# Linear models and difference from baseline $$ y_{post} - y_{pre} \sim N(d, \sigma) \\ H_0: d = 0 $$ An equivalent model $$ y_{post} \sim N(d + y_{pre}, \sigma) \\ $$ gen: $$ y_{post} \sim N(d + \beta y_{pre}, \sigma) $$ ``` lm(post ~ 1 + pre) ``` ``` lm(post ~ 1 + pre + displacement) ```