 Regression slope

In a simple linear regression with conditional mean $\mathbb{E}[Y\mid X=x]=\alpha +\beta x$, the slope $\beta$ is the change in that mean per unit increase in the predictor. The ordinary least squares estimate is $\hat{\beta }=S_{xy}/S_{xx}$ when $S_{xx}>0$. It describes a statistical association; a causal interpretation requires further assumptions.