Revision sheet

The regression model

$\hat{y} = a + bx$ estimates $\mu_y = \beta_0 + \beta_1 x$. Conditions: LINER.

Watch out: no condition on the size of $r$.

t for the slope

$t = b/SE_b$, df $= n - 2$.

Watch out: divide by $SE_b$; two parameters, so $n - 2$.

Interval for β₁

$b \pm t^* SE_b$ (df $n - 2$); 0 outside → evidence of a relationship.

Watch out: association, not causation.

Testing the slope

H₀: β₁ = 0; $t = b/SE_b$, df $= n - 2$.

Watch out: a significant slope is not proof of causation.