38 Questions
In multiple regression, what does R² represent?
The amount of variance in Y accounted for by X
What does SSY represent in the equation?
The total sum of squares
What is the relationship between Xk and Y when all other predictors are partialled out?
Semipartial correlation
What is the name of the equation that represents R²?
Regression equation
What is R² a measure of in multiple regression analysis?
The amount of variance in Y accounted for by X
What is the purpose of checking the value of R² in the Model Summary box in SPSS output?
To determine the amount of variance in Y accounted for by X
What is the relationship between R² and SS reg?
R² is proportional to SS reg
What is the difference between R² and sr²?
R² is for the set of predictors, while sr² is for a single predictor
What does the value of R2 (.323) in the regression analysis represent?
The proportion of total variance in Stats_Exam explained by the regression model
What is the effect of GRE_Q on Stats_Exam, accounting for Attendance?
19% of unique variance in Stats_Exam
What is the purpose of squaring the semi-partial correlation coefficient (sr)?
To obtain the proportion of unique variance in the dependent variable
What does the SSreg represent in the regression analysis?
The sum of squared regression in the regression model
What is the effect of Attendance on Stats_Exam, accounting for GRE_Q?
29% of unique variance in Stats_Exam
What is the relationship between GRE_Q and Stats_Exam, after controlling for Attendance?
A unique relationship between GRE_Q and Stats_Exam
What is the interpretation of the blue area in the Venn diagram?
The variance of Stats_Exam not explained by GRE_Q and Attendance
What is the purpose of the /descriptives=def option in the SPSS command?
To obtain the descriptive statistics of the variables
What is the main reason why a significant correlation between a predictor and an outcome becomes insignificant in a multiple regression?
The correlation between the predictor variables is too high
What does the semi-partial correlation coefficient (sr) represent?
The unique variance explained by the predictor variable after controlling for other predictors
What is the difference between the total variance explained and the unique variance?
The shared variance between the predictor variable and the outcome variable
What is the purpose of examining the variance explained by the predictor variable after controlling for other predictors?
To understand the strength of the relationships between the predictor variable and the outcome variable
What happens to the correlation between a predictor and an outcome when there is high correlation between the predictor variables?
The correlation between the predictor and the outcome becomes insignificant
What is the term used to describe the variance explained by the linear combination of the predictor variables?
Regression inflation
What percentage of the shared variance between the two predictor variables and the state exam performance is accounted for by attendance?
13.5%
What does the speaker imply is a more changeable behavior, attendance or aptitude?
Attendance is more changeable
What is the main purpose of using the Ben diagram with two predictor models?
To visualize the shared variance
What is the result of subtracting the unique variances from the square of the semi-partial correlation coefficient?
The shared variance
Why does the speaker suggest encouraging class attendance as an intervention?
Because attendance has a stronger correlation with exam performance
What is the speaker's conclusion about the relationship between attendance and exam performance?
Attendance has a stronger correlation with exam performance than aptitude
What does the speaker use to calculate the shared variance?
A calculator and a piece of paper
What is the main difference between the unique and shared variances?
Unique variance is specific to one predictor, while shared variance is common to both predictors
What is the primary purpose of calculating R² in multiple regression?
To quantify the proportion of variance in the dependent variable explained by the independent variables
In multiple regression, what does the squared correlation between X and Y represent?
The proportion of variance shared between X and Y
What is the difference between R² and partial R² in multiple regression?
R² measures the variance explained by all predictors, while partial R² measures the variance explained by a single predictor
What is the primary limitation of using R² as a measure of variance explanation in multiple regression?
It is sensitive to the number of predictors in the model
What is the relationship between the variance explained by a single predictor and the variance explained by a set of predictors in multiple regression?
The variance explained by a single predictor is a subset of the variance explained by a set of predictors
What is the purpose of partitioning the components of each person score in the dependent variable into two parts?
To quantify the variance explained by the model as a whole
What is the relationship between the regression equation and the variance explained by the model?
The variance explained by the model is a function of the regression equation
What is the primary advantage of using multiple regression over simple regression?
It allows for the analysis of multiple predictors simultaneously
Study Notes
Multiple Regression: Variance Explained
- In correlation, r2 represents the proportion of variance shared by two correlates (X and Y).
- In regression, r2 represents the amount of variance in Y accounted for by X (either a single predictor or the set of predictors).
- Multiple R2 is referred to simply as R2, which is the variance in Y accounted for by Xk (the set of predictors).
Proportions of Variance
- R2 is the proportion of variance in Y that is accounted for by the set of predictors Xk.
- SSY represents the total variance in Y.
- SSreg represents the variance in Y that is accounted for by the set of predictors Xk.
- SSres represents the variance in Y that is not accounted for by the set of predictors Xk.
Equations—What is R2?
- R2 = SSreg / SSY
- SSY = Σ(Y - Y)²
- SSreg = Σ(Y' - Y)²
- SSres = SSY - SSreg
Semipartial Correlations
- Semipartial correlations (sr and sr2) represent the relationship between Xk and Y when all other predictors are partialled out.
- sr2 gives the proportion of unique variance in Y accounted for by Xk.
- Semipartial correlations are a good indicator of the unique relationship between Xk and Y.
Interpretation of Regression Predictors
- R2 represents the variance in Y that is accounted for by the set of predictors Xk.
- sr2 represents the unique variance in Y accounted for by Xk.
Example: GRE_Q, Attendance, and Stats_Exam
- GRE_Q (X1) and Attendance (X2) are predictors of Stats_Exam (Y).
- R2 = 0.323 (SSreg / SSY)
- Unique variance of GRE_Q: 19%
- Unique variance of Attendance: 29%
Multiple Regression
- In multiple regression, a significant correlation between a predictor and an outcome may become insignificant due to high correlation between predictor variables.
- This is because the correlation between predictor variables leaves relatively little unique variance to explain.
Variance Explained
- Variance explained by a predictive variable is represented by R-squared (R²).
- R² is also known as regression coefficient or the model's goodness of fit.
- It measures the proportion of variance in the outcome variable explained by the predictor variables.
Unique and Shared Variance
- Unique variance is the variance explained by a predictor variable after controlling for other predictor variables.
- It is represented by semi-partial correlations (squared).
- Shared variance is the variance explained by multiple predictor variables.
- It is calculated by subtracting the unique variance from the total variance.
Calculating Shared Variance
- To calculate shared variance, subtract the combined unique variances from the total variance (R²).
- Example: R² = 0.608, semi-partial squared (predictor 1) = 0.187, semi-partial squared (predictor 2) = 0.286, shared variance = 0.608 - (0.187 + 0.286) = 0.135 or 13.5%.
Interpreting Results
- A psychologist can use the results to suggest that class attendance is a better predictor of exam performance than aptitude.
- This information can be used to design an intervention to encourage class attendance, which is a changeable behavior.
Variance Explained in Multiple Regression
- In multiple regression, R² represents the proportion of variance in the outcome variable explained by a set of predictor variables.
- It is calculated by squaring the correlation between the predictor variables and the outcome variable.
- R² is used to assess the goodness of fit of the model and to identify the proportion of variance explained by each predictor variable.
This quiz covers the concept of multiple regression, variance explained, and proportion of variance in psychology survey design and analysis.
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