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
Calculate the zero-order, partial and part as a % for Mary, Jane and Paul based on these SPSS outputs
There are no unexplained variances in this model
Mary
Unique variance = 0.6
Shared variance with Jane = 0.2
Shared variance with Paul = 0.04
Jane
Unique variance = 0.1
Shared variance with Mary = 0.2
Shared variance with Paul = N/A
Paul
Unique variance = 0.06
Shared variance with Mary = 0.04
Shared variance with Jane = N/A
Mary
Zero-order correlations = 84%
0.6 + 0.04 + 0.2 = 0.84
Partial correlations = 100%
0.6 / 0 + 0.6 = 1.0
Part correlations = 60%
0.6 = .600
Jane
Zero-order correlations = 30%
0.1 + 0.2 = 0.3
Partial correlations = 100%
0.1 / 0 + 0.1 = 1.0
Part correlations = 10%
0.1 = .100
Paul
Zero-order correlations = 10%
0.06 + 0.04 = 0.1
Partial correlations = 100%
0.06 / 0 + 0.06 = 1.0
Part correlations = 6%
0.06 = .060
What is ‘standard’ multiple regression?
All predictor variables are entered at the same time
All predictor variables are entered at the same time
a. ‘Standard’ multiple regression
b. Hierarchical regression
a. ‘Standard’ multiple regression
What is hierarchical regression?
Predictor variables are entered in a specified
order of ‘steps’, based on theoretical grounds
Predictor variables are entered in a specified
order of ‘steps’, based on theoretical grounds
a. ‘Standard’ multiple regression
b. Hierarchical regression
b. Hierarchical regression
Obtain a measure of the overall variance explained (R^2)
Obtain measures of the influence of each separate predictor (coefficients)
The most common form of regression
a. ‘Standard’ multiple regression
b. Hierarchical regression
a. ‘Standard’ multiple regression
What is the most common form of regression?
‘Standard’ multiple regression
The relative contribution of each ‘step’ (set of predictor variables) can be evaluated in terms of what it adds to the prediction of the outcome variable
(i.e. the additional variance it explains)
a. ‘Standard’ multiple regression
b. Hierarchical regression
b. Hierarchical regression
Why do we use hierarchical regression?
To examine the influence of predictor variables(s) on an outcome variable, after ‘controlling for’ (i.e. partialling out) the influence of other variables
To examine the influence of predictor variables(s) on an outcome variable, after ‘controlling for’ (i.e. partialling out) the influence of other variables
What do we use?
Hierarchical Regression
You are interested in how well optimism predicts life satisfaction, but you want to investigate the predictive power of optimism after controlling for age-associated variation in life satisfaction
What do we use?
a. Hierarchical regression
b. ‘Standard’ multiple regression
a. Hierarchical regression
Previous research has established that self-efficacy and motivation are important predictors of learning performance; you want to know if enjoyment of materials and peer support (previously unexplored variables) can explain additional variance
in learning performance
What do we use?
a. Hierarchical regression
b. ‘Standard’ multiple regression
a. Hierarchical regression
You are interested in how well optimism predicts life satisfaction, but you want to investigate the predictive power of optimism after controlling for age-associated variation in life satisfaction
What are Step 1 and Step 2 of our hierarchical regression?
Step 1 = age
Step 2 = optimism
Previous research has established that self-efficacy and motivation are important predictors of learning performance; you want to know if enjoyment of materials and peer support (previously unexplored variables) can explain additional variance
in learning performance
What are Step 1 and Step 2 of our hierarchical regression?
Step 1 = self-efficacy and motivation
Step 2 = peer support and enjoyment
On SPSS, what does ‘a. Predictors: (Constant), naughty list rating (1 = low; 10 = high)’ mean in the ‘Model Summary’ table?
Regression results for Model 1 (Step 1), which only
included naughty list rating as a predictor variable
On SPSS, what does ‘b. Predictors: (Constant), naughty list rating (1 = low; 10 = high), age’ mean in the ‘Model Summary’ table?
Regression results for Model 2 (Step 2), which included naughty list rating AND age as predictor variables
Proportion of variance explained by the model
(predictor variables combined, if >1)
This is referred to as…?
R^2
What does R^2 measure?
The proportion of variance explained by the model
(predictor variables combined, if >1)
Adjusted to account for the degrees of freedom (a better estimate of the variance explained
in the population)
This is known as…?
Adjusted R^2
What is adjusted R^2?
Adjusted to account for the degrees of freedom (a better estimate of the variance explained
in the population)
On SPSS, what does ‘b. Predictors: (Constant), naughty list rating (1 = low; 10 = high)’ mean in the ‘ANOVA’ table?
ANOVA results for Model 1 (Step 1), which only
included naughty list rating as a predictor variable
On SPSS, what does ‘b. Predictors: (Constant), naughty list rating (1 = low; 10 = high), age’ mean in the ‘ANOVA’ table?
ANOVA results for Model 2 (Step 2), which included
naughty list rating AND age as predictor variables
What do the ANOVA results for Model 2 (Step 2), which included naughty list rating AND age as predictor variables assess?
Assesses whether the overall regression model (with
all predictors included at that step) accounts for
significantly more variance than the simplest model
(b = 0)
Assesses whether the overall regression model (with
all predictors included at that step) accounts for
significantly more variance than the simplest model
(b = 0)
a. t-tests
b. correlation
c. regression
d. ANOVA
d. ANOVA
What do the ANOVA results for Model 1 (Step 1), which only included naughty list rating as a predictor variable assess?
Assesses whether the overall regression model (with
all predictors included at that step) accounts for
significantly more variance than the simplest model
(b = 0)
The change in R^2 from b = 0 to Model 1 or 2 is known as…?
R Square Change
What does R Square Change measure?
The change in R^2 from b = 0 to Model 1 or 2
R Square Change is the same as ___ for Model 1
R^2
Provides a measure of how much the model has improved the prediction of y, relative to the level of inaccuracy of the model
This is known as…?
F change
What does F change measure?
Provides a measure of how much the model has improved the prediction of y, relative to the level of inaccuracy of the model
F Change is the same as ___ for Model 1
F
Predictors: (Constant), naughty list rating (1 = low; 10 = high) on the Model Summary table on SPSS compares…?
a. The simplest model (b = 0) with Model 1 (which included just naughty list rating)
b. Model 1 (which included just naughty list rating) and Model 2 (which includes naughty list rating AND age)
a. The simplest model (b = 0) with Model 1 (which included just naughty list rating)
Predictors: (Constant), naughty list rating (1 = low; 10 = high), age on the Model Summary table on SPSS compares…?
a. The simplest model (b = 0) with Model 1 (which included just naughty list rating)
b. Model 1 (which included just naughty list rating) and Model 2 (which includes naughty list rating AND age)
b. Model 1 (which included just naughty list rating) and Model 2 (which includes naughty list rating AND age)
Tells us about the explanatory power of age, after the effects of naughty list rating are controlled for
How much overall variance in the DV is explained by predictor 2 after the effects of predictor 1 are controlled for
How do we measure this?
Refer to R Square Change
Provides a measure of how much the model has improved the prediction of y, relative to the level of inaccuracy of the model, after the predictive power of Step 1 variables have been partialled out
This is known as…?
F change
What does F change measure?
How much the model has improved the prediction of y, relative to the level of inaccuracy of the model, after the predictive power of Step 1 variables have been partialled out
