I am running a best fit curve analysis in SPSS under linear, Quadratic, Compound, Growth, Logarithmic, Cubic, Exponential, inverse, power and logistic regression models. I am consistently having high values of R square and Std. Error. And is there any rule of thumb for the Std. Error of the Estimate value of a regression ?
The more models you fit, the more likely you will get a false positive result for your statistical tests & the more likely that your results will be spurious. Effectively you are lowering the bar for statistical acceptance. You are not saying how many independent variables you are fitting & that is important when evaluating the R value. SPSS should also be giving you statistical significance levels for the R value & each of the fitted variables. This is also important information. The size of the standard error is relative depending on the units of measurement chosen & the data transformation used so it should be irrelevant. Perhaps I am misunderstanding your question.
The test is significant at 0.00 and I have high value of R square for my best fit curve which is a good sign but at the same time value of the standard error is also high. its my first time to work with non-linear regression so I am not sure what does my results actually mean. and please also kindly tell me the acceptable value if any for std. error
I have fifteen years(yearly) data of carbon emissions and I want to find out its best curve with different independent factors like GDP, GNP, Population size etc.
if there are more number of independent variables which are expected to be interrelated, you should test multicollinearit between the independent variables.
It is not clear which definition of standard error you are using, nor how you are defining "large." Standard error might be the standard deviation divided by the square root of n. Standard error might also be a description of the variability in the least square means corrected for other factors in the model.
R2 is the proportion of variability explained by the model.
Jack makes a good point. Please do not try several models and choose the one that you like best. You could choose one model and hope for the best. You could choose one model based on how the system must function. You could look at all models and then eliminate a few after closer inspection of the assumptions made by those models and how your data do not quite satisfy those assumption. If you go with the latter approach and get multiple interpretations then select the one you think is best but in a short paragraph acknowledge that there were other outcomes.
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