Regression to Points

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Regression to Points

Timothy Foster 08 Apr 2010 21:39

I have been posed this challenge by my math teacher, and after thinking about it for a bit I have become quite stumped:

• Create a program that will generate a certain number of points that will obtain a particular r value when linear regression is run on those points.

It would have the following inputs:

• x range
• y range
• number of elements/points
• the desired r value

and the following outputs:

• x list
• corresponding y list

Thus when linear regression is run on the points formed by the outputted x and y lists, the desired r value is made. Does anyone know of a method to complete this?

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Timothy Foster - @tfAuroratide
Auroratide.com - Go here if you're nerdy like me

Re: Regression to Points

samweiss 08 Apr 2010 22:58

Well, I see one big way to do something like this, but you must start with at least a few data points. Firstly, have the user enter the data in L₁, then, call the LinReg(ax+b), which is in STAT->Calc->LinReg(ax+b), then, the equation is usually stored in you y vars, which can be accessed via VARS->Y-VARS->Function->y₁. once you have accomplished this, you need to graph this function with you need to call the DrawF(equation), this will graph the line on the screen. After this, you must use the G-T function to display the data on the screen. it may look a bit like this:

if dim(L1< 5)
then
Disp "Enter data in L1 and L2","press enter"
Pause
DispTable
stop
end
LinReg(ax+b)L1
DrawF(Y1)
G-T
DispGraph

Hope this help, it's not 100 percent what you asked, but it's close, an alternative is that you pass in the equation, and calculate points along it's length, but other than that, I couldn't find anything.

Re: Regression to Points

Timothy Foster 09 Apr 2010 00:02

Well, you showed me how to find the regression line of a data set. I'm trying to reverse the process in which, given an r value (how closely the line of best fit follows the data), a data set is generated by the program.

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Timothy Foster - @tfAuroratide
Auroratide.com - Go here if you're nerdy like me

Re: Regression to Points

calccrypto 09 Apr 2010 00:39

maybe modify circle/ellipse equations as restrictions so that they would change to the top row of

according to the input r value (maybe a 3d rotation or something to stretch the conic equation). since the program is generating the points, just do something like

(a number) * rand([number of points]→X
Y₁(∟X→Y

maybe the random values will come out with a value close to r?

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Last edited on 09 Apr 2010 02:36 by calccrypto Show more

Re: Regression to Points

samweiss 09 Apr 2010 01:13

I agree with calccrypto, there is no way to know the specific points that made the original line, you simply don't have enough data, but you can generate relatively random numbers in the range you are given, and it would be possible to find a set of data that would yield the line, but there are an infinite amount of different data sets that can yield a specific line.

Re: Regression to Points

thornahawk 10 Apr 2010 02:36

Things like the Anscombe quartet show that the problem your teacher gave you is ill-posed; still, this might interest you (though you might want to review your linear algebra first before attempting to implement this).

thornahawk

Re: Regression to Points

Timothy Foster 10 Apr 2010 03:40

Hmm, I figured the problem would be near impossible. When we worked it out, we figured the absolute best output would be to find the sum of the x's and sum of the y's which doesn't help at all. My math goes up to some basic pre-calculus, so that article may fly above my head ;)

Thanks,

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Timothy Foster - @tfAuroratide
Auroratide.com - Go here if you're nerdy like me

Re: Regression to Points

Weregoose 05 May 2010 00:52

In reply to Jamin Turner, both of whose crossposts were removed when I deleted one (go figure):

After a regression, [VARS] 5:Statistics… EQ [2:a|3:b] will let you reuse the slope and intercept as you see "fit."