Linear regression calculator
Linear regression is used to model the relationship between two variables and estimate the value of a response by using a line-of-best-fit. This calculator is built for simple linear regression, where only one predictor variable (X) and one response (Y) are used. Using our calculator is as simple as copying and pasting the corresponding X and Y values into the table (don't forget to add labels for the variable names). Below the calculator we include resources for learning more about the assumptions and interpretation of linear regression.
What is a linear regression model?
Linear regression is one of the most popular modeling techniques because, in addition to explaining the relationship between variables (like correlation), it also gives an equation that can be used to predict the value of a response variable based on a value of the predictor variable.
The formula for simple linear regression is Y = mX + b, where Y is the response (dependent) variable, X is the predictor (independent) variable, m is the estimated slope, and b is the estimated intercept.
Assumptions of linear regression
If you're thinking simple linear regression may be appropriate for your project, first make sure it meets the assumptions of linear regression listed below. Have a look at our analysis checklist for more information on each:
- Linear relationship
- Normally-distributed scatter
- Homoscedasticity
- No uncertainty in predictors
- Independent observations
- Variables (not components) are used for estimation
Calculating linear regression
While it is possible to calculate linear regression by hand, it involves a lot of sums and squares, not to mention sums of squares! So if you're asking how to find linear regression coefficients or how to find the least squares regression line, the best answer is to use software that does it for you. Linear regression calculators determine the line-of-best-fit by minimizing the sum of squared error terms (the squared difference between the data points and the line).
The calculator above will graph and output a simple linear regression model for you, along with testing the relationship and the model equation. Keep in mind that Y is your dependent variable: the one you're ultimately interested in predicting (eg. cost of homes). X is simply a variable used to make that prediction (eq. square-footage of homes).
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Interpreting results
Using the formula Y = mX + b:
- The linear regression interpretation of the slope coefficient, m, is, "The estimated change in Y for a 1-unit increase of X."
- The interpretation of the intercept parameter, b, is, "The estimated value of Y when X equals 0."
The first portion of results contains the best fit values of the slope and Y-intercept terms. These parameter estimates build the regression line of best fit. You can see how they fit into the equation at the bottom of the results section. Our guide can help you learn more about interpreting regression slopes, intercepts, and confidence intervals.
Use the goodness of fit section to learn how close the relationship is. R-square quantifies the percentage of variation in Y that can be explained by its value of X.
The next question may seem odd at first glance: Is the slope significantly non-zero? This goes back to the slope parameter specifically. If it is significantly different from zero, then there is reason to believe that X can be used to predict Y. If not, the model's line is not any better than no line at all, so the model is not particularly useful!
P-values help with interpretation here: If it is smaller than some threshold (often .05) we have evidence to suggest a statistically significant relationship.
Finally the equation is given at the end of the results section. Plug in any value of X (within the range of the dataset anyway) to calculate the corresponding prediction for its Y value.
Graphing linear regression
The Linear Regression calculator provides a generic graph of your data and the regression line.
While the graph on this page is not customizable, Prism is a fully-featured research tool used for publication-quality data visualizations. See it in action in our How To Create and Customize High Quality Graphs video!
Graphing is important not just for visualization reasons, but also to check for outliers in your data. If there are a couple points far away from all others, there are a few possible meanings: They could be unduly influencing your regression equation or the outliers could be a very important finding in themselves. Use this outlier checklist to help figure out which is more likely in your case.
For more information
Liked using this calculator? For additional features like advanced analysis and customizable graphics, we offer a free 30-day trial of Prism
Some additional highlights of Prism include the ability to:
- Use the line-of-best-fit equation for prediction directly within the software
- Graph confidence intervals and use advanced prediction intervals
- Compare regression curves for different datasets
- Build multiple regression models (use more than one predictor variable)
Looking to learn more about linear regression analysis? Our ultimate guide to linear regression includes examples, links, and intuitive explanations on the subject.
Prism's curve fitting guide also includes thorough linear regression resources in a helpful FAQ format.
Both of these resources also go over multiple linear regression analysis, a similar method used for more variables. If more than one predictor is involved in estimating a response, you should try multiple linear analysis in Prism (not the calculator on this page!).
Want to see what regression analysis looks like from start to finish?
Check out our video below on How to Perform Linear Regression in Prism.
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