Free statistics calculators designed for data scientists. This linear regression calculator:

• Fits Linear Regression Trendline
• Graphs Data vs. Regression Line
• Save & Recycle Data Between Projects

### How To Use The Regression Calculator

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.

You can save your data for use with this calculator and the other calculators 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.

### Interpreting Calculator Results

This calculator fits a linear trendline to your data using the least squares technique. This approach optimizes the fit of the trendline to your data, seeking to avoid large gaps between the predicted value of the dependent variable and the actual value. The 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).

To help you visualize the trend - we display a plot of the data and the trendline 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.

## Least Squares Regression Calculator

Slope:0.9676
Intercept:2.4754
R-Square:0.7171

### Observations

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

### Saved Datasets - Click to Restore

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

#### Sharing Results of The Least Squares Regression Line Calculator

Need to pass an answer to a friend? It's easy to link and share the results of this calculator. 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.

### Real World Linear Regression Analysis

Some practical comments on using regression in real world analysis:

• The linear regression 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.
• Use of a linear regression 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.
• 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 calculation is biased against data points which are located significantly away from the projected trendline. 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).