Suppose we collect data for a group of students in a statistics class with variables \(X_1\) = hours studied, \(X_2\) = undergrad GPA, and \(Y\) = receive an A. We fit a logistic regression and produce estimated coefficient, \(\hat{\beta}_0=-6\), \(\hat{\beta}_1=0.05\), \(\hat{\beta}_2=1\).
Suppose that we take a data set, divide it into equally-sized training and test sets, and then try out two different classification procedures. First, we use logistic regression and get an error rate of 20% on the training data and 30% on the test data. Next, we use 1-nearest neighbors (i.e. \(K = 1\)) and get an average error rate (averaged over both test and training data sets) of 18%. Based on these results, which method should we prefer to use for classification of new observations? Why?
In this exercise, we will explore a data set about cars called auto which you can find here.
The data set contains 1 factor variable and 6 numeric variables. The factor variable mpg has two levels high and low indicating whether the car has a high or low miles per gallon. We will in this exercise investigate if we are able to use a logistic regression classifier to predict if a car has high or low mpg from the other variables.
Read in the data and create a test-train rsplit object of auto using initial_split(). Use default arguments for initial_split().
Create the training and testing data set with training() and testing() respectively.
Fit a logistic regression model using logistic_reg(). Use all the 6 numeric variables as predictors (a formula shorthand is to write mpg ~ . where . means everything. Remember to fit the model only using the training data set.
Inspect the model with summary() and tidy(). Which of the variables are significant?
Predict values for the training data set and save them as training_pred.
Use the following code to calculate the training accuracy
bind_cols(
training_pred,
auto_training
) %>%
accuracy(truth = mpg, estimate = .pred_class)
(auto_training should be renamed to match your training data set if needed.)