The two regression lines were found to be 4X – 5Y + 33 = 0 and 20X – 9Y – 107 = 0. Find the mean values and coefficient of correlation between X and Y.

Question Collected From Telegram Group.
The two regression lines were found to be 4X – 5Y + 33 = 0 and 20X – 9Y – 107 = 0. Find the mean values and coefficient of correlation between X and Y.

Solution:

To get mean values we must solve the given lines. 

4X – 5Y = -33 … (1) 

20X – 9Y = 107 … (2) 

(1) × 5 20X 25Y = -165 

20X 9Y = 107 

Subtracting (1) and (2),

-16Y = -272  Y = \(\frac{272}{16}\) = 17 

i.e., \(\bar{Y}\) = 17 

Using Y = 17 in (1) we get, 4X – 85 = -33 

4X = 85 – 33 

4X = 52  X = 13 

i.e., \(\bar{X}\) = 13 

Mean values are \(\bar{X}\) = 13, \(\bar{Y}\) = 17, 

Let regression line of Y on X be 

4X – 5Y + 33 = 0 

5Y = 4X + 33 Y = (4X + 33) 

Y = \(\frac{1}{5}\)(4x + 33)

Y = \(\frac{4}{5}X+\frac{33}{5}\)

Y = 0.8X + 6.6 

byx = 0.8 

Let regression line of X on Y be 20X 9Y 107 = 0 

20X = 9Y + 107 

X = \(\frac{1}{20}\)(9Y + 107) 

X = \(\frac{9}{20}Y+\frac{107}{20}\)

X = 0.45Y + 5.35 

bxy = 0.45 

Coefficient of correlation between X and Y is = ±0.6  = 0.6 

\[\begin{array}{l}r =  \pm \sqrt {{b_{yx}} \times {b_{xy}}} \\r =  \pm \sqrt {0.8 \times 0.45} \\r =  \pm 0.6\\r = 0.6\end{array}\]
Both byx and bxy is positive take positive sign.

Getting Info...

Post a Comment

Please do not enter any spam link in the comment box.
Cookie Consent
We serve cookies on this site to analyze traffic, remember your preferences, and optimize your experience.
Oops!
It seems there is something wrong with your internet connection. Please connect to the internet and start browsing again.
AdBlock Detected!
We have detected that you are using adblocking plugin in your browser.
The revenue we earn by the advertisements is used to manage this website, we request you to whitelist our website in your adblocking plugin.
Site is Blocked
Sorry! This site is not available in your country.