Editing Logistic regression (section)

===The odds ratio===
For a continuous independent variable the odds ratio can be defined as:

:[[File:Odds Ratio-1.jpg|thumb|The image represents an outline of what an odds ratio looks like in writing, through a template in addition to the test score example in the "Example" section of the contents. In simple terms, if we hypothetically get an odds ratio of 2 to 1, we can say... "For every one-unit increase in hours studied, the odds of passing (group 1) or failing (group 0) are (expectedly) 2 to 1 (Denis, 2019).]]<math> \mathrm{OR} = \frac{\operatorname{odds}(x+1)}{\operatorname{odds}(x)} = \frac{\left(\frac{p(x+1)}{1 - p(x+1)}\right)}{\left(\frac{p(x)}{1 - p(x)}\right)}
                                        = \frac{e^{\beta_0 + \beta_1 (x+1)}}{e^{\beta_0 + \beta_1 x}} = e^{\beta_1}</math>

This exponential relationship provides an interpretation for <math>\beta_1</math>: The odds multiply by <math>e^{\beta_1}</math> for every 1-unit increase in x.<ref>{{cite web|url=https://stats.idre.ucla.edu/stata/faq/how-do-i-interpret-odds-ratios-in-logistic-regression/|title=How to Interpret Odds Ratio in Logistic Regression?|publisher=Institute for Digital Research and Education}}</ref>

For a binary independent variable the odds ratio is defined as <math>\frac{ad}{bc}</math> where ''a'', ''b'', ''c'' and ''d'' are cells in a 2×2 [[contingency table]].<ref>{{cite book | last = Everitt | first = Brian | title = The Cambridge Dictionary of Statistics | publisher = Cambridge University Press | location = Cambridge, UK New York | year = 1998 | isbn = 978-0-521-59346-5 | url-access = registration | url = https://archive.org/details/cambridgediction00ever_0 }}</ref>