# Calculate the correlation coefficient of the following table

• Dec 4th 2009, 08:45 PM
zorro
Calculate 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 AM
CaptainBlack
Quote:

Originally Posted by zorro
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

Look up you notes (or look at Wikipedia or Google for it) for the correlation coefficient. Then its just arithmetic.

If you have any problems let us know what they are and we will help with those specific problems.

CB
• Dec 13th 2009, 01:33 PM
zorro
Is this correct?
Quote:

Originally Posted by CaptainBlack
Look up you notes (or look at Wikipedia or Google for it) for the correlation coefficient. Then its just arithmetic.

If you have any problems let us know what they are and we will help with those specific problems.

CB

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 PM
zorro
Captain Black please check if the answer which i have done is correct or no ?
Quote:

Originally Posted by CaptainBlack
Look up you notes (or look at Wikipedia or Google for it) for the correlation coefficient. Then its just arithmetic.

If you have any problems let us know what they are and we will help with those specific problems.

CB

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 PM
CaptainBlack
Quote:

Originally Posted by zorro
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???

Yes, except the lower limit of summation should be 1, there should ne n terms in the sum if you divide by (n-1)

Quote:

then $\displaystyle r_{xy} = \frac{4}{33}$ Is this answer correct ???
I don't think so, something closser to 0.6 would be right.

CB
• Dec 16th 2009, 12:06 AM
zorro
Thank you Captain Black
Quote:

Originally Posted by CaptainBlack
[/color]

Yes, except the lower limit of summation should be 1, there should ne n terms in the sum if you divide by (n-1)

I don't think so, something closser to 0.6 would be right.

CB

Thank you Captain Black for helping me , You dont know how much
But thanks mate for everything
• Dec 26th 2009, 05:35 AM
zorro
Is this correct?
Quote:

Originally Posted by CaptainBlack
[/color]

Yes, except the lower limit of summation should be 1, there should ne n terms in the sum if you divide by (n-1)

I don't think so, something closser to 0.6 would be right.

CB

I am using another formulae

$\displaystyle X = x - \mu_x$
$\displaystyle Y = y - \mu_y$

$\displaystyle r$ = $\displaystyle \frac{ \sum XY}{ \sqrt{ (\sum X^2)( \sum Y^2)}}$.............Is this formulae right

$\displaystyle r$= $\displaystyle 0.64$
• Dec 26th 2009, 06:18 AM
CaptainBlack
Quote:

Originally Posted by zorro
I am using another formulae

$\displaystyle X = x - \mu_x$
$\displaystyle Y = y - \mu_y$

$\displaystyle r$ = $\displaystyle \frac{ \sum XY}{ \sqrt{ (\sum X^2)( \sum Y^2)}}$.............Is this formulae right

$\displaystyle r$= $\displaystyle 0.64$