# How to Calculate MSE in R

One of the most common metrics used to measure the prediction accuracy of a model is MSE, which stands for mean squared error. It is calculated as:

MSE = (1/n) * Σ(actual – prediction)2

where:

• Σ – a fancy symbol that means “sum”
• n – sample size
• actual – the actual data value
• prediction – the predicted data value

The lower the value for MSE, the more accurately a model is able to predict values.

## How to Calculate MSE in R

Depending on what format your data is in, there are two easy methods you can use to calculate the MSE of a regression model in R.

### Method 1: Calculate MSE from Regression Model

In one scenario, you may have a fitted regression model and would simply like to calculate the MSE of the model. For example, you may have the following regression model:

```#load mtcars dataset
data(mtcars)

#fit regression model
model <- lm(mpg~disp+hp, data=mtcars)

#get model summary
model_summ <-summary(model)
```

To calculate the MSE for this model, you can use the following formula:

```#calculate MSE
mean(model_summ\$residuals^2)

[1] 8.85917```

This tells us that the MSE is 8.85917.

### Method 2: Calculate MSE from a list of Predicted and Actual Values

In another scenario, you may simply have a list of predicted and actual values. For example:

```#create data frame with a column of actual values and a column of predicted values
data <- data.frame(pred = predict(model), actual = mtcars\$mpg)

#view first six lines of data

pred actual
Mazda RX4         23.14809   21.0
Mazda RX4 Wag     23.14809   21.0
Datsun 710        25.14838   22.8
Hornet 4 Drive    20.17416   21.4
Valiant           21.29978   18.1
```

In this case, you can use the following formula to calculate the MSE:

```#calculate MSE
mean((data\$actual - data\$pred)^2)

[1] 8.85917```

This tells us that the MSE is 8.85917, which matches the MSE that we calculated using the previous method.

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