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 the line of best fit is used for prediction, and if the model is well - constructed (assuming a good correlation in the data), a prediction can be reasonable.
• 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 to predict values outside the given data points (extrapolation in this case as 80 is outside the range of \(x\) values \(60 - 72\)). Interpolation is for values within the data range.

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.