# Logistic Regression, Probability, and Odds Flashcards

What is regression?

Mathematical equation for straight line that is fitted to data as way of describing relationship between two or more variables.

What are the main purposes of regression?

Prediction (to estimate risk).

Control for confounding.

What does the regression line do?

Estimates average values for variable on vertical scale (Y) according to values on horizontal scale (X).

What happens in simple regression?

For each change in X, there is a change in Y.

What is general linear regression?

Refers to conventional linear regression models for a continuous response variable given continuous and/or categorical predictors.

What happens with transformation in a GLM?

Without transformation, the coefficient will estimate rate differences.

With transformation, the coefficient will estimate rate ratios.

What is the model for simple regression?

Yx=(D | X=x)= α+βx

Y = α + βX + ε (prediction)

Yi = BO + B1Xi + Ei (population)

What is a?

Measure when x = 0

Also B0

The y-intercept

What does slope coefficient do?

Estimate increase in risk per unit increase in X.

B1

How are mean and probability related?

Mean is estimate of probability.

Why will linear regression not work?

Probability is scale of 0-1 and regression is not within those constraints.

Linear model assumes risk changed linearly.

Why will logistic regression work?

Used for binary outcomes and on 0-1 scale showing odds.

This is because the probability curve becomes linear after taking natural log of a value.

What is the model form of logistic regression?

Logit (Y) = ln (Y/(1-Y))

OR

Logit [P (Y)] = ln ((P(Y))/(1-P(Y)))

OR

ln (Px/1-Px) = ln (D|X=x) = a +Bx

What is alpha?

Log odds of outcome when X = 0

The y-intercept.

What is beta?

Slope

Log odds RATIO comparing two exposure groups differing by one unit on scale of x.