Further Maths SAC - Transformations

[Ritzforlife]

I'm currently doing my further maths SAC. We're required to create a scatterplot with the provided data. My correlation coefficient is a strong positive with r = 0.85

The next question requires us to do a transformation that linearises the data, however my problem is that the scatterplot is already linear and all the transformations all result in a weaker correlation and the coefficient of determination is always only around 60-78%.

Am I missing something? Do transformations always result in the correlation increasing?

Any help is appreciated?

[Stick]

That sounds a bit dodgy to me. Are you sure your data is linear? You might have potentially made a mistake, because it sounds like the data should be non-linear.

To answer your question, no, transformations do not always improve the linearity of data. Think about applying a squared transformation to a straight line, for example.

[Lucho23]

I know from my SAC and what my teacher said, they will most probably ask you to apply a transformation in order to get a stronger relationship. Rarely should you end up with a weaker correlation. Check all your working, you may have made some small error.