Chapter 6 is about Regression Methods for Predicting Numeric Data. The author presents the basics of Simple Linear Regression and Multiple Linear Regression.

Regression Methods can also be used for Classification.

• Logistic Regression
• CART

The author applies linear regression to the launch data. In this data set the dependent variable is distress_ct. This variable has only 3 categories.

And making predictions less than 0 or greater than 3 does not make much sense.

Logistics Regression or Multinomial Regression would make more sense.

These are Generalized Linear Models (GLMs).

Here is a link to an R-bloggers post How to perform a Logistic Regression in R.

The author of the post creates training and test data sets. And introduces the use of the ROC to evaluate the fitted model.

A logistic regression model, models a binary dependent variable

\(Y = 1\) or Yes

or

\(Y = 0\) or No

where \(P(Y = 1 | X)\) is modeled in terms of the predictors \(X\).

Try

\(P(Y = 1 | X) = \beta_0 + \beta_1 X\)

but all probabilities need to be between 0 and 1.

What is used is the logit function, to keep the values of the probabilities between 0 and 1.

\(P(Y = 1 | X) = \frac{e^{\beta_0 + \beta_1 X}}{1+e^{\beta_0 + \beta_1 X}}\)

So it turns out that the log odds are linear

\(log\left(\frac{P(Y=1 |X)}{1-P(Y=1|X)}\right) = \beta_0 + \beta_1 X\)

This gives a nonlinear model that is estimated using MLEs by numerical methods.

Multiple Logistic Regression can be used when there is more than one predictor variable.

Categorical or Numeric variables can be used as predictors.

The AIC is used to compare models.

The ROC curve is used to compare models.

The Area under the ROC is commonly used to evaluate and compare models.

Try Logistic Regression with the launch data and the credit data.

Try CART with the credit data.

This will be using the "C" in CART.

Here is a link to a Quick-R post Generalized Linear Models.