PSCH 443 Multiple Regression 3 Evaluating Assumptions Part 1

Multiple Regression

A statistical technique that models the relationship between multiple predictors and an outcome variable.

Sample Size

The number of cases or participants used in a study to ensure that estimates are stable and statistically significant.

Statistical Power

The probability that a statistical test will correctly reject a false null hypothesis, often desired to be 0.8 or higher.

R-squared

A statistical measure representing the proportion of variance for a dependent variable that's explained by the independent variables in the model.

Multicollinearity

A situation in multiple regression where two or more predictors are highly correlated, making it difficult to determine their individual effects.

Bivariate Correlation

The relationship between two variables used to evaluate how one variable may predict or affect another.

Variance Inflation Factor (VIF)

A measure that quantifies how much the variance of an estimated regression coefficient increases when your predictors are correlated.

Outliers

Extreme values that diverge significantly from the rest of a dataset, which can affect the results of statistical analyses.

Regression Diagnostics

Techniques used to assess the reliability and validity of a regression model, often including checks for normality, homoscedasticity, and collinearity.

Residuals

The differences between observed and predicted values in a regression analysis, used to assess the fit of a model.

Power Analysis

A method to determine the sample size required to detect an effect of a given size with a certain degree of confidence.

Threshold for Tolerances

In multicollinearity analysis, the general guideline suggesting concern for tolerances below 0.2.

Cook's Distance

A measure used to identify influential data points with significant impact on fitted values in regression models.

Adjusted R-squared

A modified version of R-squared that accounts for the number of predictors in the model and adjusts for potential overfitting.

Standard Error

An estimate of the variability in a sample statistic, giving insight into how representative that statistic is of the population.

Factor Analysis

A statistical method used to identify the underlying relationships between variables by grouping them based on common factors.

Dependent Variable

The outcome variable that a researcher is trying to predict or explain in a regression analysis.

Independent Variable

A variable that is manipulated or categorized to observe its effect on the dependent variable in a study.

Significance Tests

Statistical tests used to determine if the results of an analysis are likely due to chance.

Cross-Sectional Study

A research design that collects data from a population, or a representative subset, at a specific point in time.

Naturalistic Observation

A research method involving observing subjects in their natural environment without manipulation.

Convenience Sample

A non-random sample taken from a population that is easy to access, which may introduce bias.

Coding Error

An error in data entry that involves incorrectly recording the data collected.

Normal Distribution

A probability distribution that is symmetric about the mean, indicating equal frequencies in both directions from the center.

Hypothesis Testing

A statistical method used to decide whether to accept or reject a proposed hypothesis based on sample data.