Question

You Explain it:

1. What is a residual?
2. What does it mean when a residual is positive?
3. Explain the phrase outside the scope of the model.
4. Why is it dangerous to make predictions outside the scope of the model?
5. Explain what each point on the least-squares regression line represents.

Answer 1

1.What is a residual?

A residual is the vertical distance between a data point and the regression line. Each data point has one residual.

2.What does it mean when a residual is positive?

They are positive if they are above the regression line and negative if they are below the regression line. If the regression line actually passes through the point, the residual at that point is zero.

3.Explain the phrase outside the scope of the model.

4.Why is it dangerous to make predictions outside the scope of the model?

Extrapolation of a fitted regression equation beyond the range of the given data can lead to seriously biased estimates if the assumed relationship does not hold the region of extrapolation.Thus, extrapolation can not be supported on statistical grounds alone; it must be justified by physical considerations.

5. Explain what each point on the least-squares regression line represents.

on the​ least-squares regression line represents the​ y-value of the data set at that corresponding value of x. Each point on the​ least-squares regression line represents the predicted​ y-value at the corresponding value of x.