## 35.7 Confidence intervals

Reporting the CI for the slope is also useful, which can be obtained from software or computed manually.

Think 35.4 (Approximate 95% CI) Using the output (jamovi: Fig. 35.7; SPSS: Fig. 35.8), what is the approximate 95% CI for $$\beta_1$$?

CIs have the form $\text{statistic} \pm ( \text{multiplier} \times \text{standard error}),$ The multiplier is two for an approximate 95% CI, so (using the standard error reported by the software), we obtain $$-0.181 \pm (2\times 0.029)$$, or $$-0.181 \pm 0.058$$, or from $$-0.239$$ to $$-0.123$$.

Software can be asked to produce exact CIs too (jamovi: Fig. 35.9; SPSS: Fig. 35.10). The approximate and exact 95% CIs are very similar.

We write:

The sample presents very strong evidence ($$P < 0.001$$; $$t = -6.275$$) of a relationship between age and the weight of molars in male red deer (slope: $$-0.181$$; $$n= 78$$; 95% CI from $$-0.239$$ to $$-0.124$$) in the population.