Question

2. The equation of two regressions obtained in a correlation

analysis of 60 observations are 5𝑥 = 6𝑦 + 24 and

1000𝑦 = 768𝑥 − 3608. What is the correlation coefficient?

Find the ratio of the coefficient of variability of x to that of y.

What is the ratio of the variations of x and y?

Answer 1

Regression lines:

$x=6y/5+24/5$

$y=768x/1000-3608/1000$

correlation coefficient:

$r=\sqrt{a_{xy}a_{yx}}=\sqrt{\frac{6}{5}\cdot \frac{768}{1000}}=0.92$

 ratio of the coefficient of variability of x to that of y:

$\frac{V(x)}{V(y)}=\frac{a_{xy}}{a_{yx}}=\frac{768/1000}{6/5}=0.64$

ratio of the variations of x and y:

$r^2=0.92^2=0.8464$