research methods advanced- week 4 = multiple regression

multiple regression

simple linear regression

predictor variable 1 is associated with the outcome variable. (how does y outcome change in relation to a change in x predictor)

multiple regression

a linear regression with added predictor variables. allows exploration of impact of numerous variables on one outcome. test relationships in parallel in context of other predictor

what does a regression do

focuses on relationships between predictor variables and one outcome variable.

criteria of a multiple regression

predictors can be continuous, ordinal or binary data, outcome must be continous. one hypothesis per predictor

forced entry multiple regression

forced entry, dont state particular order for variables to be entered, all variables forced into model simultaneously and known as the ENTER METHOD

hierarchal regression

researcher decides the order predictors are entered into the model, enter known ones first then new ones.

stepwise

order the variables are imputed are based on maths than previous theory. both forward and backward methods. computer programme selects predictor that best predicts the outcome and enters that into model first

parts of a regression

regression line (model/line of best fit), identify how well the model represnts the data (significant/ access this using anova), how much variance is accounted for by the model (effect size r2 value), examine relationship between predictor and outcome (intercepts, betas (standardised and unstandardised, how does y change in relation to change in x )

summary of regression

its an extension of a simple linear regression. there are diffeent tupes of regression. key statistics sucg as model fit statistics and interceots and slopes play a role in multiple regression

assumptions of multiple regression

1.sample size

2.variable types

3.non-zero variance

4.independence

5.linearity

6.lack of multicollinearity

7.homoscedacity

8.independent errors

9.normally distributed errors

variable type assumptions

predictor variables should be quantitative and can be ordinal, categorial or continuous , but the outcome variable must be continuous.

non zero variance assumption

predicor variables should not have a variance eg, should not have a variance of 0

independence

all values of the outcome variable should be independent, each value of the outcome variable should be a separate entity

linearity

assume that the relationship between the predictor and outcome variables will be linear and if the analysis is run on non linear relationships the model can be unreliable

sample size assumptions

for every one predictor we need 10 participants, but more is better. FIELD 2010 suggested 2 equations to identify an appropriate size. or you can use a power analysis

multicollinearity assumption

collinearity statistics variance inflation factor (VIF) if the average VIF is substantially greater than 1 then regression may be biased. if its greater than 10 there is definitely a problem

and tolerance, if tolerance is below 0.1 theres a serious problem, if tolerance is below 0.2 a potential problem

homoscedacity assumption

at each level of the predictor variablem variance of the residuals should be constant. if the variance of residuals are difference we have heteroscedacity not HOMOSCEDACITY

normally distributed errors

the residual values in the regression model are random and normally distributed with a mean of 0, there is an even chance of points lying above and below the best-fit line

what to check upfront

sample size, variable types, non-zero variance, independence

checking statistical assumptions

linearity, homoscedacity, normally distributed errors (analyse residuals), multicollinearity (VIF and tollerance), independent erriors (check durbin watson between 1-3)

how to report a regression

-descriptive statistics, means standard deviations and correlations

-details of the model

-is the model significant

-details of the relationship between individual predictors and outcome variables

unstandardised and standardised betas

standardised betas are standardised to provide comparable values, unstandardised betas reflect the measurement units of the scale