Question

Kardal did a study to determine the correlation between men’s heights, x, and their shoe sizes, y, and found the following data:

Answer 1

Answer:

Option - A and C

Step-by-step 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