Suppose you have a sample of children ranging from 5 to 18 years of age. You run

Question

Suppose you have a sample of children ranging from 5 to 18 years of age. You run a regression of standardized math scores on height and get a statistically significant positive coefficient estimate. Your research assistant concludes that height has a causal effect on mathematical ability - being taller makes children better at math. Bad luck for everyone who is short. Would you agree with your research assistant's interpretation of the regression results? If so, explain why. If not, offer a more likely explanation for the positive correlation and suggest how you could alter your regres­sion to address this.

Explanation / Answer

no. there is a positive correlation between standardized math score and height because the correlation is spurious.

there must be some lurking variable which is acting as a connector between these two variables.

and here that lurking variable is most preferably AGE

the sample consists of children from age 5 to 18 years.

so we have children of age 5 years as well as children of age 18 years.

now as age increases height also increases. so age and height has a positive correlation.

and as age increases the ability to understand any subject increases as a result maths score also increases.

so age and maths score has a positive correlation.

so age and maths score is positively related and age and height is positively related.

hence maths score and height is positively related.

hence the regression can be altered by regressing maths score on age.

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