Hi, I have a DV that has negative values. Lets assume a temperature range of -10 to 10celsius. I have a number of predictor variables, lets assume we are trying to predict temperature using thickness of insulation (mm). I understand statistically the DV can have a negative value, but how would you intepret that? Assuming for example thickness has a negative beta coefficient, predicting temperature. Does that mean the thinner the material the lower the temperature? Or the higher the temperature? The inclusion of the negative value is utterly confusing for me pleaseh help!
I agree with Philippe. Moreover, it is not hard to prove than in the simple linear regression Y=a+b*x+error the expression for "b" is
b=Cov(y,x,)/V(x).
The sign of "b" is simply given by the sign of the Covariance between Y and X regardless of the sign of Y.
In the case of a multiple regression the math is more complex but the same principle applies.
Cheers!
Perhaps you could clear your ideas if you convert Celsius to Kelvin scale before doing regression, then you will only have positive temperatures.
Benigno Antonio Rodriguez-Gomez thanks, but I was just using temperature in Celsius as an example for my problem. I have several scales in questions to which transforming may be theoretically problematic, and keeping the negative value is much more meaningful. But thank you for your answer anyway!
.Yiwen Tan , don't assume, and expect to have fact or meaningful interpretation from figure. No sir. If you are not happy with e negative values of temperature in Celsius [true outcome of an experiment], pls without assuming convert to Kelvin. If thickness has a negative beta coefficient (i.e.,inverse relationship) predicting temperature, the interpretation is that for every 1-unit increase in the predictor variable [thickness], the mean of the outcome variable (temperature) will decrease by the beta coefficient value. The thinner a material, the higher the temperature over time compared to that with larger area and thickness.
This really means that the thinner the insulation, the higher the temperature. A negative beta coefficient is interpreted the amount of inverse change in the dependent variable due to a unit change in the independent variable with the negative beta.
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