Transformations.

[bibinbg2002]

Does anyone know what we have to do or write if none of the transformations (from circle of transformations) linearise the original graph?

[S_R_K]

Does anyone know what we have to do or write if none of the transformations (from circle of transformations) linearise the original graph?

I have never seen this arise on a past exam - typically an exam question will tell you which transformation has been applied, and that transformation will linearise the data.

If you have been given a SAC where the data can not be linearised then I think it would be reasonable to point out that no transformations are effective, and give your reasons why. For instance, you might say that the original data has no consistent increasing / decreasing trend. Or you might point out that the coefficient of determination is not increased by any of the transformations. But in this case it is probably best to discuss with your teacher or refer to what you have been taught about how to handle a case like this.

[bibinbg2002]

Thanks a lot. Also, if one of the transformations gives us a higher 'r2' value than the original, but is still not linear, do we choose it? And if we do choose it, what can we say? Because it's still non-linear yet gives a higher r2 value. Thanks again.

[S_R_K]

Coefficient of determination is not a good way to judge the accuracy / reliability of a non-linear model. The coefficient of determination describes the amount of variation in the RV that can be attributed to the amount of variation in the EV, assuming a linear association.

If applying a transformation still gives a non-linear model, but the r^2 has increased, this does not necessarily mean that the new non-linear model is better than the old one. Strictly speaking, you can only use increasing r^2 to judge effectiveness of a transformation if the associations are linear.

But, as mentioned above, if you suspect you've got some dodgy data on a SAC, and are being asked to apply linear regression techniques to non-linear data, you should consult your teacher. They may not be able to discuss any specifics with you, but it could be considered when marking / moderating SACs.