naginterfaces.library.correg.linregs_​const

naginterfaces.library.correg.linregs_const(x, y)[source]

linregs_const performs a simple linear regression with dependent variable and independent variable .

For full information please refer to the NAG Library document for g02ca

https://www.nag.com/numeric/nl/nagdoc_27.1/flhtml/g02/g02caf.html

Parameters
xfloat, array-like, shape

must contain , for .

yfloat, array-like, shape

must contain , for .

Returns
resultfloat, ndarray, shape

The following information:

, the mean value of the independent variable, ;

, the mean value of the dependent variable, ;

the standard deviation of the independent variable, ;

the standard deviation of the dependent variable, ;

, the Pearson product-moment correlation between the independent variable and the dependent variable ;

, the regression coefficient;

, the regression constant;

, the standard error of the regression coefficient;

, the standard error of the regression constant;

, the value for the regression coefficient;

, the value for the regression constant;

, the sum of squares attributable to the regression;

, the degrees of freedom attributable to the regression;

, the mean square attributable to the regression;

, the value for the analysis of variance;

, the sum of squares of deviations about the regression;

, the degrees of freedom of deviations about the regression

, the mean square of deviations about the regression;

, the total sum of squares;

DFT, the total degrees of freedom.

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, all values of at least one of and are identical.

Notes

In the NAG Library the traditional C interface for this routine uses a different algorithmic base. Please contact NAG if you have any questions about compatibility.

linregs_const fits a straight line of the form

to the data points

such that

The function calculates the regression coefficient, , the regression constant, (and various other statistical quantities) by minimizing

The input data consist of the pairs of observations

on the independent variable and the dependent variable .

The quantities calculated are:

  1. Means:

  2. Standard deviations:

  3. Pearson product-moment correlation coefficient:

  4. The regression coefficient, , and the regression constant, :

  5. The sum of squares attributable to the regression, , the sum of squares of deviations about the regression, , and the total sum of squares, :

  6. The degrees of freedom attributable to the regression, , the degrees of freedom of deviations about the regression, , and the total degrees of freedom, :

  7. The mean square attributable to the regression, , and the mean square of deviations about the regression, :

  8. The value for the analysis of variance:

  9. The standard error of the regression coefficient, , and the standard error of the regression constant, :

  10. The value for the regression coefficient, , and the value for the regression constant, :

References

Draper, N R and Smith, H, 1985, Applied Regression Analysis, (2nd Edition), Wiley