R-square adjusted can be better utilized as opposed to simply relying on R-square when you have models to compare that have a different number of variables.

R-square adjusted is a modified version of R-square that takes into account the number of predictors used in a regression model.

The formula for R-square adjusted is:

Adj.R²= 1 – [(1 – R²)(n – 1) /(n – k – 1)]

To use the formula, aside from R-square, you will need to have:

n = the number of items in your data set
k = the independent variables

## 3 benefits of R-square adjusted

There are several reasons why you may want to use R-square adjusted in a regression model:

### 1. It can be used for a more robust comparison.

R-square adjusted may be utilized to compare multiple regression models that have different numbers of predictor variables.

### 2. It takes into account the kinds of variables you are adding.

It may be found that some of the data collected does not actually serve the model in question. R-square adjusted takes into account the kind of variables you are adding to the model.

### 3. It is easy to comprehend if you already understand R-square.

The formula for R-Square adjusted may look intimidating, but it is easy to sort out if you already know R-square. Most scientific calculators can work out the math for you as well if you don’t want to figure it out by hand.

## Why is R-square adjusted important to understand?

### 1. It can give you a fuller view of the available data.

When you add independent variables to R-square, it always goes up. This can be misleading with the more independent variables you add and can lead to you making decisions for your business that are not ideal. With R-square adjusted, you get a more well-rounded view of what is going on with your data.

### 2. It takes into account the types of variables you are adding.

Not all the data being introduced is going to be beneficial to the model. Understanding how R-square adjusted takes all your independent variables into account can help you see what is not useful.

### 3. You can add as many independent variables as you choose.

R-square adjusted is worth understanding because it allows you to incorporate as many variables as you like into the model.

## An industry example of R-square adjusted

At a manufacturing plant, several employees have been asking for raises. The heads of the company decide to explore the correlation between the cost spent on labor and output in order to see how related they are and if the raises should be granted. They create a regression model that utilizes R². In a meeting, several independent variables are brought up, some clearly related to the integrity of the model, while others are more questionable. It is suggested that R-square adjusted be used so that it can be determined which independent variables have a clear impact on the model.

When using R-square adjusted, there are a few practices that you want to keep in mind:

### 1. Understand what it means when R-square adjusted decreases.

When R-square adjusted decreases, this means that a new independent variable introduced is not reflective of the target variable.

### 2. Understand what it means when R-square adjusted increases.

If R-square adjusted increases along with R-square, then it can be surmised that the new independent variable introduced has some bearing on the data presented with the model.

### 3. The higher, the better

With R-square adjusted, higher is better as it then shows that the independent variable is relevant data that has an effect on the dependent variable.

### 1. Can R-square adjusted ever be a negative number?

Yes, but not very often.

### 2. Is it possible for the value of R-square adjusted to be more than R-square?

No. R-square adjusted will only ever be equal to or lesser than R-square.

### 3. Is it a problem if the R-square adjusted value is negative?

No. If the actual R-square is near 0, then it makes sense that you would come up with a negative number for R-square adjusted as the value is always going to be equal to or lesser than R-square.

## The value of R-square adjusted

R-square is a wonderful tool in a regression model, but not being able to determine if an independent variable is relevant to the model is a major flaw. Thankfully, we have R-square adjusted to remedy this.