Calculate the correlation coefficient of the following table

**zorro** · December 4th 2009, 08:45 PM

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

**CaptainBlack** · December 5th 2009, 01:17 AM

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

**zorro** · December 13th 2009, 01:33 PM

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

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

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

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

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

$cov(X,Y) \ = \ E(X,Y)$ ......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 ....

**zorro** · December 15th 2009, 09:07 PM

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

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

where
$\bar x , \bar y$ : Sample mean x,y
$S_x , S_y$ : Standard deviation for x , y

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

then $r_{xy} = \frac{4}{33}$ Is this answer correct ???

**CaptainBlack** · December 15th 2009, 10:42 PM

Originally Posted by zorro

This is what i have done

Sample Correlation coeff

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

where
$\bar x , \bar y$ : Sample mean x,y
$S_x , S_y$ : 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)

then $r_{xy} = \frac{4}{33}$ Is this answer correct ???

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

CB

**zorro** · December 16th 2009, 12:06 AM

Originally Posted by CaptainBlack

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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

**zorro** · December 26th 2009, 05:35 AM

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

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

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

$r$ = $0.64$

**CaptainBlack** · December 26th 2009, 06:18 AM

Originally Posted by zorro

I am using another formulae

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

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

$r$ = $0.64$

That looks about right.

CB

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Calculate the correlation coefficient of the following table

Is this correct?

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

Thank you Captain Black

Is this correct?

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