Question

If a straight-line probabilistic relationship relates the mean E(y) to an independent variable x, does it imply that every value of the variable y will always fall exactly on the line of means? Why or why not?

Short answer

No.

Step-by-step solution

Introduction.

A straight line is just a straight line with no bends. A straight line is one that has no bends and continues to infinity on both sides.

Do variable y will always fall exactly on the line of means? Why or why not?

No, not every value of the variable y will always fall exactly on the line of means since certain values may deviate from it.

Predictions are rarely perfect. Most of the time, not all of the points will fall exactly on the line. There will be some mistake in the prediction. We know the estimated value of Y for each value of X, but not the precise value.

In the graph above, blood cholesterol and fat intake are connected, however we cannot forecast cholesterol levels accurately based on fat intake. The points on the graph that deviate from the line are not completely anticipated. We may examine how much each point deviates from the line by drawing a straight line from the point to the line, as illustrated below.

Therefore,

No, not every value of variable y will fall exactly on the line of means.