Question

Linear Regression

When we use a least-squares line to predict y values for x values beyond the range of x values found in the data, are we extrapolating or interpolating? Are there any concerns about such predictions?

Answer 1

Answer:

Given that,

When we use a least-squares line to predict y values for X values beyond the range of x-values found in the data, are we extrapolating or interpolating? Are there any concerns about such predictions:

From the given information, we can write Yes, there are serious concerns about such a prediction.

Let us consider,

The data of seal weight (kg), overhead width (cm).

So,

The dependent variable (y)=Weight (kg)

The independent predictor variable (x)=Overhead width(cm)

x	7.9	7.6	9.3	7.1	8.9	7.4
y	179	195	266	141	243	184

Above table,

The least-square line is,

................(1)

The regression equation y on x,

Now assuming,

The overhead width is to predict the weight of the seal.

The x-value =1.7 cm

"x" value substituting in equation (1), we get

Therefore,

Then,

The predicted weight of seal if overhead weight 1.7(cm) is -96.306.

Beyond the range of x is -96.306.

It is unrealistic.

Since the weight of the seal is never negative.

Predicting results are very concerns.

Note:

Predict the least-square line only in the valid range of regression out of regressor if we predict least square line.

So,

This is a concern.