linregress

linregress is a function in SciPy’s statistics module that performs ordinary least squares linear regression on two 1-D arrays, x and y. It fits a line of the form y = slope * x + intercept to the data and returns several statistics that describe the fit.

Inputs and handling: x and y must be numeric, 1-D, and of equal length with at least two data pairs. Pairs containing NaN values are ignored, effectively performing pairwise deletion. The function assumes a linear relationship between x and y.

Outputs and interpretation: The function returns a LinregressResult, typically accessed as a small, six-element tuple or as named attributes: slope, intercept, rvalue, pvalue, stderr, and intercept_stderr. The slope and intercept define the best-fit line. rvalue is the Pearson correlation coefficient between x and y, reflecting the strength and direction of the linear association. pvalue tests the null hypothesis that the slope is zero (no linear relationship); by default the p-value is two-sided. stderr is the standard error of the slope, and intercept_stderr is the standard error of the intercept, providing uncertainty estimates for the fitted parameters.

Method and limitations: Calculations follow standard simple linear regression formulas. Slope is derived from the covariance of x and y relative to the variance of x; intercept is adjusted to pass through the mean values. The p-value is based on a t-statistic with n−2 degrees of freedom. The function is not robust to outliers and assumes a linear relationship; results should be interpreted within the context of the data.