Linear regression and linear relations
Linear regression is a method for modeling the relationship between two numerical variables by fitting a straight line to the data. It is used to understand how changes in an explanatory variable influence a response variable. Scatterplots provide a visual representation of these relationships, showing their direction, form, and strength, which can be measured using Pearson’s correlation coefficient (\(r\)). The least squares regression line is then used to find the line of best fit, minimising prediction errors. These techniques are widely applied in fields such as business and finance for forecasting trends, medical research for identifying risk factors, education for predicting student performance, and environmental science for analysing climate patterns.
This resource revises linear regression and linear relations and within linear regression and linear relations there are 2 key concepts:
To determine if this resource will benefit you, start by answering the following questions.
- What is the difference between the response variable and the explanatory variable when analysing data with a linear relationship?
- How does Pearson’s correlation coefficient tell the strength and direction of the relationship between two variables?
- Why is the method of least squares used in linear regression to make predictions based on data?
The answers to these questions are provided on the following pages. Use this resource to refresh your memory, reinforce your understanding of these concepts, and prepare more effectively for university-level learning.