Linear and logistic regression

Question 1

What is regression

Answer 1

It is a statistical method for estimating the numerical relationship between one dependent variable and one or more independent variables

It can be r used to address a wide variety of research questions involving a dependency relationship between one or more variable

Question 2

What are dependent or independent variables

Answer 2

Variables

Independent (predictors/ control)

Dependent (outcomes/ measure)

Question 3

Regression models

Answer 3

The type of model is determined by the dependent variable and the research question

Most common types
- linear regression
- logistics regression

Others
- Cox regression
- ordered logistic regression
- multinominal regression
- poison regression

Question 4

Data types

Answer 4

Can be broadly categories into two groups

1. categorical (qualitative)
   - nominal
   - binary
   - ordinal
2. Numeric
   - discrete
   - continuous

Question 5

What is linear regression

Answer 5

It summarises the observed data by using a line equation that best fit the data to describe the dependency relationship between the dependent (y) and independent variable (x)

Interpretation
- when linear regression models are presented in publications, the statistic usually quoted is the beta coefficient

The beta coefficient measures the increase/ decrease in the dependent variable for each unit increase in the independent variable.

Question 6

Assumptions of linear regression

Answer 6

• independence (the observations are independent)
• linearity (the relationship between (y) and (x) is linear)
• normality (the residuals are normally distributed)
• homoscedasticity (the residuals have constant variance)

Question 7

What are residuals

Answer 7

They are the difference between the predicated value obtained from the model and observed value of the dependent variable.

A good model will have small residuals

Question 8

Multi variable regression

Answer 8

Sometimes we are interested in including more than one predictors variable in the same regression model.

This is usually done because we want to control for the fact that sometimes a variable it’s related to both the exposure and the outcomes of interest (‘cofounder’)

Question 9

What is logistic regression

Answer 9

Logistic regression is used when the outcome is binary (I.e disease/ disease free)

^ we want our regression model to estimate the probability p of the outcomes occurring (I.e the probability of having disease X)

Odds ratio is usually reported instead of beta coefficient