# naginterfaces.library.correg.linregs_​noconst¶

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

linregs_noconst performs a simple linear regression with no constant, with dependent variable and independent variable .

For full information please refer to the NAG Library document for g02cb

https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/g02/g02cbf.html

Parameters
xfloat, array-like, shape

must contain , for .

yfloat, array-like, shape

must contain , for .

Returns
resultfloat, ndarray, shape

The following information:

 result[0] ¯x, the mean value of the independent variable, x; result[1] ¯y, the mean value of the dependent variable, y; result[2] sx, the standard deviation of the independent variable, x; result[3] sy, the standard deviation of the dependent variable, y; result[4] r, the Pearson product-moment correlation between the independent variable x and the dependent variable y; result[5] b, the regression coefficient; result[6] the value 0.0; result[7] se(b), the standard error of the regression coefficient; result[8] the value 0.0; result[9] t(b), the t value for the regression coefficient; result[10] the value 0.0; result[11] SSR, the sum of squares attributable to the regression; result[12] DFR, the degrees of freedom attributable to the regression; result[13] MSR, the mean square attributable to the regression; result[14] F, the F value for the analysis of variance; result[15] SSD, the sum of squares of deviations about the regression; result[16] DFD, the degrees of freedom of deviations about the regression; result[17] MSD, the mean square of deviations about the regression; result[18] SST, the total sum of squares; result[19] 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

linregs_noconst fits a straight line of the form

to the data points

such that

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

The input data consists 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, :

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:

10. The value for the regression coefficient:

References

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