Question

The R2 value is an important guide when judging the relationship between two quantities. If you performed linear 2DStats calculations on the original non-linearized data y versus t explain how the value of R2 would help you spot such a mistake

I don't understand how to approach this question but the value is

0.999892

Answer 1

Nonlinear regression is an extremely flexible analysis that can fit most any curve that is present in your data. R-squared seems like a very intuitive way to assess the goodness-of-fit for a regression model. Unfortunately, the two just don’t go together. R-squared is invalid for nonlinear regression.

some statistical software calculates R-squared for these models even though it is statistically incorrect. Consequently, it’s important that you should not trust R-squared for models that are not linear.

the variances always add up in a particular way: Explained variance + Error variance = Total variance.

This arrangement produces an R-squared that is always between 0 – 100%.

However, this math works out correctly only for linear regression models. In nonlinear regression, these underlying assumptions are incorrect.

Explained variance + Error variance DO NOT add up to the total variance! The result is that R-squared isn’t necessarily between 0 and 100%.

if you use R-squared for nonlinear models, their study indicates you will experience the following problems:

• R-squared is consistently high for both excellent and appalling models.
• R-squared will not rise for better models all of the time.
• If you use R-squared to pick the best model, it leads to the proper model only 28-43% of the time.

conclusion -  R-squared just can’t differentiate between good and bad nonlinear models.

There are other goodness-of-fit measures you can use for regression models that are not linear. For instance, you can use the standard error of the regression. For this statistic, smaller values represent better models.