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:

The given data set has heights ranging from 60 - 72 inches. Predicting for a height of 80 inches is an extrapolation (not interpolation) since 80 inches is outside the range of the given data. Just because there is no data at 80 inches doesn't mean a prediction can't be made using the line of best - fit. Whether the prediction is reasonable depends on how well the line of best - fit models the relationship in general and if the relationship remains linear outside the observed data range. There is no evidence to suggest a size 12.5 shoe for an 80 - inch - tall man based on the given information.

Answer:

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