Question

Evaluating a Prediction
Kardal did a study to determine the correlation between men’s heights, x, and their shoe sizes, y, and found the following data:

(60, 8.5), (65, 10), (66, 12), (68, 11.5), (63, 9.5), (72, 12.5), (62, 8.5), (69, 12.5), (70, 11.5)

Kardal used the line of best fit to predict that a man 80 inches tall would wear about a size 16 shoe. What can be concluded about this prediction? Check all that apply.

The prediction is reasonable.
The prediction is an interpolation.
No data is given in the scatterplot for a height of 80 inches, but a shoe size can still be predicted.
A prediction cannot be made for a man who is 80 inches tall.
A man who is 80 inches tall will likely wear a size 12.5 shoe.

Answer 1

Answers:
- The prediction is reasonable. — False. 80 in is well outside the observed heights (60–72), so this is extrapolation and not reliably reasonable.
- The prediction is an interpolation. — False. It is extrapolation (outside the data range), not interpolation.
- No data is given in the scatterplot for a height of 80 inches, but a shoe size can still be predicted. — True. You can use the fitted line to predict, but the prediction is an extrapolation and may be unreliable.
- A prediction cannot be made for a man who is 80 inches tall. — False. A prediction can be made, but it is uncertain because it is extrapolation.
- A man who is 80 inches tall will likely wear a size 12.5 shoe. — False. The fitted prediction was about size 16, and 12.5 is just one of the observed sizes; there is no basis to assert 12.5 is the likely value.