## LINFIT

The LINFIT function fits the paired data { xi , yi } to the linear model, y = A + Bx, by minimizing the Chi-square error statistic. The result is a two-element vector containing the model parameters [A, B].

This routine is written in the IDL language. Its source code can be found in the file ``` linfit.pro``` in the ``` lib``` subdirectory of the IDL distribution.

### Calling Sequence

Result = LINFIT( X, Y )

### Arguments

#### X

An n -element integer, single-, or double-precision floating-point vector.

#### Y

An n -element integer, single-, or double-precision floating-point vector.

### Keywords

#### CHISQ

Set this keyword to a named variable that will contain the Chi-square error statistic as the sum of squared errors between yi and A + B xi . If individual standard deviations are supplied, then the Chi-square error statistic is computed as the sum of squared errors divided by the standard deviations.

#### DOUBLE

Set this keyword to force the computation to be done in double-precision arithmetic.

#### PROB

Set this keyword to a named variable that will contain the probability that the computed fit would have a value of CHISQ or greater. If PROB is greater than 0.1, the model parameters are "believable". If PROB is less than 0.1, the accuracy of the model parameters is questionable.

#### SDEV

An n -element integer, single-, or double-precision floating-point vector that specifies the individual standard deviations for { xi , yi } used for weighting, where the weight is defined as 1/SDEV 2 . If SDEV is not set, no weighting is used.

#### SIGMA

Set this keyword to a named variable that will contain a two-element vector of probable uncertainties for the model parameters.

### Example

Define two n -element vectors of paired data.

X = [-3.20, 4.49, -1.66, 0.64, -2.43, -0.89, -0.12, 1.41, \$

2.95, 2.18, 3.72, 5.26]

Y = [-7.14, -1.30, -4.26, -1.90, -6.19, -3.98, -2.87, -1.66, \$

-0.78, -2.61, 0.31, 1.74]

Define an n -element vector of standard deviations with a constant value of 0.85

sdev = REPLICATE(0.85, N_ELEMENTS(X))

Compute the model parameters, A and B.

PRINT, LINFIT(X, Y, SDEV=sdev)

IDL prints:

[-3.44596, 0.867329]