PSY4MIP Week 10 - Multiple Regression and Hierarchical Regression

Flashcards from PSY4MIP Week 10 lecture on multiple regression and hierarchical regression.

What is the difference between simple linear regression and multiple regression?

Simple linear regression involves one independent variable (X) predicting a dependent variable (Y), while multiple regression involves multiple independent variables (Xs) predicting a single dependent variable (Y).

How is the strength of a regression assessed?

The strength of a regression is assessed by measuring the residuals, which are the distances between the actual data points and the predicted values on the regression line.

What does residual analysis help identify?

Residual analysis helps identify outliers, issues with restricted range, and heterogeneous sub-samples that may affect the conclusions drawn from the data.

What are the key assumptions needed for multiple regression?

The key assumptions are normality, linearity, homoscedasticity, independence, and no multicollinearity.

What does homoscedasticity mean in the context of regression assumptions?

Homoscedasticity means that the variance of the errors is the same across all levels of the independent variables. The data should not look like a 'shotgun blast'.

What is multicollinearity, and how can it be avoided?

Multicollinearity is a high degree of overlap between predictor variables, which can weaken the power of the model. It can be avoided by ensuring the tolerance statistic is greater than 0.10.

What is a tolerance statistic, and what does it indicate?

A tolerance statistic indicates the degree of multicollinearity among predictor variables. A value greater than 0.10 suggests that multicollinearity is not a major issue.

What are the five main variables that can singly predict course quality?

Enrollment, Exam quality, Grade Expected, Lecturer Knowledge, and Lecturer ability.

What statistical value increases as F moves away from 1.0?

The probability of a statistically significant finding increases..

In multiple regression output, what key information should be understood?

The overall model fit with all predictors included, and which individual predictors are actually significant.

What do unstandardized betas tell us?

Unstandardized betas (partial regression coefficients) tell us about the average unit change in the dependent variable (Y) for each unit change in the independent variable (X).

What is the advantage of using standardized betas?

Standardized betas allow for a direct comparison of the predictors, as they represent the average standard deviation change in Y for each standard deviation change in X.

What factors contribute to statistical power in regression?

A larger sample size (N) and fewer, but strong, predictors increase statistical power.

In the research example given, what were the elements to report after deciding to do a regression?

Report descriptives, inferential statistics of the equation and inferential statistics of the predictors.

What is the purpose of hierarchical regression?

Hierarchical regression allows us to test the impact of each variable when it's entered in a specific order, determining if additional predictors add extra value beyond those already included.

In what order should predictors in hierarchical regression be entered?

The order of entry should be developed a priori (before looking at the data) based on theory or existing research.

What are the main goals of ordered entry of predictors in hierarchical regression?

To qualify or clarify the existence of an effect and to remove the effect of nuisance variables or reduce error.

What are the types of statistical regression?

Forward selection, backward elimination, and stepwise regression.

How does logistic regression differ from multiple regression?

Logistic regression is used when the dependent variable is binary or non-continuous, while multiple regression is used when the dependent variable is measured on a continuous scale.