correlation coefficient

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steller

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The annual repair cost for a vegetable garden tiller is related to its age in years.
A sample of 5 tillers revealed the following data:


cost.PNG


a. Compute the correlation coefficient.

What i have so far and i seem to be confused on the proper formula.

\(\displaystyle \sum X = 33 \)
\(\displaystyle \sum Y= 54 \)
\(\displaystyle \sum X^2 = 253 \)
\(\displaystyle \sum Y^2 = 690 \)
\(\displaystyle \sum XY = 413 \)
\(\displaystyle n = 5 \)

formula:
\(\displaystyle r = \frac{(\sum XY - n \bar{x} \bar{y})} { (n-1) SxSy }\)

I think the \(\displaystyle \bar{x} = \sum X ? \)
I am not sure how to find \(\displaystyle SxSy \) are they just sum of X and sum of y seperately?
Can i just put everything into the formula and solve?

I am not sure if i need to find \(\displaystyle y - \hat{y} \) and \(\displaystyle (y - \hat{y})^2 \)
or what it would be used for..

If i am wrong can you provide some help?

Thank you
 
steller said:
The annual repair cost for a vegetable garden tiller is related to its age in years.
A sample of 5 tillers revealed the following data:


View attachment 3102


a. Compute the correlation coefficient.

What i have so far and i seem to be confused on the proper formula.

\(\displaystyle \sum X = 33 \)
\(\displaystyle \sum Y= 54 \)
\(\displaystyle \sum X^2 = 253 \)
\(\displaystyle \sum Y^2 = 690 \)
\(\displaystyle \sum XY = 413 \)
\(\displaystyle n = 5 \)

formula:
\(\displaystyle r = \frac{(\sum XY - n \bar{x} \bar{y})} { (n-1) SxSy }\)

I think the \(\displaystyle \bar{x} = \sum X ? \) =======> NO
I am not sure how to find \(\displaystyle SxSy \) are they just sum of X and sum of y seperately? =======> NO
Can i just put everything into the formula and solve?

I am not sure if i need to find \(\displaystyle y - \hat{y} \) and \(\displaystyle (y - \hat{y})^2 \)
or what it would be used for..

If i am wrong can you provide some help?

Thank you
Click to expand...

x-bar and y-bar are the means of the x and y data, respectively

Sx and Sy are the standard deviatons of the x and y data, respectively
 
Last edited:
steller said:
can you help me find those?
Click to expand...

You're telling me that you do not know how to find the mean of a bunch of numbers? I am not trying to be a tool, but I just find it shocking that someone taking statistics does not know how to find the mean of some data as that is taught to kids in middle school. Do you have a textbook? Teacher? Try googling.

Or....click on the little blue word above for some insight ;)
 
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