3B - Flashcards
What is effect size in regression?
It measures the strength of the relationship between X and Y.
How can effect size be interpreted?
1) Steepness of regression line (Unstandardized coefficient).
2) Closeness of points to the line (Standardized coefficient).
Why is the p-value not a measure of effect size?
A very small p-value does not mean a strong effect; even weak effects can be significant in large samples.
What are standardized coefficients?
Regression coefficients adjusted to a common scale (-1 to +1) that indicate how well X predicts Y.
How do standardized coefficients help?
They allow comparison of effect sizes across variables with different measurement units.
What does a standardized coefficient of +1 or -1 mean?
+1 = Perfect positive relation (Y can be predicted 100% from X). -1 = Perfect negative relation. 0 = No relationship.
What is the formula for standardized coefficients?
They are the regression coefficients from a regression using z-scores instead of raw data.
What are z-scores?
A standardized measure that shows how far a value is from the mean, in standard deviation units.
How do standardized coefficients relate to z-scores?
A standardized coefficient tells us how many standard deviations Y changes per 1 standard deviation change in X.
Why compare standardized coefficients?
They allow comparison between different X variables to see which is the strongest predictor of Y.
Why is it hard to compare unstandardized coefficients?
Different X variables use different units, making direct comparison meaningless.
When can unstandardized coefficients be compared?
Only when all X variables have the same unit (e.g., all in millions of euros).
What is R² (R-squared)?
A measure of how well all independent variables in a model together explain the variation in Y.
What is the range of R² values?
0 (no explanatory power) to 1 (perfect prediction).
How is R² interpreted?
Example: R² = 0.25 → 25% of the variation in Y is explained by the model.
What is Adjusted R²?
A corrected version of R² that adjusts for the number of predictors in the model.
How is R² calculated?
R² = Sum of Squares Regression / Sum of Squares Total.
What does the p-value of R² indicate?
Whether the R² is significantly greater than 0, meaning the model explains some variation in Y.
What is the F-test in regression?
A test to determine if the overall model (not just individual coefficients) is significant.
How does R² relate to standardized coefficients?
In simple regression, R² is just the squared correlation (R² = r²). In multiple regression, R² does not have a direct one-to-one relationship with standardized coefficients.
