # Now write the for loop for the k-fold cross validation
   for(k in 1:K){
   # Split your data into the training and test datasets
   test_index <- which(kth_fold==k)
   train <- Data[-test_index,]
   test <- Data[test_index,]
   # Now that you've split the data, 
   RSME[k,] <- ... # write your code for computing RMSE for each k here
   # You should consider using your code for question 7 above
   }
   ... #Calculate the average of all values in the RSME matrix here.

2. Now, do EDA to explore interaction effects between all your predictors. Summarize your findings in a few sentences.

3. Extend your linear model to include interaction terms between weekend and the other two predictors. Are the interaction terms significant? What are the implications of these findings in the context of the data?

   To include an interaction term between two variables x1 and x2 in your linear model, use

   "model object here" <- lm(y ~ x1 + x2 + x1:x2)

   OR

   "model object here" <- lm(y ~ x1*x2)

4. Do stepwise model selection using AIC and BIC with the “full model” set to the model from question 3. Summarize your findings in a few sentences.

5. Use your code for the \(k\)-fold cross validation from question 1 to compute the average RMSE for the new model in question 3. Is the new RMSE model lower or higher than your result from question 1? What can you infer from that?

Acknowledgement

This exercise is based on ideas proposed by Sam Voisin.