[R] Using R to Compute Covariance

[David Winsemius]

On Jul 26, 2014, at 11:07 AM, Robert Sherry wrote:

> I have the following data set:
> x    y           p
> 1    1          1/2
> 2    2          1/4
> 3    9          1/4
>
> In this case, p represents the probability of the values occurring. I
> compute the covariance of x and y by hand and come up with a value  
> of 41/16.
> When computing the covariance, I am dividing by n (in this case 3)  
> not n-1.
>
> I now want to use R to find the [covariance]. I understand that R  
> will [divide]
> by n-1 not n.

Please read what the help page says about the choice of the method  
parameter.


>  Here are the commands that I issued:
>
> x = c(1,2,3)
> y = c(1,2,9)
> df =dataframe(x,y)

# There's no function named 'dataframe'.\\

> df =data.frame(x,y)
> w1 = c(1/2,1/4,1/4)
> cov.wt(df, wt = w1 )
>

 > cov.wt(df, wt = w1 ,method="ML")$cov[2,1]
[1] 2.5625
 > all.equal (41/16, cov.wt(df, wt = w1 ,method="ML")$cov[2,1] )
[1] TRUE


> The last command returns:
>
> $cov
>    x    y
> x 1.1  4.1
> y 4.1 17.9
>
> $center
>   x    y
> 1.75 3.25
>
> $n.obs
> [1] 3
>
> $wt
> [1] 0.50 0.25 0.25
>
> Therefore, I conclude that R is finding the covariance of x and y to  
> be 4.1.
> However, I need to adjust that number by multiplying it by 2 and then
> dividing by 3. However, when I get that I still do not get 41/16.   
> What am I
> missing?

-- 

David Winsemius, MD
Alameda, CA, USA