Free statistics calculators designed for data scientists. This Least Squares Regression Calculator:

- Generate Trend Line Parameters
- Graphs Data vs. Trend Line
- Save & Recycle Data Between Projects

Intercept:2.4754

R-Square:0.7171

Can be comma separated or one line per data point; you can also cut and paste from Excel.

Saved in your browser; you can retrieve these and use them elsewhere on this site.

Need to pass an answer to a friend? It's easy to link and share the results of this tool. Hit calculate - then simply cut and paste the url after hitting calculate - it will retain the values you enter so you can share them via email or social media.

This is a online regression calculator for statistical use. Enter your data as a string of number pairs, separated by commas. Enter each data point as a separate line. Then hit calculate. The linear regression calculator will estimate the slope and intercept of a trendline that is the best fit with your data.

This page includes a regression equation calculator, which will generate the parameters of the line for your analysis. It can serve as a slope of regression line calculator, measuring the relationship between the two factors. This tool can also serve as a sum of squared residuals calculator to give you a perspective on fit & accuracy.

You can save your data for use with this webpage and the similar tools on this site. Just hit the "save data" button. It will save the data in your browser (not on our server, it remains private). It will appear on the list of saved datasets below the data entry panel. To retrieve it, all you need to do is click the "load data" button next to it.

This linear regression calculator fits a trend-line to your data using the least squares technique. This approach optimizes the fit of the trend-line to your data, seeking to avoid large gaps between the predicted value of the dependent variable and the actual value. The Least Squares Regression Calculator will return the slope of the line and the y-intercept. It will also generate an R-squared statistic, which evaluates how closely variation in the independent variable matches variation in the dependent variable (the outcome). For a deeper view of the mathematics behind the approach, here's a regression tutorial.

To help you visualize the trend - we display a plot of the data and the trend-line we fit through it. If you hover or tap on the chart (in most browsers), you can get a predicted Y value for that specific value of X.The equation of the line is of particular interest since you can use it to predict points outside your original data set. Similarly, the r-squared gives you an estimate of the error associated with effort: how far the points are from the calculated least squares regression line.

Some practical comments on real world analysis:

- The modeling process only looks at the mean of the dependent variable. This is important if you're concerned with a small subset of the population, where extreme values trigger extreme outcomes.
- Data observations must be truly independent. Each observation in the model must truly stand on its own. Two common pitfalls - space and time. The first - clustering in the same space - is a function of convenience sampling. The model can't predict behavior it cannot see and assumes the sample is representative of the total population. If you attempt to use the model on populations outside the training set, you risk stumbling across unrepresented (or under-represented) groups. Clustering across time is another pitfall - where you re-measure the same individual multiple times (for medical studies). Both of these can bias the training sample away from the true population dynamics.
- Using a linear model assumes the underlying process you are modeling behaves according to a linear system. This is often not the case; many engineering and social systems are driven by different dynamics better represented by exponential, polynomial, or power models. Keep this in mind when you use the Least Squares Regression Calculator - are you fitting the correct curve?
- The R-squared metric isn't perfect, but can alert you to when you are trying too hard to fit a model to a pre-conceived trend.
- On the same note, the linear regression process is very sensitive to outliers. The Least Squares Regression Calculator is biased against data points which are located significantly away from the projected trend-line. These outliers can change the slope of the line disproportionately.
- On a similar note, use of any model implies the underlying process has remained 'stationary' and unchanging during the sample period. If there has been a fundamental change in the system, where the underlying rules have changes, the model is invalid. For example, the risk of employee defection varies sharply between passive (happy) employees and agitated (angry) employees who are shopping for a new opportunity.

The underlying calculations and output are consistent with most statistics packages. It applies the method of least squares to fit a line through your data points. The equation of the regression line is calculated, including the slope of the regression line and the intercept. We also include the r-square statistic as a measure of goodness of fit. This equation can be used as a trendline for forecasting (and is plotted on the graph).

Want to know more? This page has some handy linear regression resources.