# RegressionFitProb

## RegressionFitProb(Y, B,I, K*, C*)

Once you've obtained regression coefficients «C» (indexed by «K») by calling the Regression function, this function returns the probability that a fit this poor would occur by chance, given the assumption that the data was generated by a process of the form:

`Y = Sum( C*B, K) + Normal(0, S)`

If this result is very close to zero, it probably indicates that the assumption of linearity is bad. If it is very close to one, then it validates the assumption of linearity.

## Library

Multivariate Distributions library functions (Multivariate Distributions.ana)

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This is not a distribution function - it does not return a sample when evaluated in Sample mode. However, it does complement the multivariate RegressionDist function also included in this library.

## Example

To use, first call the Regression function to obtain the linear coefficients. You also need to estimate the measurement noise using the RegressionNoise function, unless you know it a priori:

`Var E_C := Regression(Y, B, I, K);`

`Var S := RegressionNoise(Y, B, I, K, C);`

`Var PrThisPoor := RegressionFitProb(Y, B, I, K, E_C, S)`

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