Question

kardal did a study to determine the correlation between mens 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.

Explanation:

• Interpolation vs Extrapolation: Interpolation is predicting within the range of given data points. Extrapolation is predicting outside the range. The given data points have \(x\) (height) values ranging from \(60\) to \(72\) inches. A height of \(80\) inches is outside this range, so it is extrapolation, not interpolation.
• Prediction Feasibility: Just because \(80\) inches is not in the original data set, we can still use the line of best - fit (which models the relationship between height and shoe size based on the existing data) to make a prediction.
• Reasonableness of Prediction: There is no information to suggest that a size \(16\) shoe for an \(80\) - inch - tall man is unreasonable. Also, there is no data to support that a size \(12.5\) shoe is the prediction (the prediction given in the problem is size \(16\)).

Answer:

• The prediction is reasonable.
• No data is given in the scatterplot for a height of \(80\) inches, but a shoe size can still be predicted.