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An excerpt from what Will recently wrote:
The effect of activity in a multiple linear regression that includes SES is the effect of activity "controlled for" SES; that is, the effect with SES effectively held constant. But how do you express the magnitude of the resulting effect of activity on health? That's was the substance of my query to the list.
You have two choices for interpreting the magnitude. You use either the regression coefficients (the terms in the multiple linear regression that convert values of the predictors into values of the dependent variable) or correlation coefficients. It's hard to get a good idea of magnitude from the regression coefficients without invoking Cohen's concepts in some manner. In other words, the between-subject standard deviation (variation) in the predictor and dependent have to come into the story. Correlation coefficients already have between-subject SDs built in, so they are good candidates for interpreting magnitude.
Let's go back to basics and univariate analysis and a thought experiment. Everyone should remember that you can have a correlation of 0.9 with a slope that is very small, and a correlation that is 0.7 with a slope that is large. So, what do you mean by magnitude of effect? Let's say X1 is physical activity, X2 is calories consumed, and Y is weight. For each increase in physical activity, there is very small change in weight (small slope which means small regression coefficient) but the correlation is 0.9. For each decrease in calorie consumed, there is a large decrease in weight (large negative slope which means large negative regression coeffiient) but there is a lot more noise and the correlation coefficient is only 0.7.
Okay, if you want magnitude of effect to decrease weight, do you want to increase physical activity (high correlation, small regression coefficient) or decrease caloric intake (low correlation, large regession coefficient)?
Multiple regression is conceptually the same.
Ian Shrier MD, PhD, Dip Sport Med (FACSM)
Past-president, Canadian Academy of Sport Medicine
check out: www.casm-acms.org
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