This is from my textbook:
it says that ...an ordinary residual divided by an estimate of its standard deviation $s(e_{i})$
As we can see from the example that mean for four residuals is 0, so $s(e_{i})=\sqrt{\frac{(-0.2-0)^2+(0.6-0)^2+(-0.6)^2+(0.2-0)^2}{4-1}}=\sqrt{\frac{0.8}{3}}\neq\sqrt{0.4(1-0.7)}$
where did I get it wrong?
The studentized residuals are
$$t_i=\frac{\epsilon_i}{\hat\sigma\sqrt{1-h_{ii}}}$$
Where $\epsilon_i$ is the residual, $h_{ii}$ the leverage and $\hat\sigma$ is the estimate of the standard deviation of residuals, that is
$$\hat\sigma^2=\frac1{n-m}\sum_{i=1}^n\epsilon_i^2$$
Where $n$ is the number of observations (here $4$) and $m$ the number of estimated parameters (here $2$). The sum of square residuals is $0.8$, hence $\hat\sigma^2=\frac12\times0.8$, and
$$t_i=\frac{-0.2}{\sqrt{0.4\times(1-0.7)}}$$
See also studentized residuals on Wikipedia and this question on Cross Validated.