Added variable plot provides information about the marginal importance of a predictor variable, given the other predictor variables already in the model. It shows the marginal importance of the variable in reducing the residual variability.

## Arguments

- model
An object of class

`lm`

.- print_plot
logical; if

`TRUE`

, prints the plot else returns a plot object.

## Details

The added variable plot was introduced by Mosteller and Tukey (1977). It enables us to visualize the regression coefficient of a new variable being considered to be included in a model. The plot can be constructed for each predictor variable.

Let us assume we want to test the effect of adding/removing variable *X* from a
model. Let the response variable of the model be *Y*

Steps to construct an added variable plot:

Regress

*Y*on all variables other than*X*and store the residuals (*Y*residuals).Regress

*X*on all the other variables included in the model (*X*residuals).Construct a scatter plot of

*Y*residuals and*X*residuals.

What do the *Y* and *X* residuals represent? The *Y* residuals represent the part
of **Y** not explained by all the variables other than X. The *X* residuals
represent the part of **X** not explained by other variables. The slope of the line
fitted to the points in the added variable plot is equal to the regression
coefficient when **Y** is regressed on all variables including **X**.

A strong linear relationship in the added variable plot indicates the increased
importance of the contribution of **X** to the model already containing the
other predictors.

## References

Chatterjee, Samprit and Hadi, Ali. Regression Analysis by Example. 5th ed. N.p.: John Wiley & Sons, 2012. Print.

Kutner, MH, Nachtscheim CJ, Neter J and Li W., 2004, Applied Linear Statistical Models (5th edition). Chicago, IL., McGraw Hill/Irwin.

## Examples

```
model <- lm(mpg ~ disp + hp + wt, data = mtcars)
ols_plot_added_variable(model)
#> `geom_smooth()` using formula = 'y ~ x'
#> `geom_smooth()` using formula = 'y ~ x'
#> `geom_smooth()` using formula = 'y ~ x'
```