Hypothesis Testing For Regression Slope

The alternative hypothesis in testing the slope might state $H_a: \beta \neq 0$ or $H_a: \beta > 0$, depending on the test.

Assumptions such as linearity, independence, and normally distributed residuals must be satisfied for the t-test on $\beta$ to be valid.

A very low p-value indicates that the observed sample result is highly unlikely if $H_0$ were true.

Under the null hypothesis $H_0: \beta = 0$, the t-statistic is computed with df = $n-1$.