People with university education tend to hold higher paying jobs than those with

Question

People with university education tend to hold higher paying jobs than those with fewer educational qualifications. This could be due to the fact that a university education provides important skills that employers value highly. Alternatively, it could be the case that smart people tend to go to university and that employers want to hire these smart people (i.e., the university degree is of no interest in and of itself to employers). Suppose you have data on income (Y), number of years of schooling (X) and the results of an intelligence test of many people (Z), and that you have calculated rXY, rXZ, rYZ. In practice, what signs would you expect these correlations to have? Assuming the correlations do have the signs you expect, can you tell which of the two stories in the paragraph above is correct?

Explanation / Answer

X: number of years of schooling

Y: income

Z: the results of an intelligence test of many people

rXY: We expect income increases as number of years of schooling increases. Therefore, the expected correlation between X and Y is positive.

rXZ: We expect the results of an intelligence test of many people increases as number of years of schooling increases. Therefore, the expected correlation between X and Z is positive.

rYZ: We expect income increases as the results of an intelligence test of many people increases increases. Therefore, the expected correlation between Y and Z is positive.

Stories rXY and rYZ are correct because we expect X and Z are independent and correlation is between independent and dependent variables only.

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