Regressions Flashcards
Pearson’s Correlation
- Something that can be used t measure an effect size
- Varies between -1-1
- A correlation coefficient of zero indicates there is no relationship between the variables
Correlation = .12, p=<.01
What is the relationship between the two variables
Small, but significant
Pearson’s Correlation of -.1 is
Mildly good fit
Pearson’s Correlation of .5
Moderately good fit
Pearson’s Correlation of .8
Strong good fit
If r=.67 then the variables…
share variance
Coefficient of Determination
Measure of the amount of variability in one variable that is shared by the other
Pearson’s Correlation of -.71, n=300
Strong negative relationship
if r=.21 then the effect is
small to medium
Multicollinearity
When predictor variables correlate very highly with each other
T-Statistics are not:
equal to the regression coefficient divided by its standard deviation
Multiple Regression Assumptions
- Continuous outcome variable, and continuous or dichotomous predictor variables
- Independence
- Non-zero variance:
- No Outliers
- No Perfect or High Multicollinearity
- Homoscedasticity
- Linearity
- Normally Distributed Errors
- Independent Errors (Residuals)
Independence (MR Assumption)
All values of the outcome variable should come from a different participant
Non-Zero Variance (MR Assumption)
The predictors should have some variation in value, e.g. variances ≠ 0
No Outliers (MR Assumption)
- No data points outside 3 SD’s from the mean
- Generally 1% outliers ok
No Perfect or High Multicollinearity (MR Assumption)
Predictor variables should not have multicollinearity
Homoscedasticity (MR Assumption)
Variance of residuals should be similar across of the scores on the continuum
Heteroscedasticity (MR Assumption)
Variance of residuals (errors) differs across the variable continuum
Linearity (MR Assumption)
There exists a linear relationship between the predictor variables and the outcome variable and the predictor variables combine additively
Normally Distributed Errors (MR Assumption)
Residuals follow bell curve
Independent Errors (MR Assumption)
The errors between pairs of observations should not be correlated, e.g. if observations are made over time it is likely that successive observations would be correlated
Tested with Durbin-Watson Test
Needs to be between 1.5-2.5
Pearson’s R
Standardized version of covariance
Cannot be used to determine causation
Regression
Predicting variable y (outcome) from variable x (variable)
