Hello everyone,
I plan to include coordinates as covariates in the regression equation in order to adjust for the spatial trend that exists in the data. After that, I want to test residuals on spatial autocorrelation in random variation. I have several questions:
1. Should I perform linear regression in which only independent variables are x and y coordinates and then tests residuals on spatial autocorrelation, or should I rather include not only coordinates as covariates but also other variables and then test residuals.
2. If I expect to have quadratic trend, and then include not only x,y, but also , xy, x squared and y squared, but then some of them (xy and y squared) have the p-value higher than the threshold --should I exclude those variables with higher p-value as being nonsignificant? How should I then interpret the trend, it is certainly not quadratic anymore?
3. I guess I should treat x and y coordinates as any other covariates, and test them on having linear relationship with dependent variable by constructing partial residual plots ... but then once I transform them (if they show they need transformation), that will not be that kind of trend any more (especially if I include xy, x squared and y squared for quadratic trend). It may show that x squared, for example, needs transformation, while x does not or so? How should I react in these situations?
Thank you.
I plan to include coordinates as covariates in the regression equation in order to adjust for the spatial trend that exists in the data. After that, I want to test residuals on spatial autocorrelation in random variation. I have several questions:
1. Should I perform linear regression in which only independent variables are x and y coordinates and then tests residuals on spatial autocorrelation, or should I rather include not only coordinates as covariates but also other variables and then test residuals.
2. If I expect to have quadratic trend, and then include not only x,y, but also , xy, x squared and y squared, but then some of them (xy and y squared) have the p-value higher than the threshold --should I exclude those variables with higher p-value as being nonsignificant? How should I then interpret the trend, it is certainly not quadratic anymore?
3. I guess I should treat x and y coordinates as any other covariates, and test them on having linear relationship with dependent variable by constructing partial residual plots ... but then once I transform them (if they show they need transformation), that will not be that kind of trend any more (especially if I include xy, x squared and y squared for quadratic trend). It may show that x squared, for example, needs transformation, while x does not or so? How should I react in these situations?
Thank you.
http://dl.acm.org/citation.cfm?id=1294455
http://spatial-analyst.net/wiki/index.php?title=Regression-kriging_guide
http://en.wikipedia.org/wiki/Regression-kriging