## Regression Analysis

Regression analysis is performed using the following functions in MathStudio.

## Linear (a*x+b)

LinearFit([1, 4, 9, 5, 7, 5, 4, 2, 9], [3, 4, 5, 7, 8, 10, 4, 7, 6])
LinearFitModel([1, 4, 9, 5, 7, 5, 4, 2, 9], [3, 4, 5, 7, 8, 10, 4, 7, 6])
LinearFitPlot([1, 4, 9, 5, 7, 5, 4, 2, 9], [3, 4, 5, 7, 8, 10, 4, 7, 6])

## Median-Median (a*x+b)

MedianFit([1, 4, 9, 5, 7, 5, 4, 2, 9], [3, 4, 5, 7, 8, 10, 4, 7, 6])
MedianFitModel([1, 4, 9, 5, 7, 5, 4, 2, 9], [3, 4, 5, 7, 8, 10, 4, 7, 6])
MedianFitPlot([1, 4, 9, 5, 7, 5, 4, 2, 9], [3, 4, 5, 7, 8, 10, 4, 7, 6])

QuadraticFit([7, 5, 8, 10, 13], [15, 19, 14, 18, 25])
QuadraticFitModel([7, 5, 8, 10, 13], [15, 19, 14, 18, 25])
QuadraticFitPlot([7, 5, 8, 10, 13], [15, 19, 14, 18, 25])

## Cubic (a*x^3+b*x^2+c*x+d)

CubicFit([80, 84, 86, 91, 93, 96], [10, 7, 9, 18, 19, 15])
CubicFitModel([80, 84, 86, 91, 93, 96], [10, 7, 9, 18, 19, 15])
CubicFitPlot([80, 84, 86, 91, 93, 96], [10, 7, 9, 18, 19, 15])

## Quartic (a*x^4+b*x^3+c*x^2+d*x+e)

QuarticFit([80, 84, 86, 91, 93, 96], [10, 7, 9, 18, 19, 15])
QuarticFitModel([80, 84, 86, 91, 93, 96], [10, 7, 9, 18, 19, 15])
QuarticFitPlot([80, 84, 86, 91, 93, 96], [10, 7, 9, 18, 19, 15])

## Exp (a*exp(b*x))

ExpFit([0, 5, 10, 15, 20, 30, 40], [140, 129, 119, 112, 105, 95, 87])
ExpFitModel([0, 5, 10, 15, 20, 30, 40], [140, 129, 119, 112, 105, 95, 87])
ExpFitPlot([0, 5, 10, 15, 20, 30, 40], [140, 129, 119, 112, 105, 95, 87])

## Exponential (a*b^x)

ExponentialFit([0, 5, 10, 15, 20, 30, 40], [140, 129, 119, 112, 105, 95, 87])
ExponentialFitModel([0, 5, 10, 15, 20, 30, 40], [140, 129, 119, 112, 105, 95, 87])
ExponentialFitPlot([0, 5, 10, 15, 20, 30, 40], [140, 129, 119, 112, 105, 95, 87])

## Power (a*x^b)

PowerFit([1.3, 2.5, 2.9, 4.321, 5.35], [2.015, 11.15, 16.55, 36.65, 65.725])
PowerFitModel([1.3, 2.5, 2.9, 4.321, 5.35], [2.015, 11.15, 16.55, 36.65, 65.725])
PowerFitPlot([1.3, 2.5, 2.9, 4.321, 5.35], [2.015, 11.15, 16.55, 36.65, 65.725])

## Logarithmic (a+b*ln(x))

LnFit([1.3, 2.5, 2.9, 4.321, 5.35], [2.015, 11.15, 16.55, 36.65, 65.725])
LnFitModel([1.3, 2.5, 2.9, 4.321, 5.35], [2.015, 11.15, 16.55, 36.65, 65.725])
LnFitPlot([1.3, 2.5, 2.9, 4.321, 5.35], [2.015, 11.15, 16.55, 36.65, 65.725])

## Logistic (c/(1+a*exp(-b*x))

LogisticFit([3, 5, 8, 10], [7, 8, 14, 18])
LogisticFitModel([3, 5, 8, 10], [7, 8, 14, 18])
LogisticFitPlot([3, 5, 8, 10], [7, 8, 14, 18])

## Sinusoidal (a*sin(b*x+c)+d)

SinFit([21, 24, 34, 46, 58, 67, 72, 70, 61, 50, 40, 27])
SinFitModel([21, 24, 34, 46, 58, 67, 72, 70, 61, 50, 40, 27])
SinFitPlot([21, 24, 34, 46, 58, 67, 72, 70, 61, 50, 40, 27])

## Curve Fitting

FindFit(a*x^2+b*x+c, x, [7, 5, 8, 10, 13], [15, 19, 14, 18, 25])
FindFitModel(a*x^2+b*x+c, x, [7, 5, 8, 10, 13], [15, 19, 14, 18, 25])
FindFitPlot(a*x^2+b*x+c, x, [7, 5, 8, 10, 13], [15, 19, 14, 18, 25])

## References

http://en.wikipedia.org/wiki/Regression_analysis

## Related Functions

ExpFitModel, ExpFitPlot, ExponentialFit, ExponentialFitModel, ExponentialFitPlot, FindFit, FindFitModel, FindFitPlot, LinearFit, LinearFitModel, LinearFitPlot, LnFit, LnFitModel, LnFitPlot, LogisticFit, LogisticFitModel, LogisticFitPlot, MedianFit, MedianFitModel, MedianFitPlot, PowerFit, PowerFitModel, PowerFitPlot, QuadraticFit, QuadraticFitModel, QuadraticFitPlot, QuarticFit, QuarticFitModel, QuarticFitPlot, SinFit, SinFitModel, SinFitPlot, ExpFit