Blog posts and articles about the statistical method called Linear Regression and its use in real-world quality projects.

Using a sample to estimate the properties of an entire population
is common practice in statistics. For example, the mean from a
random sample estimates that parameter for an entire population. In linear
regression analysis, we’re used to the idea that the regression coefficients are estimates of the
true parameters. However, it’s easy to forget that R-squared
(R2) is also an estimate.... Continue Reading

I’ve written about the importance of checking your residual plots when performing
linear regression analysis. If you don’t satisfy the assumptions
for an analysis, you might not be able to trust the results. One of
the assumptions for regression analysis is that the residuals are
normally distributed. Typically, you assess this assumption using
the normal probability plot of the residuals.
Are... Continue Reading

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Previously, I showed why there is no R-squared for nonlinear regression. Anyone
who uses nonlinear regression will also notice that there are no P
values for the predictor variables. What’s going on?
Just like there are good reasons not to calculate R-squared for
nonlinear regression, there are also good reasons not to calculate
P values for the coefficients.
Why not—and what to use instead—are the... Continue Reading

Previously,
I’ve written about when to choose nonlinear regression and
how to model curvature with both linear and
nonlinear regression. Since then, I’ve received several
comments expressing confusion about what differentiates nonlinear
equations from linear equations. This confusion is understandable
because both types can model curves.
So, if it’s not the ability to model a curve, what isthe... Continue Reading

There is more than just the p value in a probability plot—the
overall graphical pattern also provides a great deal of useful
information. Probability plots are a powerful tool to better
understand your data.
In this post, I intend to present the main principles of
probability plots and focus on their visual interpretation using
some real data.
In probability plots, the data density distribution... Continue Reading

In regression analysis, you'd like your regression model to have
significant variables and to produce a high R-squared value. This
low P value / high R2 combination indicates that changes
in the predictors are related to changes in the response variable
and that your model explains a lot of the response variability.
This combination seems to go together naturally. But what if
your regression model... Continue Reading

You
know what really gets on my nerves? A lot of things.
That slow, slinky way that cats walk by. Grrrr.
The rude, abrupt arrival of delivery persons in their
obnoxiously loud trucks. (Why do they always pull up
just as I’m settling down for a nap?) Grrrr.
Total strangers who reach down and poke me with fat, clumsy
fingers that reek of antibacterial soap.
Grrrr.
And this one always gets my dander up:... Continue Reading

In Minitab, the Assistant menu is your interactive guide to choosing
the right tool, analyzing data correctly, and interpreting the
results. If you’re feeling a bit rusty with choosing and using a
particular analysis, the Assistant is your friend!
Previously, I’ve written about the new linear model features in Minitab 17. In
this post, I’ll work through a multiple regression analysis example
and... Continue Reading

Nonlinear regression is a very powerful
analysis that can fit virtually any curve. However, it's not
possible to calculate a valid R-squared for nonlinear regression.
This topic gets complicated because, while Minitab statistical software doesn’t calculate R-squared for
nonlinear regression, some other packages do.
So, what’s going on?
Minitab doesn't calculate R-squared for nonlinear models... Continue Reading

By popular demand, Release 17 of Minitab
Statistical Software comes with a new graphical analysis called
the Bubble Plot.
This exploratory tool is great for visualizing the relationships
among three variables on a single plot.
To see how it works, consider the total medal count by country
from the recently completed 2014 Olympic Winter Games. Suppose I
want to explore whether there might be a... Continue Reading

We released Minitab 17 Statistical Software a couple of days ago.
Certainly every new release of Minitab is a reason to celebrate.
However, I am particularly excited about Minitab 17 from a data
analyst’s perspective.
If you read my blogs regularly, you’ll know that I’ve
extensively used and written about linear models. Minitab 17 has a
ton of new features that expand and enhance many types of... Continue Reading

R-squared gets
all of the attention when it comes to determining how well a linear
model fits the data. However, I've stated previously that R-squared is overrated. Is there a different
goodness-of-fit statistic that can be more helpful? You bet!
Today, I’ll highlight a sorely underappreciated regression
statistic: S, or the standard error of the regression. S provides
important information that... Continue Reading

Just
how high should R2 be in regression analysis? I hear
this question asked quite frequently.
Previously, I showed how to interpret R-squared (R2). I
also showed how it can be a misleading statistic because a low
R-squared isn’t necessarily bad and a high R-squared isn’t
necessarily good.
Clearly, the answer for “how high should R-squared be” is . . .
it depends.
In this post, I’ll help you answer... Continue Reading

I’ve
written a number of blog posts about regression analysis and I
think it’s helpful to collect them in this post to create a
regression tutorial. I’ll supplement my own posts with some from my
colleagues.
This tutorial covers many aspects of regression analysis
including: choosing the type of regression analysis to use,
specifying the model, interpreting the results, determining how
well the... Continue Reading

Face it, you love regression analysis as much as I do.
Regression is one of the most satisfying analyses in Minitab:
get some predictors that should have a relationship to a response,
go through a model selection process, interpret fit statistics like
adjusted R2 and predicted R2, and make
predictions. Yes, regression really is quite wonderful.
Except when it’s not. Dark, seedy corners of the data... Continue Reading

For
one reason or another, the response variable in a regression
analysis might not satisfy one or more of
the assumptions of ordinary least squares regression. The
residuals might follow a skewed distribution or the
residuals might curve as the predictions increase. A common
solution when problems arise with the assumptions of ordinary least
squares regression is to transform the response... Continue Reading

by Laerte de Araujo Lima, guest blogger
A few weeks ago, my football friends and I were talking about
the football in the UEFA Champions league (UEFA CL), and what we could
expect for the 2013-14 season.
Some of us believe that the quality of the football played in
the UEFA CL has improved in the last few years, as evidenced by
more goals per match, more teams with strategies based in the
attack... Continue Reading

Imagine
that you’ve studied an empirical problem using linear regression
analysis and have settled on a well-specified, actionable model to
present to your boss. Or perhaps you’re the boss, using
applied regression models to make decisions.
In either case, there’s a good chance a costly mistake is about
to occur!
How regression results are presented can lead decision-makers to
make bad choices. Emre... Continue Reading

John
Tukey once said, “The best thing about being a statistician is that
you get to play in everyone’s backyard.” I enthusiastically
agree!
I frequently enjoy reading and watching science-related
material. This invariably raises questions, involving other
"backyards," that I can better understand using statistics. For
instance, see my post about the statistical analysis of dolphin sounds.
The latest... Continue Reading

We
often think of a relationship between two variables as a straight
line. That is, if you increase the predictor by 1 unit, the
response always increases by X units. However, not all data have a
linear relationship, and your model must fit the curves present in
the data.
This fitted line plot shows the folly of using a line to fit a
curved relationship!
How do you fit a curve to your data?... Continue Reading