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2 changes: 1 addition & 1 deletion 02-sim_pop.Rmd
Original file line number Diff line number Diff line change
Expand Up @@ -33,7 +33,7 @@ $$
y_i = \beta_0 + \beta_1 x_{1i} + \beta_2 x_{2i} + \beta_3 x_{3i} + \epsilon_i
$$

, where each observation (denoted by the index $i$) of our response variable ($y_i$) is the sum of an intercept ($\beta_0$; value of the response when the predictor variables are all 0), the associated value of our predictor variables ($x_{1i}$, $x_{2i}$, $x_{3i}$; which also vary at the level of the observation), each with a certain magnitude and direction of their effect (effect size or slope; $\beta_1$ etc), and some unexplained, residual variation ($\epsilon_i$).
where each observation (denoted by the index $i$) of our response variable ($y_i$) is the sum of an intercept ($\beta_0$; value of the response when the predictor variables are all 0), the associated value of our predictor variables ($x_{1i}$, $x_{2i}$, $x_{3i}$; which also vary at the level of the observation), each with a certain magnitude and direction of their effect (effect size or slope; $\beta_1$ etc), and some unexplained, residual variation ($\epsilon_i$).

We can write this in more compact notation,
$$
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