PSCH 443 Multiple Regression Overview and Example

Multiple Regression

A statistical technique used to explain the relationship between one outcome variable and multiple predictor variables.

Predictor Variables

Variables used in regression analysis to predict the outcome of another variable.

Outcome Variable

The variable that we are trying to predict or explain in regression analysis.

R-squared

A statistical measure that represents the proportion of variance for the outcome variable that is explained by the predictor variables in the model.

B Parameters

Unstandardized regression coefficients that indicate the effect size of predictor variables on the outcome variable in their original units.

Standard Error of Estimate

A measure of the average distance that the observed values fall from the regression line.

Beta Weights

Standardized regression coefficients that indicate the relationship between predictor variables and the outcome variable in standard deviation units.

T-Statistics

A ratio used in hypothesis testing to determine the statistical significance of the regression coefficients.

Significance Test

A statistical test used to determine if the effect observed in the data is likely to be genuine or if it could have occurred by chance.

Residual Degrees of Freedom

Calculated as the total degrees of freedom minus the regression degrees of freedom, reflecting the amount of information available to estimate the error.

ANOVA in Regression

Analysis of variance used to determine whether there are any statistically significant differences between the means of independent groups within regression analysis.

Degrees of Freedom

A measure of the amount of independent information available for estimating a parameter.

Correlation Matrix

A table showing correlation coefficients between multiple variables, indicating the strength and direction of their relationships.

Error Term

The difference between the observed values and predicted values in a regression model, representing unexplained variability.

Adjusted R-squared

A modified version of R-squared that adjusts for the number of predictors in the model, providing a more accurate estimate of the explained variance.

Sampling Error

The error caused by observing a sample instead of the whole population, affecting the accuracy of statistical estimates.

Unstandardized Coefficients

Coefficients in regression that are interpreted in the units of the original data, showing the change in the outcome variable for a one-unit change in the predictor.

Statistical Significance

A determination that a result is unlikely to have occurred by chance, often assessed using a p-value.

Practical Importance

The relevance of an effect or finding in a real-world context, beyond statistical significance.

Overlapping Predictors

The situation in multiple regression where two or more predictor variables share a common variance with the outcome variable.

Least Squares Method

A statistical technique used to estimate the parameters of a regression model by minimizing the sum of the squares of the residuals.