Question

Evaluating a Prediction
A graph titled men's shoes has height (inches) on the x-axis, and shoe size on the y-axis. A trend line goes through points (64, 7) and (70, 9.5).

Kardal used the trend line to predict that a man 72 inches tall would wear about a size 10.5 shoe. What can be concluded about this prediction? Check all that apply.
The prediction is not reasonable.
The prediction is an interpolation.
No data is given in the scatterplot for a height of 72 inches, but a shoe size can still be predicted.
A prediction cannot be made without the linear regression equation.
A 72-inch tall man will wear a size 11.5 shoe.

Answer 1

Check: "No data is given in the scatterplot for a height of 72 inches, but a shoe size can still be predicted."

Reasoning (brief):
- The trend line through (64,7) and (70,9.5) has slope (9.5−7)/(70−64)=2.5/6≈0.4167 and equation y = 7 + (5/12)(x−64). For x = 72 this gives y ≈ 10.33, so Kardal's estimate of about 10.5 is reasonable.
- The prediction is not interpolation (72 is beyond 70), so that statement is false.
- You do not need the exact regression equation to make a prediction from the trend line, so that statement is false.
- There is no basis for the claim "a 72-inch tall man will wear a size 11.5," so that is false.