How to interpret multiple regression
Regression is useful for making a predictive model. Let's say there's a positive linear correlation between K and N, but you suspect that Factors L and M also contribute to Outcome N.
Make up a story—say, that Factors K, L, and M represent intelligence, persistence, and amount of sleep per night and N refers to a course grade.
So, to test the relative impacts of Factors K, L, and M on Outcome N, you can feed each factor into a regression model, and test whether each factor increases the fit. That is, a correlation between Factor K and Outcome N yields a Pearson's r of .64 and R2 of .4096.
But, when you run a regression testing the effect of Factors K and L on Outcome N, you find an R2 of .5625, with a significant change in the R2 value. That means that Factors K and L together do a better job of explaining the relationship than Factor K alone.
Then, you run a regression with Factors K, L, and M together, and find an R2 of .5929, with no significant change—this means that Factor M does not help to explain the relationship. Outcome N is due mostly to Factors K and L; Factor M is an unimportant predictor of Outcome N.
Voilà! There's regression in a nutshell!
And, if you're confused about the math...remember in middle school or high school math, when you learned about "rise over run" and learned the formula y = mx + b? Yeah, that's a simple linear regression. With multiple regression, you can add multiple terms, such that y = ax1 + bx2 + cx3...+ z. But it's still the same concept, just with more predictors than that lone "mx" term.
For more help explaining statistical concepts and when to use them,
In case you missed it, there are some fantastic, easy-to-use, and FREE stats programs available now! I review them here.
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