## Linear Regression Calculator

Least Squares Regression Line Calculator - estimates slope & intercept.
Enter observations in box, use a separate line or comma between each measurement.

#### TrendLine Equation

Slope:1
Intercept:1
R-Squared:1

Graph to Show predicted value and degree of fit. Tap or Hover over the trendline in the graph below to get the predicted value of the series for a given value of X.

### Tool Overview - Linear Regression Calculator

This linear regression calculator fits a linear trendline to your data using the least squares technique. It optimizes the fit of the trendline and returns the y-intercept and slope of the line. Then - 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. The calculator also evaluates how well the linear trendline fits the data via the R-squared statistic.

Enter your sample data as a string of numbers - separated by commas or with a new line for each measurement. The linear regression calculator will estimate the slope and intercept of a linear trendline that is the best fit with your data.

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 slop 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.

#### Sharing Results of The Linear Regression 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.