Calculate the slope coefficient of a simple linear regression and test it.
The slope is the covariance divided by the variance of the predictor. Dividing it by its standard error gives a t statistic, and values beyond about two indicate a coefficient distinguishable from zero. A large coefficient with a large standard error tells you nothing, which is why the t statistic rather than the coefficient governs interpretation.
Regression Coefficient
β = covariance(x, y) ÷ variance(x); t = β ÷ standard error of β
β = covariance(x, y) ÷ variance(x); t = β ÷ standard error of β The slope is the covariance divided by the variance of the predictor. Dividing it by its standard error gives a t statistic, and values beyond about two indicate a coefficient distinguishable from zero.
A large coefficient with a large standard error tells you nothing, which is why the t statistic rather than the coefficient governs interpretation.
This calculator takes 4 inputs: Covariance of x and y, Variance of x, Standard error of the slope, Sample size. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.