# Interpretation of the regression coefficient of a proportion type independent variable

If I want to use some proportion type independent variables in a logistic regression, then what will be the interpretation of the regression coefficients corresponding to those proportion type variables? Will that mean- "The change in log odds for per unit change in the proportions"?

But what will be meant by "per unit change" in this case? As the proportions lie within [0,1], I am getting a little confused with what a "per unit change" will mean in this scale. Does it mean 0.01 or 1%? (I am sorry for my noob thoughts!)

In my data the range of the proportions is 0 to 1, not multiplied by 100. Do I need to multiply them by 100? So that I can say "per unit change" means 1% change? I have seen that the coefficients do differ in scale if I multiply the proportions by 100. For example, a coefficient of -1.3 for proportions becomes -0.013 for percentages (when the proportions are multiplied by 100).

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The interpretation for the regression coefficient is always for a 1 unit change regardless of what a "unit" is. In your case, if the IV is a proportion falling between 0 and 1, a one unit change is the same as 100%.

If instead you want to look at the "effect" of a 1% change, simply multiply your IV by 100 before using it in the regression.

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Thank you. You are absolutely right. Actually FMZ is also right. "Per unit change" for a proportion type variable should always mean change by 1 (or 100%) unit in the independent variable. Just that for my example, Y goes down by 1.3 units when X (measured in proportions) increases by 1 unit also implies that, Y goes down by 0.013 (1.3/100=-0.013) units when X (measured in proportions) increases by 0.01 (1/100=0.01) units. That makes it consistent with the sense of proportions. Thank you all. – Blain Waan Jan 11 '13 at 11:16

They are the same, aren't they?

Let's take the first model, coefficient is -1.3 and variable is in original scale (0-1). So if the variable increases by 0.01, say from 0.08 to 0.09, then the log odds are down by 1.3*0.01 = 0.013.

Now the second model, coefficient is -0.013 and variable is multiplied by 100 (0 - 100). So if the variable increases by 1 from 8 to 9 (which is actually from 0.08 to 0.09), then the log odds are down by 0.013*1=0.013.

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Dear FMZ, thank you for your kind reply, but could you please confirm me when I use proportions as independent variables then "per unit change" in the independent variable means an increase by 0.01. I was guessing it, but as it is a continuous variable just like the other continuous variables (which would generally mean an increase by 1), so I was afraid if a unit change meant '+1' or '+0.01' in this case! Probably very immature question, but I would like you to explain this a little. – Blain Waan Jan 11 '13 at 10:15
Ok I have got it. I would like to thank you too for your kind thoughts. – Blain Waan Jan 11 '13 at 11:21