Nonlinear function to linear function conversion (as part of linear regression)

[Dr.Peterson]

@Dr.Peterson I'm just trying to clarify my doubts. At first Google sheets graphs squared perfectly with what was taught in the lessons but then I couldn't get Desmos to do the correct thing. I don't know why [imath]g(f(x)) = 3f(x)[/imath] doesn't return an error and also fails to show a graph.

It's not that I haven't defined the functions
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I have no idea what Desmos thinks your line could mean; as far as I can tell, it's just confused, because it expects g to be either a number or a function, and you haven't defined it as either. It clearly does not take what you wrote as defining g, and I would not take it that way either. If you follow it with a definition of g, either way, it acts accordingly:



Now the blue equation means [imath]4x^2=3x^2[/imath], whose solution is [imath]x=0[/imath].



Here the blue equation means [imath]4-x^2=3x^2[/imath], whose solution is [imath]x=\pm1[/imath].

You haven't said what you entered into Google sheets, or what it produced; presumably it isn't the same thing, so there's nothing to compare.

But I'll say this just one more time: If you would show us the problem that started this, there would be something worth discussing. As it is, this is all meaningless. What was it that you were "taught in the lessons"? What lessons? I still have no idea what is "the correct thing".

 

[Agent Smith]

But I'll say this just one more time: If you would show us the problem that started this, there would be something worth discussing. As it is, this is all meaningless. What was it that you were "taught in the lessons"? What lessons? I still have no idea what is "the correct thing".

I was on the topic Linear Regression (least squares regression line). Then we had to do some exercises, one of which is to decide (MCQs), given various graph shapes with different y and x axes, whether the relation being displayed is linear, quadratic, or exponential.