Research Methods- Multiple regression
how to analyse
- analyse - regression - linear - DV- survival - IV- social, optimism - Method: enter - gives standard multiple regression ==regression stats= regression coefficients, estimates, model fit, descriptives, collinearity diagnosis
checklist for interpreting MR output
- check ANOVA table- is F sig - check r-squared- how much variance have you explained - check coefficients- which variables = sig - To calculate the regression equation, write down the variables, look at the B (unstandardised) values of each + that of the intercept. - To put the variables into order of importance, look at the Beta (standardised) values, as these will tell you the relative importance of each variable.
3 steps to regression analysis
- examine the relationship between the predictor and response variables separately - perform and interpret the multiple regression - assess the appropriateness of regression analysis
regression
- extension of correlation - allows you to make predictions about one variable from other variables - Linear regression produces same result as correlation ( 1IV 1DV) - Multiple regression goes one step further than correlation (1+IV 1DV)
assumptions that need to be met during regression
- sample size- equal or greater than 8 X the number of explanatory variables. Stevens (1996) says 15 per predictor variable - criterion variable drawn from normally distributed population - variables should be linearly related to criterion variable - outliers (scatterplots) - multi-collinearity (explanatory variables correlating highly with each other, 8 and above.
what can be used to see which predictor variable contributes most o the response variable
in coefficients use standardised regression coefficient
example study
A health psychologist is interested in a theory which suggests that a person's level of optimism (X1) and the social support (X2) that they have in their life predicts how long they will survive (Y) after being diagnosed with cancer.
example MR results
A multiple regression was run to try and predict the variability in spelling performance (M=59.77; SD 23.93) using chronological age (93.40; SD= 7.49), reading age (M=89.02; SD=21.36), standardised reading score (M=95.57; SD= 17.78) and standardised spelling score (M=107.09; SD= 14.99) The assumptions relating to multicollinearity were met. Together the predictor variables explained 83.8% (Adjusted R2 = .838) of the variability in spelling performance. The overall association between the predictor variables and spelling performance was significant, F (4,46) = 60.42, p <.001. Three of the predictor variables, Chronological age (b=1.30; p< 0.001); standardised reading score (b=0.53; p=.002) and standardised spelling score (b=1.25, p<0.001) displayed a significant and positive association with Spelling performance
to write up
F(df reg, df total) = F value, p < significance level
How to find out the estm=imated population that survived due to the two IV's
model summary- R Squared adjusted- then turn to a percentage e.g. 0.401= 40.1%
how to write regression equation up
optimism= coefficients- t= LOT score for t, p < sig value social support- coefficients- t= SS score, p < sig value
correlation
strength/direction between two variables
purpose of multiple regression
to predict Y given combination of predictor variables - to assess the relative importance of each predictor variable in explaining the response
