Week 1 - from association to modelling causlity

Question 1

what are the benefits of regression

Answer 1

• allows you to test hypotheses using the null hypothesis significance testing framework as each model gives associated p value
• flexibility
• can model secondary variables with ease (extraneous/nuisance)
  *no need for post-hoc testing
• has higher statistical power
• generates predictions
• easily extends into other types of forms
• potential to mix categorical type variables with continuous variables

Question 2

what is correlation to simple regression

Answer 2

• is a decision to make one of the variables predict the other variables
• now talking about predictor and outcome variables
• line of best fit is now a regression line

Question 3

what are the parts of a regression line

Answer 3

• has an intercept - average in the outcome variable
• slope - line of best fit
• m = beta weights or coefficients
• slope tells you the rate of change in y for a one unit change in x
• simple regression is very similar to correlation when in venn diagram form

Question 4

what is the equation for the regression line

Answer 4

y = b0 + b1 * x1 + e
* outcome variable
* intercept
* beta coefficient
(slope term)
* predictor variable
* residual error

Question 5

what are the predictions from simple regression

Answer 5

y = b0 + b1 * x1
* predictions from either values in data set, observed values or values not in sample

Question 6

what are the assumptions of simple regression

Answer 6

• linearity
• independence of observations
• homoscedasticity of residuals
• normally distributed residuals

Question 7

how do you interpret the output of simple regression

Answer 7

• intercept term - average when all continuous predictors are at 0 or categorical predictors are at their reference level
• continuous coefficients - one unit increase in X gives a change in Y by the amount of B
• categorical coefficients - change to another level or group within X gives a change in Y by the amount of B

Question 8

what is multiple regression

Answer 8

• more predictor variables
• still one intercept
• still one error term
• can still have predictors that show no or weak relationship
  *

Question 9

what is the equation for multiple regression

Answer 9

Y = b0 * x1 + b2 * X2 + e