# Simple stats question-correlation coefficient

Let's say we have two exams, each out of 50 points. The correlation rate between them is 0.75. If the teacher decides to add 10 points to the results of the first test, what will happen to the corr. rate?

The way I see it, the correlation should decrease, but by how much? Would it decrease by 1/5=20%? And the result would have been the same even if she subtracted 10 points from the first test, correct?

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By "correlation rate", you probably mean something like "correlation coefficient" or "covariance"? Note that all formulas for such quantities measuring correlation only depend on the differences between values (and expectation values) for the same variable. What does that tell you about what happens when you add the same constant to all values for a variable? – joriki Mar 19 '11 at 6:47

If by correlation you mean the usual (Pearson) correlation coefficient, then nothing will happen. If we have two random variables $X$ and $Y$, then their correlation coefficient is $$\frac{E((X-\mu_X)(Y-\mu_Y))}{\sigma_X\sigma_Y}$$ where the symbols have their usual meaning. If $Z=Y+10$, then $Z-\mu_{Z}=Y-\mu_Y$ and $\sigma_{Z}=\sigma_Y$, so the correlation coefficient of $X$ and $Z$ is the same as the correlation coefficient of $X$ and $Y$.