Linear regression analysis (Multiple Logistic regression, Likelihood Ratio test, Stepwise Selection)

• Consider the heart dataset below.

It has data from the Framingham Study, one of the largest and longest running longitudinal study in the US, helpful reference for reading: (https://framinghamheartstudy.org/fhs-about).

The goal is to develop a multiple logistic regression model for predicting the risk of ten year CHD.

For each predictor, fit a separate simple (univariate) logistic regression model.

Select the predictors that are significant at univariate p-value of 0.1.

Fit a multiple logistic regression model with these selected predictors and use a likelihood ratio test (LRT) to test

if these predictors are significant jointly.

If they aren't found to be significant jointly, remove the least significant variable and test the significance of the reduced model using LRT.

Repeat the steps until you have a model with all significant predictors.

Interpret the coefficients of this model.

Next, fit a multiple logistic regression (starting with all predictors in the dataset) using stepwise selection procedure.

Compare the two multiple logistic regression models.

http://faculty.marshall.usc.edu/gareth-james/ISL/data.html