Regression Assumptions

This set of flashcards covers key vocabulary and concepts from Chapter 18 on regression assumptions, aimed at aiding in the understanding and review of the material for successful exam preparation.

Linearity

The relationship between the independent variable (x) and the dependent variable (y) is linear, meaning the rate of change in y for a given change in x is constant.

Independent Variables

Independent variables are not correlated with the error term. This means there should be no omitted variable bias affecting the slopes of the model.

Omitted Variable Bias

Bias that occurs when a model leaves out relevant variables that correlate with both the error term and the independent variable.

Curvilinear Relationship

A relationship that cannot be adequately described by a straight line, where the relationship between the variables varies.

Homoscedasticity

The assumption that the variance of residuals is constant across all levels of the independent variables.

Heteroscedasticity

A violation of the homoscedasticity assumption, where the variance of the residuals varies at different levels of an independent variable.

Residuals

The differences between observed and predicted values in a regression model.

Mean of the Error Term

The expected value of the error term, which should equal zero to avoid bias in the constant.

Shapiro-Wilk Test

A statistical test used to check the normality of residuals in a regression model.

Breusch-Pagan Test

A statistical test used to check for homoscedasticity in regression models.

VIF (Variance Inflation Factor)

A measure used to detect multicollinearity in regression models.

Multicollinearity

A situation in multiple regression models where two or more independent variables are highly correlated.

Serial Correlation

The presence of correlation between the error terms of different observations, often a concern in time-series data.

Diagnostic Tests

Tests conducted to check the validity of regression assumptions.

Life Expectancy Model

A regression model developed to analyze the relationship between various factors and life expectancy.

Data Sets Used

The countries2 and states20 data sets are referenced for analysis in this chapter.

Transformations of Variables

Mathematical adjustments made to variables to meet the assumptions of regression analysis.

Linear Model

A model that assumes a linear relationship between independent and dependent variables.

Scatterplots

Visual representations used to examine the relationships between two quantitative variables.

R programming

A programming language widely used for statistical analysis and data visualization.

Statistical Significance

A measure of whether the results of a study or analysis are meaningful and likely not due to chance.

Adjusted R-squared

A modification of R-squared that adjusts for the number of predictors in the model.

Constant Error Variance

Another term for homoscedasticity, indicating that the spread of the residuals remains consistent across all values.

Goodness of Fit

A measure of how well a statistical model fits the data.

Causation vs. Correlation

The distinction between a relationship that implies one variable causes changes in another versus a mere association.

Statistical Models

Mathematical representations that aim to explain relationships among variables.

Least Squares Method

A standard approach to find the line of best fit in regression analysis by minimizing the sum of the squares of the residuals.

Residual Standard Error

An estimate of the standard deviation of the residuals in regression.

Influence Statistics

Statistics that measure the impact of individual data points on the overall regression results.

Normal Distribution

A probability distribution that is symmetric about the mean, showing that data near the mean are more frequent than data far from the mean.

Regression Coefficients

Values that represent the relationship between independent variables and the dependent variable in a regression model.

Predictive Power

The ability of a model to accurately predict outcomes based on input variables.

Causal Relationships

Relationships where one event is understood to be the direct result of another event.

Outliers

Observations that lie outside the overall pattern of the data and may disproportionately influence regression results.

Statistical Testing

Processes for determining if the observed effects are statistically significant.

Sample Residuals

The residuals calculated from a sample used to evaluate regression assumptions.

Model Specification

The process of developing a statistical model that accurately represents the data being analyzed.

Standard Errors

Estimates of the amount of variation in the sample data that affect the coefficients in regression models.

Two-Tailed Test

A statistical test where the critical area of a distribution is split between the two tails, allowing for deviations in both directions.

Null Hypothesis

A statement that there is no effect or no difference, often set for testing purposes.

Alternative Hypothesis

The hypothesis that there is an effect or a difference, contrary to the null hypothesis.

Confidence Interval

A range of values constructed from sample data that is likely to contain the true parameter value.

Regression Diagnostics

Procedures for checking the assumptions of regression analysis for validity.

Statistical Inference

The process of using data analysis to deduce properties of an underlying distribution.

Data Analysis

The systematic application of statistical and logical techniques to describe and evaluate data.

Regression Model Fit

A measure of how well the regression model explains the variability of the dependent variable.

Inferential Statistics

Statistics that are used to infer or generalize conclusions about a population based on sample data.

Competing Models

Different model specifications used to explain the same data set.

Variance

A measure of how far a set of numbers are spread out from their average value.

Standard Deviation

A statistic that measures the dispersion of a dataset relative to its mean.

Data Visualization

The graphical representation of information and data.

R-Squared

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

Residual Analysis

The process of analyzing the difference between observed and predicted values in a regression model.

Multivariate Regression

A type of regression analysis that models the relationship between two or more predictor variables and a dependent variable.

Collapsing Variables

Reducing multiple variables into fewer categories to simplify modeling and interpretation.

Factor Analysis

A statistical technique used to describe variability among correlated variables in terms of fewer unobserved variables.

Experimental Data

Data derived from experiments where subjects are randomly assigned to groups.

Observational Data

Data collected without manipulation of variables, often raising concerns about bias.

Scatterplot Matrix

A grid of scatterplots used to visualize the relationships among multiple variables.

Dependent Variable

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

Independent Variable

Variables that are manipulated or measured to see their effect on the dependent variable.