Correlation

[Jep]

Hello,

I have three variables a,b, and c. Variable c is obtained by dividing a by b and multiplying by 100, in other words c=a/b*100.

Can I calculate a correlation or even a linear regression where the dependent variable is c and the explanatory variable is b; given that variable b was involved in calculating variable c? variables a and b are measured in a continuous scale.

Appreciate your help.

[PaigeMiller]

Yes, you can calculate a correlation.

Yes, you can calculate a regression.

Why don't you give it a try?

[Jep]

Appreciate your reply. So I did run a regression and a correlation, but the question now is that, are the results/estimate valid given that one of the variables being compared was used in calculating the other variable being compared with?

[PaigeMiller]

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@Jep wrote:

Appreciate your reply. So I did run a regression and a correlation, but the question now is that, are the results/estimate valid given that one of the variables being compared was used in calculating the other variable being compared with?

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Since we really know nothing about the problem, and we also don't know what use the correlation/regression will be put to, the answer is: "It depends".

[Rick_SAS]

I hope a scatter plot of (a[i], b[i]) shows a quadratic relationship that passes near the origin. That is what your model says:

Find the least-squares values (beta0, beta1)such that 

100*a[i] / b[i] ~ beta0 + beta1 * b[i]

or 

a[] ~ gamma0*b[i] + gamma1*b[i]^2

Thus your model assumes a quadratic relationship (no intercept) between a and b. IMHO, it would be clearer to drop c and write the model as

MODEL a = b b*b;

[Jep]

Thanks for your reply. The scatter plot for a and b actually shows a linear positive relationship. But when I do a scatter plot for b and c, it shows a linear negative relationship or correlation. So the problem that I have is that is the estimate obtained by running a correlation or a linear regression between variable's b and c valid given that variable b was part of the variable used to obtain/calculate variable c?

[ballardw]

You can calculate a correlation between any numeric variables that have 2 or more pairs of values.

The interpretation may be pretty difficult if there isn't much of a natural relationship such a number of hairs on your head and your first grade teachers dress size.