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I have a set of records from 68 different watersheds that previously mined but reclaimed later. After some years a portion of mined area were converted to forest and there was no difference between unmined sites and reclaimed forest areas.

I am trying to conduct a regression analysis to predict stream conductivity (dependent variable) and my independent variables are reclamation age (year), reclaimed forest area(%) and mined area(%). I ran stepwise multivariate regression in SPSS. It results reclaimed forest was not a significant predictor but only reclamation age and mined area were significant and R-square for the model 0.81.

Then I created another independent variable called mined area without reclaimed forest. Basically I removed reclaimed forest areas from mined areas. I ran the regression model again. Reclamation age and mined w/o rec forest as Independent variable while conductivity was dependent variable. It improved my R-square 0.83.

As a conclusion, even though there was no direct correlation between reclaimed forest areas and conductivity, taking reclaimed forest areas out and running the model again improved my R-square value. So, I would like to ask, Is it OK to do that? I would like to use this in a scientific project. here is model summary and coefficients enter image description here

enter image description here

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  • $\begingroup$ reclaimed forest area could have a non-linear impact on stream conductivity. Comparing R squared quantities does not necessarily provide us with a basis to conclude about relationships as proposed. Try other models and options. $\endgroup$ – Subhash C. Davar Jan 27 '18 at 3:01
  • $\begingroup$ @subhas c. davar Thanks for your response! I have tried other options as well such as log, Ln, power none of them worked. I don't know what else should I try. $\endgroup$ – Amadeus Jan 27 '18 at 18:41
  • $\begingroup$ stepwise multivariate regression (analysis) ? what is the summary output ? $\endgroup$ – Subhash C. Davar Jan 28 '18 at 12:31
  • $\begingroup$ @subhas c. davar I have checked forward and remove options as well I got the same output. However, when I enforced all variables reclaimed forest insignificant (p=0.076). Also, I did not find linear relationship between mined and conductivity. Thank you! $\endgroup$ – Amadeus Jan 28 '18 at 18:50
  • $\begingroup$ However, when I enforced all variables reclaimed forest insignificant (p=0.076). I can't trace this value in your models. $\endgroup$ – Subhash C. Davar Jan 30 '18 at 1:18
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A few things suggest that it would be at least a bit dangerous to use this method.

First, stepwise regression is always a bad idea, whether it is done automatically (by SPSS as in your first step) or manually (by making a linear combination of two of your explanatory variables and adding that to the model). You should base your inference on the fullest model you have fit (ie the one with the most variables and interactions, whether you fit it explicitly or implicitly by just looking at graphics), otherwise your inferential statistics will all be biased towards reporting things as more "significant" and further away from zero than there is evidence to justify.

Second, I presume conductivity is a rate of some kind that has realistic upper and lower bounds that don't really relate to the size of the watershed, whereas the independent variables you have (or subtracting one from the other) will be very much correlated with just the size of the watershed. It would seem more sensible to me to relate conductivity to something on a scale that is not related to the size of the watershed, such as the proportion of the watershed that was mined and the proportion of the watershed that was reclaimed. Otherwise, it seems to me that each watershed is effectively measured on a different scale. Of course, if the absolute size of the watershed is suspected to be important for theoretical reasons, it could maybe be added in as a third explanatory variable in addition to the proportion mined and the proportion reclaimed.

Third, as @subhash points out in the comments, there is no obvious reason to think the relationship between your variables and the stream conductivity is linear. You need a modelling approach that can handle the possibility of this. However, with only 68 data points you have a limited number of degrees of freedom to play around with when it comes to non-linear relationships and interactions. A Generalized Additive Model of some sort, with modest curvature allowed for each of the two variables, would be appropriate.

Finally, whatever model you finish with, you should use diagnostic methods, including graphical ones, to check the assumptions (eg normality of the residuals, if that is part of assumptions of the model).

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  • $\begingroup$ I have checked non linear functions (Ln, power, logarithmic) but I did not get any better results. My measurements are in % as you suggested. I have validated all assumptions that necessary for linear regression model. I have a few other variables so I thought it would be easier to use an automated model such as stepwise. Would you mind explaining how I will choose parameters for the model? Should I use all parameters together and force the entire model, then I should remove/check not significant ones, collinearity and re-run the model? $\endgroup$ – Amadeus Jan 27 '18 at 17:10

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