Question

When choosing within non-linear models for trend lines, how does the model highest r² value perform an amazing job, AND conversely, how could highest r² perform a poor job (ex: why is it not good at extrapolating or what the data is trying to do)? In this case, the model with the highest r² value is polynomial. Please respond with as much details in order to build my conceptual understanding in Canadian highschool statistics level.

Answer 1

R squared is coefficient of determination. It says amount of variation explained in Y by the model. Now when we are trying to find the good model using R squared, then it means we are trying to find a model that has explained better variation in Dependent variable. So we choose that model which has higher R squared. Now what is Higher in this case?? Anything as good as 0.7 is considered higher. But when Rsquared value cross 0.95,we suspect the model because the model is overfitted in this case.

When R squared is highest this means Model has tried to fit each and every point which is not good for extrapolation. Because this model has been trained perfectly on available data and when we have any new test data available this model may fit poor. Hence Highest R squared is also not good.