10.8: Chapter 10 - Key Terms and Symbols

Key Terms

Bivariate Data: Data involving two numerical variables that are analyzed together to explore possible relationships.

Coefficient of Determination (r²): A value between 0 and 1 that indicates how much of the variation in the dependent variable is explained by the independent variable.

Correlation: A statistical measure that describes the strength and direction of the linear relationship between two variables.

Correlation Coefficient (r): A numerical value between −1 and 1 that quantifies the strength and direction of a linear relationship. Values near 1 indicate strong positive correlation, near −1 indicate strong negative correlation, and near 0 indicate no linear correlation.

Identifying Relationships: Bivariate analysis helps determine if two variables are related and the nature of that relationship (positive, negative, or none).

Intercept (a): In a linear regression equation, this is the value of the dependent variable when the independent variable is zero; the point where the regression line crosses the y-axis.

Linear Regression: A method used to model the relationship between a dependent variable and an independent variable by fitting a straight line to the data.

Predicting Outcomes: Regression models use one variable to estimate or predict the value of another, based on observed trends.

Regression Coefficients: The values in the regression equation (slope and intercept) that quantify how the independent variable affects the dependent variable.

Scatterplot: A graph that displays pairs of values as points on a coordinate plane, helping to visualize the relationship between two variables.

Slope (b): In a linear regression equation, the slope represents the rate of change; it tells how much the dependent variable changes for each unit increase in the independent variable.

Standard Error of the Estimate: A measure of the typical distance between the observed data points and the regression line; it reflects the accuracy of predictions.

Key Symbols

\( a \) - y-intercept of the regression line (value of \( y \) when \( x = 0 \)).

\( b \) - slope of the regression line (rate of change in \( y \) with respect to \( x \)).

\( \bar{x} \) - mean of the \( x \)-values in the sample.

\( \bar{y} \) - mean of the \( y \)-values in the sample.

\( y' \) - predicted value of the dependent variable from the regression equation.

\( r \) - sample correlation coefficient (measures strength and direction of a linear relationship in sample data).

\( r^2 \) - coefficient of determination (proportion of the variance in \( y \) explained by \( x \)).

\( \rho \) - population correlation coefficient (measures strength and direction of a linear relationship in the population).

\( s_{EST} \) or SE - standard error of the estimate (typical deviation between observed and predicted values).

\( x \) - independent variable (predictor or explanatory variable).

\( y \) - dependent variable (response or outcome variable).