What Is the Difference between Linear and Nonlinear Equations in Regression Analysis?

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 is the difference between a linear and nonlinear regression equation?

Linear Regression Equations

Linear regression requires a linear model. No surprise, right? But what does that really mean?

A model is linear...

Using Probability Plots to Understand Laser Games Scores

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 is transformed into a linear plot. To do this, the cumulative density function (the so-called CDF, cumulating all probabilities below a given threshold) is used (see the graph below). For a normal...

Is Your Statistical Software FDA Validated for Medical Devices or Pharmaceuticals?

We're frequently asked whether Minitab has been validated by the U.S. Food and Drug Administration (FDA) for use in the pharmaceutical and medical device industries.

Minitab does extensive testing to validate our software internally, but Minitab’s statistical software is not—and cannot be—FDA-validated out-of-the-box.

Nobody's can.

It is a common misconception that software vendors can go through a certification process to achieve FDA software validation. It's simply not true.

Software vendors who claim their products are FDA-validated should be scrutinized. It is up to the software purchaser to...

My Favorite Quality Tool: Process Mapping

We all seem to have our favorite statistical or quality improvement tool. Jim Frost wrote a tribute to regression analysis. Dawn Keller seems to enjoy control charts. Eston Martz discusses reliability analysis and the Weibull distribution pretty regularly. So, I started thinking … what’s my favorite quality tool?

I’ve always been drawn to process mapping, or what's sometimes referred to as ‘flow charting.’ Even before I started my work with Minitab and learning about quality improvement techniques, I’ve considered myself somewhat of a visual learner. I notice myself explaining things to others...

Truth, Beauty, Nonparametrics & Symmetry Plots

  “Shall I compare thee to a standard normal distribution?
  Thou art more symmetric and more bell-shaped…”  — Melvin Shakespeare (William’s lesser-known statistician brother)

The Greek philosopher Aristotle believed that symmetry was one of the primary elements of the universal ideal of beauty. Over 2000 years later, emerging research seems to bear him out. 

Studies suggest we tend to be more attracted to people with symmetrical bodies. Using motion-capture technology to record the movements of people dancing to a popular song, one recent study concluded that we even prefer those who dance...

Why the Weibull Distribution Is Always Welcome

In college I had a friend who could go anywhere and fit right in. He'd have lunch with a group of professors, then play hacky-sack with the hippies in the park, and later that evening he'd hang out with the local bikers at the toughest bar in the city. Next day he'd play pickup football with the jocks before going to an all-night LAN party with his gamer pals. On an average weekend he might catch an all-ages show with the small group of straight-edge punk rockers on our campus, or else check out a kegger with some townies, then finish the weekend by playing some D&D with his friends from the...

Will the Weibull Distribution Be on the Demonstration Test?

Over on the Indium Corporation's blog, Dr. Ron Lasky has been sharing some interesting ideas about using the Weibull distribution in electronics manufacturing. For instance, check out this discussion of how dramatically an early first-failure can affect an analysis of a part or component (in this case, an alloy used to solder components to a circuit board). 

This got me thinking again about all the different situations in which the Weibull distribution can help us make good decisions. The main reason Weibull is so useful is that it's very flexible in fitting different types of data, because it...

Lightsaber Capability Analysis: Picking the Right Distribution

In my previous post, you learned how to prepare your data for capability analysis in Minitab. Now let's see where we need to go in the statistical software to run the correct Capability Analysis.

When it comes to capability analysis, Minitab offers a few different choices. We offer Normal Capability Analysis for when your data follow a normal distribution. If your data follow a different distribution, such as the Weibull distribution, there's Non-normal Capability Analysis. We also offer Binomial Capability and Poisson Capability for when you are looking to produce a process capability report...

Choosing the Right Distribution Model for Reliability Data

Recently I've been refreshing my knowledge of reliability analysis, which is the use of data to assess a product's ability to perform over time. Quality engineers typically use reliability analysis to predict the likelihood that a certain percentage of products will fail over a given amount of time.   

Statistical software will do the calculations involved in a reliability analysis, but there's a catch: first, you must choose a distribution to model your data. Put plainly, you need to tell the software to base its analysis on the normal distribution, the Weibull distribution, or perhaps some...

Transformers! Normal Data in Disguise?

Many statistical analyses require an assumption of normality. In cases when your data are not normal, sometimes you can apply a function to make your data approximately normal so that you can complete your analysis.

If you've seen any of the Transformers movies, you know that these extraordinary robots can, with some Hollywood magic, turn themselves into apparently normal items like cars and appliances.

You may not get quite the same special-effects thrill, but when you have an extraordinary (i.e., non-normal) data set, Minitab Statistical Software can pull a Transformers-like metamorphosis on...

What I Learned from Treating Childbirth as a Failure

My wife and I are expecting a baby girl soon—very soon, in fact, as in "Will this blog post be published before the baby is born?" soon. The due date given is May 19th, but we stat geeks know that a point estimate just isn't good enough...we want probability intervals that reflecting the uncertainty in the data.

I found a chart that lets me know the number of babies born to "spontaneous labor" by each week of pregnancy, but I'm interested in more precision than just the week.  I converted the data to days instead of weeks (for example Week 40 starts on day 280 and runs through day 286), and...

When a P-value Might Be Misleading

In my last post, I talked about the danger of excluding interactions between factors in ANOVA and DOE models. Let’s now look at what can happen if you exclude an important factor altogether.

Warning: misleading high p-value up ahead...

Minitab regularly hosts webinars on different statistical topics. Let’s suppose we want to evaluate if certain webinar topics are more popular than others, so we collect data on the number of people who register for various sessions, including t-tests, control charts, design of experiments and Weibull analysis. Here’s an example of what the data might look like:


The Graphical Benefits of Identifying the Distribution of Your Data

In my previous post, we identified the distribution of the body fat data. Today, we're going to explore several benefits of knowing the distribution, with a special emphasis on creating informative graphs! After all, if you are not sure what a specific distribution with such and such parameters looks like, a graph gives you the picture!

Using the Distribution Information

So far, we have identified the distribution and the parameter values for the body fat data from 14-year-old girls.

3-Parameter Weibull Distribution:

  • Shape = 1.85718
  • Scale = 14.07043
  • Threshold = 16.06038

How does that help us? What...

How to Identify the Distribution of Your Data using Minitab

I love all data, whether it’s normally distributed or downright bizarre. However, many people are more comfortable with the symmetric, bell-shaped curve of a normal distribution. It is not as intuitive to understand a Gamma distribution, with its shape and scale parameters, as it is to understand the familiar Normal distribution with its mean and standard deviation.

However, it's a fact of life that not all data follow the Normal distribution. Hey, a lot of stuff is just abnormal...er...non-normally distributed. How to understand and present the practical implications of your non-normal...

More March Madness with Minitab and Nonlinear Regression

What, it’s still not March? Blasted February, why won't you just end already! Oh well, at least it gives us time for some more data analysis.

In my last post, I used Minitab’s Fitted Line Plot to create a regression model that predicted the probability of a home team winning a basketball game based on the difference in ranks between the two teams. This model had an r-squared value of 95.2%, which is great. But since it’s still February, let’s spend some time trying to improve on that number.

Improving the Regression Model

My last model used the difference in ranks between two teams. This assumes...

Weibull Wobble? Process Capability Analysis with Nonnormal Data

Manufacturers need to make items that meet a customer’s standards, or they’ll soon be out of business. That’s why quality engineers devote a good deal of time to making sure that processes are able to meet those standards. 

The first step is to make sure your process is stable. After all, you can’t predict the performance of an unstable process. But you can predict and improve on a stable process. 

If we know our process is stable, we can use a statistical technique called process capability analysis to see if the process is capable of consistently producing products that meet...