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### REGRESS

REGRESS

The REGRESS function performs a multiple linear regression fit and returns an Nterm-element column vector of coefficients.

REGRESS fits the function:

yi = const + a0x0, i + a1x1, i + ... + aNterms-1xNterms-1, i

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

## Examples

`; Create two vectors of independent variable data:X1 = [1.0, 2.0, 4.0, 8.0, 16.0, 32.0]X2 = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0]; Combine into a 2x6 arrayX = [TRANSPOSE(X1), TRANSPOSE(X2)]; Create a vector of dependent variable data:Y = 5 + 3*X1 - 4*X2; Assume Gaussian measurement errors for each point:measure_errors = REPLICATE(0.5, N_ELEMENTS(Y)); Compute the fit, and print the results:result = REGRESS(X, Y, SIGMA=sigma, CONST=const, \$   MEASURE_ERRORS=measure_errors)PRINT, 'Constant: ', constPRINT, 'Coefficients: ', result[*]PRINT, 'Standard errors: ', sigma`

IDL prints:

`Constant:    4.99999`
`Coefficients:    3.00000    -3.99999`
`Standard errors:    0.0444831    0.282038`

## Syntax

Result = REGRESS( X, Y, [, CHISQ=variable] [, CONST=variable] [, CORRELATION=variable] [, /DOUBLE] [, FTEST=variable] [, MCORRELATION=variable] [, MEASURE_ERRORS=vector] [, SIGMA=variable] [, STATUS=variable] [, YFIT=variable] )

## Return Value

REGRESS returns a 1 x Nterm array of coefficients. If the DOUBLE keyword is set, or if X or Y are double-precision, then the result will be double precision, otherwise the result will be single precision.

## Arguments

### X

An Nterms by Npoints array of independent variable data, where Nterms is the number of coefficients (independent variables) and Npoints is the number of samples.

### Y

An Npoints-element vector of dependent variable points.

## Keywords

### CHISQ

Set this keyword equal to a named variable that will contain the value of the unreduced chi-square goodness-of-fit statistic.

### CONST

Set this keyword to a named variable that will contain the constant term of the fit.

### CORRELATION

Set this keyword to a named variable that will contain the vector of linear correlation coefficients.

### DOUBLE

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

### FTEST

Set this keyword to a named variable that will contain the F-value for the goodness-of-fit test.

### MCORRELATION

Set this keyword to a named variable that will contain the multiple linear correlation coefficient.

### MEASURE_ERRORS

Set this keyword to a vector containing standard measurement errors for each point Y[i]. This vector must be the same length as X and Y.

Note: For Gaussian errors (e.g., instrumental uncertainties), MEASURE_ERRORS should be set to the standard deviations of each point in Y. For Poisson or statistical weighting, MEASURE_ERRORS should be set to SQRT(Y).

### SIGMA

Set this keyword to a named variable that will contain the 1-sigma uncertainty estimates for the returned parameters.

Note: If MEASURE_ERRORS is omitted, then you are assuming that the regression model is the correct model for your data, and therefore, no independent goodness-of-fit test is possible. In this case, the values returned in SIGMA are multiplied by SQRT(CHISQ/(NM)), where N is the number of points in X, and M is the number of coefficients. See section 15.2 of Numerical Recipes in C (Second Edition) for details.

### STATUS

Set this keyword to a named variable that will contain the status of the operation. Possible status values are:

• 0 = successful completion
• 1 = singular array (which indicates that the inversion is invalid)
• 2 = warning that a small pivot element was used and that significant accuracy was probably lost.

Note: If STATUS is not specified, any error messages will be output to the screen.

### YFIT

Set this keyword to a named variable that will contain the vector of calculated Y values.

## Version History

 Original Introduced 5.4 Deprecated the Weights, Yfit, Const, Sigma, Ftest, R, Rmul, Chisq, and Status arguments, RELATIVE_WEIGHT keyword.