Correlations and Regressions Flashcards
What is a correlation?
- Measure of relation between two variable, often continuous
- Association
- Linear, cant estimate other types of relations
- No causality
- Gives us a bivariate association
What is the coefficent used for correlation?
- Pearson (most commonly used) r
- Values greater than 1.00 is an error
- 0.00 = no relation
- Positive and negative direction
What can the magnitude of r tell us?
- How to infer the association
- .10 small
- .30 moderate
- .50 large
Covariation
How much one variable increase or decrease is dependent on the second variable
- No covariation= r should be zero
Variation
Variation between each variable
Example: variation in depression scores
Correlation - APA style
- r(N-groups)=, p
- Positive or negative association
What are other types of correlations?
- Spearman Rank-Order Correlation
One or both variables are measured on a ordinal scale - Point-biserial Correlation
One continuous and one is dichotomous - Phi-coefficient
Both are dichotomous
What is a partial correlation?
- Looking at an association while controlling some other factors
Example; looking at shyness and social anxiety, controlling for gender
What can a regression analysis give us?
- Being able to make a prediction
Often a predetermine direction on DV - Unique effect of predictors on the outcome variable
Still a linear association
Which predictor is stronger? - A correlation
How do you decide the direction of the prediction?
- Based on theories and/or conceptual arguments
What equation is commonly used with regression analysis?
Y=a + bX + e
- Y = outcome variable
- X = predictor
- a = intercept
- b = the slope, how many points Y changes for one unit change in X
- e = error, refers to variation not explained by X
What is the relation between the slope and explained variance?
“In summary, while both models may have positive correlation coefficients, Model A would likely have a higher coefficient and explain more of the variation in the dependent variable compared to Model B, due to the tighter clustering of data points around the line.”
- A has a stronger linear correlation
What are the types of regressions?
- Simple regression model
- Multiple regression model
Simple Regression
- One predictor
- One outcome variable
Simple Regression - SPSS output
Table 1
- List predictors
Table 2
- R square = what portion of variance that explains outcome
Table 3
- Is the explained variance significant
Table 4
- R first lvl=intercept , level of outcome variable when predictor variable is 0
- R second lvl = slope, relation between predictor and outcome variable
- Beta = relation between outcome and predictor, is it significant? Standardised slope (compared to other studies)
Simple Regression - APA style
- Variance %
- F value
- Beta
Multiple Regression
- 2 or more predictors
- One outcome variable
Continuous variable
Multiple Regression - SPSS output
Table 1
- Descriptives
Table 2
- Correlations
Table 3
- List of all predictors
Table 4
- R square, all predictors
Table 5
- Significant or not?
Table 6
- Beta, unique effect of predictor on outcome
Multiple Regression - APA style
- % variance on outcome
- F value
- Beta, each predictor
- Positive or negative prediction?
What are some assumptions and restrictions with regression models?
Outliers
- Extreme data?
- Distribution of data and histogram; skewness(2 okay) and kurtosis(7 okay)
- Boxplots
Residual outliers
- Is it +/- 3.00? Inspect those over it
- Difference between predicted and observed outcome values
Linearity
- Test to see if the association is linear
- Multicollinearity
What is multicollinearity?
- When the predictor variables are too similar to each other
- Inspecting bivariate associations among predictors
- Raised association gives a biased result
How can you see if there is multicollinearity?
Collinearity diagnostics
- Tolerance, under .25
- VIF Variance Inflation Factor, not above 5
What can we do if the predictors are highly correlated?
- Remove one of the predictors
- Combine the predictors, composite score
What is standardized regression coefficient?
- Beta value
- How big the change in standard deviation of the independent variable to the dependent variable
- Can be bigger than 1, the higher the number the greater the impact
