Apart from describing relations, models also can be used to predict values for new data. For that, many model systems in R use the same function, conveniently called predict(). Every modeling paradigm in R has a predict function with its own flavor, but in general the basic functionality is the same for all of them.

## How to get the data values

For example, a car manufacturer has three designs for a new car and wants to know what the predicted mileage is based on the weight of each new design. In order to do this, you first create a data frame with the new values — for example, like this:

> new.cars <- data.frame(wt=c(1.7, 2.4, 3.6))

Always make sure the variable names you use are the same as used in the model. When you do that, you simply call the predict() function with the suited arguments, like this:

> predict(Model, newdata=new.cars)
1    2    3
28.19952 24.45839 18.04503

So, the lightest car has a predicted mileage of 28.2 miles per gallon and the heaviest car has a predicted mileage of 18 miles per gallon, according to this model. Of course, if you use an inadequate model, your predictions can be pretty much off as well.

In order to have an idea about the accuracy of the predictions, you can ask for intervals around your prediction. To get a matrix with the prediction and a 95 percent confidence interval around the mean prediction, you set the argument interval to 'confidence' like this:

> predict(Model, newdata=new.cars, interval='confidence')
fit   lwr   upr
1 28.19952 26.14755 30.25150
2 24.45839 23.01617 25.90062
3 18.04503 16.86172 19.22834

Now you know that — according to your model — a car with a weight of 2.4 tons has, on average, a mileage between 23 and 25.9 miles per gallon. In the same way, you can ask for a 95 percent prediction interval by setting the argument interval to 'prediction':

> predict(Model,newdata=new.cars, interval='prediction')
fit   lwr   upr
1 28.19952 21.64930 34.74975
2 24.45839 18.07287 30.84392
3 18.04503 11.71296 24.37710

This information tells you that 95 percent of the cars with a weight of 2.4 tons have a mileage somewhere between 18.1 and 30.8 miles per gallon — assuming your model is correct, of course.

If you’d rather construct your own confidence interval, you can get the standard errors on your predictions as well by setting the argument se.fit to TRUE. You don’t get a vector or a matrix; instead, you get a list with an element fit that contains the predictions and an element se.fit that contains the standard errors.