### Introduction to Backward Deletion Method

With many predictor variables, one can create the most statistically significant model from the data. There are two main choices: forward stepwise regression and backward deletion method.

In Forward Stepwise Regression: Start with the single best variable and add more variables to build your model into a more complex form.In

*Backward Deletion (Backward Selection) Regression*: put all the variables in the model and reduce the model by removing variables until you are left with only significant terms.

## Table of Contents

### Backward Deletion method (Step by Step Procedure)

Let’s start with a big model and trim it until you get the best (most statistically significant) regression model. This drop1() command can examine a linear model and determine the effect of removing each one from the existing model. Complete the following steps to perform a backward deletion. Note that the model has different R packages for the Backward and Forward Selection of predictors.

#### Step 1: (Full Model)

**Step 1:** To start, create a “full” model (all variables at once in the model). It would be tedious to enter all the variables in the model, one can use the shortcut, the dot notation.

mod <- lm(mpg ~., data = mtcars)

#### Step 2: Formula Function

**Step 2:** Let’s use the `formula()`

function to see the response and predictor variables used in **Step 1.**

formula(mod)

#### Step 3: Drop1 Function

**Step 3:** Let’s use the `drop1()`

function to see which term (predictor) should be deleted from the model

drop1(mod)

#### Step 4: Remove the Term

**Step 4:** Look to remove the term with the lowest AIC value. Re-form the model without the variable that is non-significant or has the lowest AIC value. The simplest way to do this is to copy the model formula in the clipboard, paste it into a new command, and edit out the term you do not want

mod1 <- lm(mpg ~ ., data = mtcars)

#### Step 5: Examine the Effect

**Step 5:** Examine the effect of dropping another term by running the `drop1()`

command once more:

drop1(mod1)

If you see any variable having the lowest AIC value, if found, remove the variable and carry out this process repeatedly until you have a model that you are happy with.