I have 1 dependent variable (y1) and 2 independent variables (x1, x2) in raster format. I want to choose the best, single, variable for simple linear regression. My goal is two-fold:
Based on my goals, should I select the covariate based on Pearson correlation or based on R² and why? For example, a linear model using x1 maybe yields higher R² value compared to the other model but the x2 yields higher Pearson correlation.
Emphatically no you you don't want to use your suggested approach and I suggest you look at the attached to see why not and see other alternatives. Best wishes David Booth
correlation (Pearson's)is good to identify the direction of relation and pattern in the data but does not serve any purpose when one is concerned about the performance of model. In that case use r squared value is helpful identify the model performance at local level when using GWR.
Thanks
See this link, please:
https://www.stat.purdue.edu/~dkjlin/documents/publications/2020/2020_JQT.pdf
Very nice papers and suggestions, thank you all. I didn't know that there are so many alternatives for variable selection. Based on your suggestions, I should not pay attention on Pearson correlation between the target variable and the covariates when it comes to identify the "best" model. That's a good starting point. Now I think I have a clearer image on how I should proceed.
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