Why is the r-value independent of translation and scaling? #1

Two days ago, I was teaching correlation & regression to my students and a few of the are rather puzzled why the r-value is independent of any translation and scaling. Let us first look at the formula that we are all given.

Credits: MF15

Credits: MF15

First of all, examples of a translation can be increment in base wage, etc while example of a scaling can be a change in units of measure say from pounds to yen.

Next, if its a translation, observe the sample points will all translate upwards or downwards accordingly and this does not ultimately affect regression line at all. The r-value which measures the degree of correlation will not be affected either. But shouldn’t scaling have some effect then?

The answers is no, because the proportion and degree of correlation will remain the same.

Click here for a mathematical approach.

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