I can't understand: In order to transform the data to make it appear more linear, how can I choose what transformation to use, if I don't have any data, but just scatterplot in front of me....(I hope, you understand me)
There are certain transformations that work better, depending on the original relationship between x and y. Your text probably has a table that shows the appropriate or "recommended" transformation, based on the approximate equation between x and y.
I have a task in test, where the image of scatterplot is given and then 4 possible types of transformation. I know how to transform the data by the method of trying different combinations (log x, log y, y2 etc.) on graphic calculator. But what if they don't give any data, but just the image of scatterplot with a certain pattern and then they ask what method of transformation to use?
If the scatterplot includes the x and y axis marks with numbers, then you should be able to sketch a "best fit" line through it and estimate the equation of the best fit line by picking a few values of x and seeing what y would be. This is normally done in algebra --> given a few data pairs (x,y), determine the slope and y-intercept of the line.
In your example, I imagine it would be a pretty simple relationship even though it won't be linear...
Does it look something like y = x^2 or y = ln(x) or y = n^x ?