Question

Kardal did a study to determine the correlation between men’s 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.
A. The prediction is reasonable.
B. The prediction is an interpolation.
C. No data is given in the scatterplot for a height of 80 inches, but a shoe size can still be predicted.
D. A prediction cannot be made for a man who is 80 inches tall.
E. A man who is 80 inches tall will likely wear a size 12.5 shoe.

Answer 1

Option - A and C

Explanation:

Given : Kardal did a study to determine the correlation between men’s 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.

To find : What can be concluded about this prediction? Check all that apply.

Solution :

We plot the given residual points in the excel and we get,

The equation of the line
`y=0.377x-14.214`

And the value of
`R^2=0.7784`

If the value of R is approx 1 then, the data is the best fit.

So, The prediction is reasonable.

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

as
`y=0.377x-14.214`

substitute x=80

`y=0.377(80)-14.214=15.946`

Approximately y=16.

Therefore, Option A , C are correct.

Refer the attached figure.

Answer 2

A. The prediction is reasonable.
C. No data is given in the scatterplot for a height of 80 inches, but a shoe size can still be predicted.
because y = 0.3726 * 80 - 13.91 = 15.898 which is about size 16