Question

select the correct answer.

the scatter plot represents the purchase prices and selling prices of x-ray machines made by five different manufacturers. which of the following points show errors of prediction or residuals?

points (14, 25) and (15, 25)
points (15, 25) and (18, 26)
points (14, 25) and (16, 25)
points (12, 24) and (18, 26)

Explanation:

Identify the line of prediction and the data points

The line represents the predicted values (the regression line). The individual plotted points represent the actual observed data points:

• Point 1: \((12, 24)\) lies exactly on the line.
• Point 2: \((14, 25)\) lies above the line.
• Point 3: \((15, 25)\) lies exactly on the line (at the intersection of the grid lines).
• Point 4: \((16, 25)\) lies below the line.
• Point 5: \((18, 26)\) lies exactly on the line.

Define errors of prediction (residuals)

An error of prediction (residual) occurs when an observed data point does not lie directly on the prediction line. Points that lie exactly on the line have a residual of \(0\) (no prediction error). Points off the line have non-zero residuals.

Determine which points have non-zero residuals

• The points off the line are \((14, 25)\) and \((16, 25)\).
• Therefore, these two points show errors of prediction.

Answer:

• Points (14, 25) and (15, 25)
• Points (15, 25) and (18, 26)
• (C) Points (14, 25) and (16, 25) (Correct answer)
• Points (12, 24) and (18, 26)