Root mean squared error (RMSE) is the square root of the mean of the square of all of the error. RMSE is considered an excellent general-purpose error metric for numerical predictions. RMSE is a good measure of accuracy, but only to compare prediction errors of different models or model configurations for a particular variable and not between variables, as it is scale-dependent. It is the measure of how well a regression line fits the data points. The formula for calculating RMSE is:

In R programming, Root-Mean-Square Error (RMSE) is a commonly used metric to evaluate the accuracy of a predictive model. It is the square root of the average of the squared differences between the predicted and actual values. RMSE measures how well a model is able to predict the target variable, and it is a popular choice because it penalizes large errors more heavily than small ones.

To calculate RMSE in R, you first need to create a model that can predict the target variable. Then, you can use the predict() function to generate predicted values, and compare them to the actual values using the sqrt() and mean() functions to calculate the RMSE. Here is an example of how to calculate RMSE for a linear regression model in R: 

# create a linear regression model
model <- lm(y ~ x, data = mydata)

# generate predicted values
predictions <- predict(model, newdata = mydata)

# calculate RMSE
rmse <- sqrt(mean((mydata$y - predictions)^2))

The RMSE value can be interpreted as the standard deviation of the residuals (the differences between the predicted and actual values). A lower RMSE value indicates better performance of the model. RMSE is widely used in machine learning, statistics, and other fields to evaluate the accuracy of predictive models.