# Backward Deletion Method Step by Step in R

### 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.

### 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.

Learn more about lm() function

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