# Thread: Calculate the correlation coefficient of the following table

1. ## 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

2. 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

3. ## Is this correct?

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 ....

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

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 ???

5. 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)

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

6. ## Thank you Captain Black

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

7. ## Is this correct?

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

$\displaystyle r$= $\displaystyle 0.64$

8. 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

$\displaystyle r$= $\displaystyle 0.64$

CB

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### calculate the correlation coefficient for the following heights of fathers

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