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 prediction is reasonable: Since line of best fit can be used to predict values even if the exact \(x\) - value (height) is not in the data set.
• No data is given in the scatterplot for a height of 80 inches, but a shoe size can still be predicted: The line of best fit is used for extrapolation (predicting outside the range of the given data points). Here, the given \(x\) - values (heights) range from \(60\) to \(72\) (approx). A height of \(80\) inches is outside this range, but we can still use the line of best fit (which models the relationship between \(x\) and \(y\)) to predict the \(y\) - value (shoe size).

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.