Lesson 10 - Correlation and Regression

Term: Correlation Analysis
Definition: A method to measure the strength and direction of the linear association between two variables, describing how they change relative to each other.

Term: Scatter Diagram
Definition: A two-dimensional graph that visualizes the possible underlying relationship between two variables by plotting individual pairs of observations.

Term: Linear Correlation Coefficient
Definition: A statistic that quantifies the strength and direction of the linear relationship between two variables, independent of their scales.

Term: Properties of Linear Correlation Coefficient
Definition: Includes the following: values range from -1 to 1, the sign indicates the direction of the relationship, and the magnitude reflects the strength of the relationship.

Term: Pearson’s r
Definition: A point estimator of the linear correlation coefficient that measures the linear relationship between two variables.

Term: Simple Linear Regression
Definition: A statistical method that models the relationship between one explanatory variable and one response variable using a linear equation.

Term: Purpose of Linear Regression
Definition: To describe the relationship between variables, quantify the effect of one variable on another, and predict the value of the dependent variable from the independent variable.

Term: Regression Coefficients
Definition: Constants in a regression model where one represents the y-intercept and the other the slope, indicating the rate of change in the dependent variable.

Term: Random Error Term
Definition: Represents the effects of unobserved factors or measurement errors that influence the dependent variable in a regression model.

Term: Method of Least Squares
Definition: A procedure to find the line of best fit by minimizing the sum of the squares of the differences between observed and predicted values.

Term: Coefficient of Determination (R²)
Definition: Indicates the proportion of variability in the dependent variable that is explained by the independent variable through a linear model.

Term: Hypothesis Test on Correlation
Definition: A statistical test to determine if there is significant evidence to conclude that a relationship exists between two variables.

Term: Prediction in Regression
Definition: Estimating the value of the dependent variable using the regression equation with a specific value of the independent variable.