Watch Your Units

A section of this week’s reading discussed applications of multiple regression. In specific, the authors gave examples of how one can use multiple regression models to predict sales based on advertising expenditures. As X money is spent on TV and radio advertisement, product sales increase Y amount. In this example, the units of the variables are the same (amount in dollars: spend more money on advertising — receive more money in revenue).

However, what happens if coefficients do not have the same units? As I was researching this topic I found out that one can standardize coefficients. For example, if I were to use a regression model to predict income based on education level (given in years) and IQ (given as an standardized score). I would have to standardize the coefficients. Although, I do not understand all the math behind it, I gather from the example given that standardization converts all independent variables so that they have a mean of 0 and a variance of 1. Pretty cool … Well, yes, but there are some drawbacks.

As far as I gather the two main issues are: results can harder to interpret and it can make it difficult to compare results across groups!

References
https://www3.nd.edu/~rwilliam/stats1/x92.pdf

http://www.pmean.com/09/StandardizedBetas.html

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013) An Introduction to Statistical Learning: with Applications in R. New York, New York: Springer New York