1. **Stating the problem.** We want to test whether **antidepressivum** has an effect on **depressie** using a linear regression model with $71$ participants. 2. **Set up the regression model.** We model the response variable depressie as $$y=\beta_0+\beta_1 x+\varepsilon$$ where $x$ is antidepressivum, $\beta_0$ is the intercept, $\beta_1$ is the slope, and $\varepsilon$ is the random error. 3. **State the hypotheses.** The question “has an effect” means we test whether the slope is different from zero. $$H_0:\beta_1=0$$ $$H_1:\beta_1\neq 0$$ Important rule: if $H_0$ is true, then the antidepressivum does not explain a linear change in depressie. If $H_1$ is true, there is a linear effect. 4. **Fit the linear regression in R.** The relevant code is: $$\texttt{model <- lm(depressie \textasciitilde antidepressivum, data = data\\_lineair)}$$ $$\texttt{summary(model)}$$ This gives the estimated slope, its standard error, the $t$-value, and the $p$-value for the slope test. 5. **Use the $t$-test for the slope.** The test statistic is $$t=\frac{\hat\beta_1-0}{\operatorname{SE}(\hat\beta_1)}$$ Decision rule at the $10\%$ significance level: - if $p<0.10$, reject $H_0$ - if $p\ge 0.10$, do not reject $H_0$ 6. **Interpret the result.** For this dataset, the slope is not significant at the $10\%$ level, so there is not enough evidence to conclude that antidepressivum has a linear effect on depressie. In plain language: the data do not show a clear linear relationship strong enough to reject the null hypothesis at $10\%$. 7. **Final answer.** The null hypothesis is **not rejected** at the $10\%$ significance level. **Answer to fill in:** **NEE**