Question

Suppose you found the least squares line of best fit, and then later added another data point from a subject added to your study. You found the new regression line included this point. If the data point were not on the line, which statement below will always be true?

A) The line will not change.
B) The line will move toward the new point.
C) The line will move away from the new point.
D) The line will go through the new point.

Answer 1

If a new data point is added to a set for a least squares regression line and the point is not on the original line, the revised line will typically move toward the new data point to minimize the sum of squared residuals.

Step-by-step explanation:

When a new data point is added to a set that is used to create a least squares line of best fit and the new point does not lie on the existing regression line, the new regression line will generally move towards the new point. This is because the least squares line attempts to minimize the sum of the squares of the residuals (the differences between the observed values and the values predicted by the line) across all points, including the new one.

The correct statement is B) The line will move toward the new point. It will do so to minimize the overall distance between the line and all of the points, which may result in changes to both the slope and the intercept of the line.