Formulas to remember for final

Study guide for formulas for the final exam for BIOS 600, section 602/002, spring 2026.

There will be no formula sheet for the final–there are a small number of formulas you need to memorize for the final:

  1. Logit function: \[ logit(p) = log(\frac{p}{1-p}) \] Typically \(p\) is a probability.

  2. Linear regression model (multiple regression with \(p\) predictors):

\[ Y_i = \beta_0 + \beta_1x_{i1} + \beta_2x_{i2}+ ... + \beta_px_{ip} + \epsilon_i,\\ \epsilon_i \sim N(0, \sigma^2)\]

  1. Logistic regression model (with \(p\) predictors):

\[ Y_i \sim Ber(p_i), \\logit(p_i)=\beta_0 + \beta_1x_{i1} + \beta_2x_{i2}+ ... + \beta_px_{ip}\]

  1. Interpreting an interaction term

For the model \[ Y_i = \beta_0 + \beta_1x_{i1} + \beta_2x_{i2} + \beta_3(x_{i1}\cdot x_{i3}) + \epsilon_i,\\ \epsilon_i \sim N(0, \sigma^2)\]

Suppose you estimate the parameters of the model to get the estimates, \(\hat{\beta_1}, \hat{\beta_3}\) (and the other \(\hat{\beta}\)’s). Then the expected change in \(Y\) when increasing \(x_{1}\) by 1 unit is equal to \(\hat{\beta_1} + \hat{\beta_3}x_{3}\).