Simple linear regression

Simple linear regression is a statistical method that examines the statistical relationship between the independent variable and a dependent variable. ‘Simple’ linear regression only concerns the relationship go one independent variable, whereas ‘multiple’ linear regression concerns two or more independent variables.

Example applications

Consider a situation where you have two variables of concern, and would like to understand whether there is a linear relationship between the two: that is, if one variable goes up or down, we can anticipate what the other variable will do. Examples include:

• height and weight - if height increases, we could expect that weight would increase

• time spent studying and marks - if you spend more time studying, we could expect that you earn a better mark (in reality, there is probably a low correlation here!)

• responsibility and income - if the responsibility in your job increases, we could expect that the amount of money you earn increases

Steps

When preparing your answer, you should:

• create a scatter plot of the data - determine the line of best fit using the least squares method (using a statistical package such as RStudio or a spreadsheet application makes this very easy){: .link-ext target=”_blank” }

• report the regression equation, and the S and r values (whether it is positive or negative)
• provide a prediction of a value based on the regression equation

Key concepts

• an explanation of the type of data that can be using in simple linear regression
• an example that walks through how to build a scatter plot and solve the regression equation
• advice to the student engineer on how to interpret the results

Core resources

• John McDonald has authored an online textbook Handbook of Biological Statistics, which has a very clear entry on Linear Regression.

• RStudio has an active help community, R-Bloggers. See their example of conducting simple linear regression.

Similar tools…

There are many statistical approaches for examining the relationship between variables that can be more appropriate given the assumptions in a simple linear model. If your data exhibits non-linear behaviour when you draw your scatter plot, you should consider digging a little deeper to find a better statistical approach.