# Curve Fit, Correlation, and Computer Software

## Main Question or Discussion Point

A computer program, MicroLab, deals with finding the best fit curve, or allowing for linear regression of the first, second, and third orders, of a given set of data (particularly modeling nonlinear data).

I am trying to stimulate this analysis on a graphing calculator (i.e., TI-83 Plus and TI-84 Silver Edition) used in some statistics courses. However, I am confused about how to define the second and third orders before executing the command to find the regression line’s equation/correlation. For the second (quadratic) order curve fit choice, do I plot the original y-values versus the square of the x-values? Based on the same concept, do I plot the original y-values versus x-values cubed for the third (cubic) order curve fit choice?

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EnumaElish
Homework Helper
Yep; a third-order regression line would be y = b0 + b1x + b2x2 + b3x3 + u.

Really? Um, could you explain that long part there for me, pretty please? I'm sure it's not that overwhelming once one understands a few principles, but I got lost in the variables . . .

Thanks again!

EnumaElish
Homework Helper
Suppose you have a general 2nd-order polynomial:

y - y0 = a1(x - x0) + a2(x - x0)2

or

y = y0 + a1x - a1x0 + a2x2 + a2x02 - 2a2x02x

Re-write it as:

y = b0 + b1x + b2x2

where
b0 = y0 - a1x0 + a2x02 = sum of the constant terms
b1 = a1 - 2a2x02 = sum of the coefficients of x
b2 = a2 = coefficient of x2

You can generalize this to an arbitrary order.