Regression Flashcards
What is Regression?
Understanding the relationship between variable X and variable Y
Can X cause/predict Y
Variable X
“Independent variable”
“factor”
“predictor”
“regressor”
Variable Y
“Dependent variable”
“outcome”
What is Covariance?
A measure of association
1. Gives us strength and direction of the linear relationship of X and Y
- Concept is similar to variance (a weighted sum of squared deviations of individual scores around the mean score of a variable)
3.Covariance is a weighted sum of the product of deviations of individual X scores around the mean of X by deviations of individual Y scores around the mean of Y
Covariance Relationships
Covariances (Sxy) equation
Problem with covariance as a stand alone measure
The covariance reflects the underlying raw scales of X and Y. The covariance is scale dependent.
Correlation: A standardized measure of association
Calculating a correlation coefficient is about rescaling covariance, similar to the logic behind z-scores.
correlation coefficient:
Correlation coefficient (Pearson’s r)
- Measures strength of linear relationship between x and y
- Sign (+ or -) indicates direction
- Upper limit is a perfect positive or negative relationship
Zx = +/-Zy then
rxy= +/-1.0 - Independent of measurement scale
Slide 19
Slide 20
Simple linear regression
Correlation: association between x and y
Regression: predict or explain y from x
y is the dv
x is the iv
This relationship may be causal ‘if the study design allows for such an interpretation’
Alternatively, we seek to understand how an IV is ‘related’ to a DV
A simple equation for a line
What is B0?
Regression intercept (value of Y when X=0)
What is B1?
Regression slope (“rise over run”; change in Y associated with a one-unit change in X)
Regression using a sample of the population
sample estimates of intercept and slope and predicted values of Y
Predicted values…
ADD EQUATION IMAGE PROBABLY
of Y are points on the regression line that correspond to given values of X
Residuals…
ADD EQUATION IMAGE PROBABLY
are distances between observed and predicted values of Y for corresponding X
What is needed to find the regression line
Covariances
Variances
Means of X
Means of Y
B1 Equations
B0 Equations
Shared variance
