What is the point of having a bunch of raw data if you don’t have the tools to analyze it? Regression models provide you with the ability to see if there is a relationship between two types of variables, helping make some sense of data that has been collected by fitting it to a line. Linear regression models use straight lines, while nonlinear and logistic models use curved ones. We will be looking at simple linear regression below.
Simple linear regression can be used for all sorts of applications, from presenting to stakeholders predictions for a company’s future to assisting in predicting how a crop will do in the following season.
Overview: What is simple linear regression?
Simple linear regression estimates the relationship between one independent variable and one dependent variable. It is a parametric test that assumes the data has a consistent degree of variance, was collected statistically soundly, follows a normal distribution, and that there is a linear relationship between the dependent and independent variable.
2 benefits and 2 drawbacks of simple linear regression
There are some clear benefits and drawbacks of simple linear regression that should not be overlooked:
Benefit 1: Relationship strength
Using simple linear regression can help you determine how strong of a relationship there is between a dependent variable and an independent variable.
Benefit 2: Finding values
Simple linear regression is useful in finding a particular value of an independent variable when the dependent variable is at a certain level.
Drawback 1: Limited based on the number of variables
If there is more than one independent and dependent variable, then you will have to use multiple linear regression.
Drawback 2: It doesn’t tell the whole story
While simple linear regression will tell you if there is a relationship between a dependent and independent variable, it does not tell you if one necessarily causes the other. In order to find out if there is actual causation, it will require further analysis beyond what simple linear regression can provide.
Why is simple linear regression important to understand?
Simple linear regression is important to understand for the following reasons:
Finding patterns – Understanding simple linear regression is important because it can help find patterns in your data.
Forecasting – With a knowledge of simple linear regression, you have a tool that can help you use your data to make more accurate predictions for the future.
Data transformation – By understanding simple linear regression, you are able to turn raw data into data that is meaningful and interpretable.
An industry example of simple linear regression
A toy company is planning the release of a new teddy bear in time for the holiday season. In order to gauge potential customer excitement, they have launched a focus group. One relationship they want to gauge the strength of is if a potential customer was aware of one of the company’s toys being recalled the year prior and how interested they seemed in purchasing the company’s new teddy bear. In order to display the relationship between these two variables, data analysts constructed a simple linear regression model for the next board meeting.
3 best practices when thinking about simple linear regression
Here are some key practices to consider when working with simple line regression:
1. Finding the line of best fit
When graphing out the relationship between the independent variable and the dependent variable, you are going to want to plot out a line that fits the points as well as possible. The best-fit line is found through the minimization of the Residual Sum of Squares.
2. Use evaluation metrics to determine the strength of your simple linear regression model
In order to find out just how strong your simple linear regression model is, you will want to use some evaluation metrics. The most common evaluation metrics for this purpose are typically Coefficient of Determination or Root Mean Squared Error and Residual Standard Error.
3. Exploring potential relationships
Scatterplots are an ideal first step in exploring the possible relationships between a dependent variable and an independent variable.
Frequently Asked Questions (FAQ) about simple linear regression
What is one difference between simple linear regression and ANOVA?
In ANOVA, a response is continuous but the predictor is nominal. With simple linear regression, however, both predictor and response are continuous.
What equation is used to represent a simple linear regression model?
Mathematically, a simple linear regression model is represented by the equation y = β0 +β1x+ε.
What are some other names for the input and output variables in simple linear regression?
Other names for input variables can be explanatory variables, X variables, predictors, and effects. For output variables, you can also use outcomes, dependent variables, and Y variables.
Understanding data with simple linear regression
With simple linear regression, you can easily see if there is a relationship between two variables. This takes a lot of the guesswork out of determining if something has an effect on something else. It is a simple, albeit limited tool that can help make sense of data, forecast possible outcomes, and predict future trends. You may not be able to see into the future, but simple linear regression can help give you the data that may make it seem like you can.