Lesson 10 - Correlation and Regression

Correlation Analysis

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

Scatter Diagram

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

Correlation Analysis

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

Scatter Diagram

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

Linear Correlation Coefficient

A statistic that quantifies the strength and direction of the linear relationship between two variables, independent of their scales.

Properties of Linear Correlation Coefficient

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.

Pearson’s r

A point estimator of the linear correlation coefficient that measures the linear relationship between two variables.

Simple Linear Regression

A statistical method that models the relationship between one explanatory variable and one response variable using a linear equation.

Purpose of Linear Regression

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.

Regression Coefficients

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.

Random Error Term

Represents the effects of unobserved factors or measurement errors that influence the dependent variable in a regression model.

Method of Least Squares

A procedure to find the line of best fit by minimizing the sum of the squares of the differences between observed and predicted values.

Coefficient of Determination (R²)

Indicates the proportion of variability in the dependent variable that is explained by the independent variable through a linear model.

Hypothesis Test on Correlation

A statistical test to determine if there is significant evidence to conclude that a relationship exists between two variables.

Prediction in Regression

Estimating the value of the dependent variable using the regression equation with a specific value of the independent variable.