Class #15: Regression

1. Regression analysis: drawing a straight line through the scatter plot, mathematically. Regression analysis can be used to predict the relationship between 2 or more variables.

2. Simple Linear Regression:
y = B₀ + B₁ x 

e.g.: Predicting your grade of PSY310 from the frequency of checking this blog. >:)

3. Multiple Regression Analysis: predicting the outcome variable from more than one predictors.
y = B₀ + B₁x +B₂x +B₃x

Three types:
– Standard Multiple Regression: enter in all predictor variables at once; predicting the outcome variable from all other variables together.
– Stepwise Multiple Regression: enter the predictors one at a time based on the ability to predict the outcome; looking at the unique contributions of individual predictors.
– Hierarchical Multiple Regression: choose order of predictors based on their hypothesis; investigating confounds or mediating variables and possible spurious correlations (controlling for the third variable; whether the chosen new variable uniquely contributes to the variance in the outcome).

4. Output of multiple regressions
Multiple correlation coefficient (R): the degree of relationship between y and a set of x(s). R ranges from 0 to 1.
Coefficient of Multiple Determination (R²): shows the proportion of variance in y that can be accounted for by the set of x(s).
To compare r and R: see post #13.

5. Structural Equation Modeling: hypothesizing how variables are causally related by testing models with directional arrows in them.