Interpreting Regression Coefficients: Changing the scale of predictor variables

by Karen Grace-Martin

Sometimes it makes sense to change the scale of predictor variables so that interpretations of parameter estimates, including odds ratios, make sense.  It is generally done by multiplying the values of a predictor by a constant, often a factor of 10.

Since parameter estimates and odds ratios tell you the effect of a one unit change in the predictor, you should multiply them so that a one unit change in the predictor makes sense.

Here is a really simple example that I use in my logistic regression workshop.

Y= whether or not a student goes on academic probation after the first semester in college

X1= high school GPA (measured on a 4 pt scale)
X2=SAT score

If you don’t multiply either predictor, neither makes sense. A one-unit change in GPA is huge– a .1 unit change makes much more sense.

Likewise, a one-unit change in SAT score is too small. In fact, the way the SAT is scored, you couldn’t have two SAT scores one unit apart–they go by 10’s.

In my (completely made up) example the odds ratio for SAT score is something like 1.03. Tiny, but significant, because a one-unit difference in SAT score is tiny. But if you divide SAT score by 10, 10 points becomes 1 unit, so the odds ratio is based on that scale.

Likewise, you could multiply GPA by 10 (essentially changing it from a 4 to a 40 point scale). Now a 1 unit change is meaningful.

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If you want to learn all the ins and outs of interpreting regression coefficients, check out our 6-hour online workshop Interpreting (Even Tricky) Regression Coefficients.  This workshop will teach you the real meaning of coefficients for all the tricky regression terms: correlated predictors, dummy variables, interactions, polynomials, and more.

Interpreting Linear Regression Coefficients: A Walk Through Output
Learn the approach for understanding coefficients in that regression as we walk through output of a model that includes numerical and categorical predictors and an interaction.

{ 2 comments… read them below or add one }

Farmanullah

Dear Sir/ Madam
how can i calculate odds ratio in linear regression?
I have analysed simple linear regression and multiple linear regression. now i need to calculate both crude and odds ratio. Please suggest me what formula i should use to calculate ODDs ratio from coeffecients.

Reply

Karen

You can’t get an odds ratio for linear regression. That may be why you’re stuck.

You can calculate an odds ratio for logistic regression. I did a whole webinar on it. You can get the recording for free here:
http://thecraftofstatisticalanalysis.com/understanding-probability-odds-ratios-regression

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