1 What is the correlation between hand length and foot lengt

1. What is the correlation between hand length and foot length?

2. Predict hand length when foot lengths are 8.75, 9.40 and 7.80 respectively. Explain why each prediction is valid or not.

Let and y be the lengths in inches of a foot and a hand, respectively. The following measurements were made on 15 women: foot 9.00 8.50 9.25 9.75 9.00 hand 6.50 6.25 7.25 7.00 6.75 foot 10.00 9.50 9.00 9.25 9.50 hand 7.00 6.50 7.00 7.00 7.00 foot 9.25 10.00 10.00 9.75 9.50 hand 7.00 7.50 7.25 7.25 7.25 Foot and Hand Length, in inches y 1.896 0.5385 x 7.6 7.4 7.2 C 6.8 6.6 6.4 6.2 8.50 8.75 9.00 9.25 9.50 9.75 10.00 Foot Length The least squares regression line is given by y = 1.896 + 0.5385x, and r2-0.488

Solution

1. What is the correlation between hand length and foot length?

Given r² =0.488

The relation is positive( regression coefficient is positive)

Correlation r = sqrt(0.488) = 0.6986

2. Predict hand length when foot lengths are 8.75, 9.40 and 7.80 respectively. Explain why each prediction is valid or not.

Y=1.896+0.5385*x

When x=8.75,

y=1.896+0.5385*8.75 = 6.607875

this is valid because 8.75 within the range of x

When x=9.40,

y=1.896+0.5385*9.40 = 6.9579

this is valid because 9.40 within the range of x

When x=7.80,

y=1.896+0.5385*7.80 = 6.9579

this is NOT valid because 7.80 NOT within the range of x