Question :

Calculate the correlation coefficient of the following heights(in inches) of fathers and their sons:

X: 65 66 67 67 68 69 70 72

Y: 67 68 65 68 72 72 69 71

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- Dec 4th 2009, 08:45 PMzorroCalculate the correlation coefficient of the following table
Question :

Calculate the correlation coefficient of the following heights(in inches) of fathers and their sons:

X: 65 66 67 67 68 69 70 72

Y: 67 68 65 68 72 72 69 71 - Dec 5th 2009, 01:17 AMCaptainBlack
- Dec 13th 2009, 01:33 PMzorroIs this correct?

Correlation Coefficient $\displaystyle \rho= \frac{cov(X,Y)}{\sigma_x \sigma_y}$

$\displaystyle \mu_x$ = $\displaystyle \sum_{i} \frac{x_i}{n_1}$ = $\displaystyle 68$

$\displaystyle \mu_y$ = $\displaystyle \sum_{i} \frac{y_i}{n_2}$ = $\displaystyle 69$

$\displaystyle \sigma_x ^2$ = $\displaystyle \sum_{i} \frac{(x_i - \mu_x)^2}{n_1} $ = $\displaystyle \frac{9}{2}$

$\displaystyle \sigma_y ^2$ = $\displaystyle \sum_{i} \frac{(y_i - \mu_y)^2}{n_1} $ = $\displaystyle \frac{11}{2}$

$\displaystyle cov(X,Y) \ = \ E(X,Y)$ ......I am stuck at this protion now ....

I dont know how to calculate the cov of x,y from the table provided ....please advice

Also please check if am i doing it correctly or no .... - Dec 15th 2009, 09:07 PMzorroCaptain Black please check if the answer which i have done is correct or no ?

This is what i have done

Sample Correlation coeff

$\displaystyle r_{xy} = \sum_{i=0}^{n} \frac{(x_i - \bar x)(y_i - \bar y)}{(n-1) S_x S_y}$

where

$\displaystyle \bar x , \bar y$ : Sample mean x,y

$\displaystyle S_x , S_y$ : Standard deviation for x , y

Is this the right formula that i am using???

then $\displaystyle r_{xy} = \frac{4}{33}$ Is this answer correct ??? - Dec 15th 2009, 10:42 PMCaptainBlack
- Dec 16th 2009, 12:06 AMzorroThank you Captain Black
- Dec 26th 2009, 05:35 AMzorroIs this correct?
- Dec 26th 2009, 06:18 AMCaptainBlack