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.