What happens if you don't use the right points?

[questionposter]

Basically I'm just wondering what happens if you use create a quadratic/cubic/quadic formula from scratch with the equation system substitution with the needed amount of data points but end up using a point that's not actually possible as part of the equation, like let's say I have just x^2, and for my data point I have 1,20 for the x,y substitution. What would I see?

I would do it myself but creating polynomial formulas from scratch takes a long time for me, so I'm just wondering if anyone else has done than and can tell me what happens or what I should look for.

Edited April 26, 2012 by questionposter

[ecoli]

I'm not a mathematician, but I'm assuming the question is universally confusing. Can you clarify? What do you mean by "point is not actually possible by the equation" and " for my data point I have 1,20 for the x,y substitution."?

[Bignose]

like let's say I have just x^2, and for my data point I have 1,20 for the x,y substitution. What would I see?

 

An inequality (I am assuming you meant y = x^2, without an equals sign, you haven't stated any equations). Since the LHS and RHS sides won't be equal, you know that (1,20) isn't a valid solution to the equation. That is what an equation does -- it maps out valid solutions. It really doesn't say diddly about points that aren't solutions except that they aren't solutions.

[questionposter]

An inequality (I am assuming you meant y = x^2, without an equals sign, you haven't stated any equations). Since the LHS and RHS sides won't be equal, you know that (1,20) isn't a valid solution to the equation. That is what an equation does -- it maps out valid solutions. It really doesn't say diddly about points that aren't solutions except that they aren't solutions.

 

But let's just say I have data points maybe mapping out the acceleration of a falling object or how light get's weaker as it get's further from a source, but I end up setting up a system of equations to solve of it like this

 

y=ax^3+bx^2+cx+d

y=ax^3+bx^2+cx+d

y=ax^3+bx^2+cx+d

y=ax^3+bx^2+cx+d

 

and I plug 4 different data points in for x and y to find a,b, c and d, but one data point isn't really possible to have considering the other three points, what would the graph or equation look like?

[Bignose]

But let's just say I have data points maybe mapping out the acceleration of a falling object or how light get's weaker as it get's further from a source, but I end up setting up a system of equations to solve of it like this

 

y=ax^3+bx^2+cx+d

y=ax^3+bx^2+cx+d

y=ax^3+bx^2+cx+d

y=ax^3+bx^2+cx+d

 

and I plug 4 different data points in for x and y to find a,b, c and d, but one data point isn't really possible to have considering the other three points, what would the graph or equation look like?

 

 

This happens all the time when taking experimental data. It requires careful analysis of the data to know how to handle it properly. Sometimes, it is appropriate to just take the curve that fits all the data best. Sometimes it is best to just throw out that point and figure out if you need to take another sample. Sometimes, the data will tell you that the model you picked is wrong. It really depends a lot on the errors expected from your measuring device, and just the random errors that always exist in real data. As you can image, talking about this field is far more lengthy than just a single forum post can handle.

Edited April 29, 2012 by Bignose