What is Prediction and Extrapolation

Why do we need least squares line?

This gives relation between the explanatory variable and the response variable which is X and Y. It can give the interpretation of how one variable reacts on change to the other variable, what percentage is the change and is the change positive or negative? It answers so many such questions.

Lets move one step ahead. The least squares line can also be used to predict the data in future or certain value of X what would be response value.

Prediction — Using the linear model to predict the value of the response variable for a given value of explanatory variable is called prediction.

It is just plugging in the value of X in the linear model equation and see what would be the value of Y

Does this prediction hold good for any value of X and Y?

Extrapolation — Applying the model estimate to values outside of the realm of the original data is called extrapolation

It is plugging in the value of X which is not in the range of original data. sometimes, the intercept might be extrapolation as well.

The data points can be in a different range, in the above case we are predicting the value of Y when the value of X is 0. This might not be true always. The points may not be linear. It can be going downwards, upwards or may not be extending till infinity.

Now that we understood the Extrapolation and prediction, we always have to evaluate our prediction if the data points are in the range and is it wise to do the prediction for certain value.