Regression 2.0 Flashcards
The proportion of variance explained by the model (predictor variables combined) is known as…?
R^2
What does R^2 measure?
The proportion of variance explained by the model (predictor variables combined)
Variance explained by x1 expressed as a proportion of the total variance in y
This is known as…?
Zero-order^2
What is zero-order^2?
Variance explained by x1 expressed as a proportion of the total variance in y
Unique variance explained by x1, expressed as a proportion of the total variance in y
This is known as…?
Part^2
What is part^2?
Unique variance explained by x1, expressed as a proportion of the total variance in y
Unique variance explained by xi, expressed as a proportion of the variance in y that remains after the variance explained by other predictors has been removed
This is known as…?
Partial^2
What is partial^2?
Unique variance explained by xi, expressed as a proportion of the variance in y that remains after the variance explained by other predictors has been removed
How do we report zero-order, partial and part as a %?
- Square the correlations to determine the proportion of variance
- Multiply by 100 to express in percentage terms
Calculate the zero-order, partial and part as a % for age and naughty list ratings based on these SPSS outputs
Age
Zero-order correlations = .573
Partial correlations = .523
Part correlations = .473
Naughty list rating
Zero-order correlations = -.430
Partial correlations = -.344
Part correlations = -.282
Age
Zero-order % = .573^2 * 100 = 32.8
Partial % = .523^2 * 100 = 27.4
Part % = .473^2 * 100 = 22.4
Naughty list rating
Zero-order % = -.430^2 * 100 = 18.5
Partial % = -.344^2 * 100 = 11.8
Part % = -.282^2 * 100 = 8.0
What is the formula for the variance explained by both x1 and x2 (i.e. shared variance), expressed as a proportion of the total variance in y?
Zero-order correlation^2 - part correlation^2
What is the formula for unexplained variance?
1-R^2
Variance explained by each predictor is measured using…?
Zero-order^2
Unique variance explained by each predictor is measured using…?
Part^2
Explained variance shared by multiple predictors is measured using…?
Variance overlap between each predictor
Variance explained all predictors combined (their unique and their shared variance), expressed as a proportion of the total variance in y
This is known as…?
Total Explained Variance
What is the formula for partial correlation^2?
Partial correlation^2 = unique variance / (unexplained variance + unique variance)
Calculate the partial correlation^2 based on these results:
Age
Zero-order % = .573^2 * 100 = 32.8
Part % = .473^2 * 100 = 22.4
Naughty list rating
Zero-order % = -.430^2 * 100 = 18.5
Part % = -.282^2 * 100 = 8.0
Age
Partial correlation^2 = unique variance / (unexplained variance + unique variance)
22.4 / ((1- (22.4 + (32.8 - 22.4) + 8.0)) + 22.4
= 27.4
Naughty list rating
8.0 / ((1- (22.4 + (32.8 - 22.4) + 8.0)) + 8.0
= 11.8
What does the zero-order correlation^2 of age tell us about the total variance in Christmas Joy?
Age
Zero-order % = .573^2 * 100 = 32.8
Partial % = .523^2 * 100 = 27.4
Part % = .473^2 * 100 = 22.4
Age can explain 33% of the total variance in Christmas joy
Same result as a simple regression that only includes age as a predictor
What does the part correlation^2 of age tell us about the total variance in Christmas Joy?
Age
Zero-order % = .573^2 * 100 = 32.8
Partial % = .523^2 * 100 = 27.4
Part % = .473^2 * 100 = 22.4
Age can explain 22% of the total variance in Christmas joy uniquely
i.e. variance explained by age when we don’t include variance also explained by other variables
What does the partial correlation^2 of age tell us about the total variance in Christmas Joy?
Age
Zero-order % = .573^2 * 100 = 32.8
Partial % = .523^2 * 100 = 27.4
Part % = .473^2 * 100 = 22.4
Age can explain 27% of the remaining variance in Christmas joy, after removing variance explained by other predictors
i.e. variance uniquely explained by age, expressed as a proportion of the variance that remains after the variance explained by other predictors has been removed
What does the zero-order correlation^2 of naughty list ratings tell us about the total variance in Christmas Joy?
Naughty list rating
Zero-order % = -.430^2 * 100 = 18.5
Partial % = -.344^2 * 100 = 11.8
Part % = -.282^2 * 100 = 8.0
Naughty list ratings can explain 19% of the total variance in Christmas joy
Same result as a simple regression that only includes naughty list ratings as a predictor
What does the part correlation^2 of naughty list ratings tell us about the total variance in Christmas Joy?
Naughty list rating
Zero-order % = -.430^2 * 100 = 18.5
Partial % = -.344^2 * 100 = 11.8
Part % = -.282^2 * 100 = 8.0
Naughty list ratings can explain 8% of the total variance in Christmas joy uniquely
i.e. variance explained by naughty list ratings when we don’t include variance also explained by other variables
What does the partial correlation^2 of naughty list ratings tell us about the total variance in Christmas Joy?
Naughty list rating
Zero-order % = -.430^2 * 100 = 18.5
Partial % = -.344^2 * 100 = 11.8
Part % = -.282^2 * 100 = 8.0
Naughty list ratings can explain 12% of the remaining variance in Christmas joy, after removing variance explained by other predictors
i.e. variance uniquely explained by naughty list ratings, expressed as a proportion of the variance that remains after the variance explained by other predictors has been removed