Question

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

Select only: "No data is given in the scatterplot for a height of 80 inches, but a shoe size can still be predicted."

Reason: the observed heights range from 60 to 72 inches, so predicting at 80 inches is an extrapolation (not interpolation) — you can compute a predicted shoe size from the fitted line, but it lies outside the data range and is therefore less reliable. The prediction is not necessarily reasonable, and you cannot conclude the person will likely wear size 12.5.