This is question from an AJC prelim exams, I’m not really sure which year. The question prompts students if there will be a change in the r-value should, the scientists change the unit of measurement from Celsius to Fahrenheit.
My student was uncertain if he had phrased his answers well. His answer is as follows, “the change in each value will still be the same so only the magnitude of the values themselves are affected and not their linear relations. Thus r will be the same.”
I feel that he has gotten the correct idea for this question. However, his explanation can be really confusing and misleading to examiner. A better way will just to showcase to examiner that you know that r is independent of scaling and translation.
Intuitively, any form of scaling and translation will simply move my data points, PROPORTIONATELY. So the resultant correlation observed when we measure in celsius and fahrenheit will be same. Students can refer to this webpage for a technical proof.
Now, my question back will be: Given two variables, annual wage and expenditure, will the r-value change if we consider hourly wage and expenditure, instead of using annual wage.