Curve Fit, Correlation, and Computer Software

[Soaring Crane]

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?

Thank you for your time.

 

[EnumaElish]

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

 

[Soaring Crane]

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]

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.