Regression Analysis

Blog posts and articles about regression analysis methods applied to Lean and Six Sigma projects.

Step 2 in our DOE problem-solving methodology is to design the data collection plan you will use to study the factors in your experiment. Of course, you will have to incorporate blocking and covariates in your experiment design, as well as calculate the number of replications of run conditions needed in order to be confident in your results. We will address these topics in future posts, but for... Continue Reading
I recently guest lectured for an applied regression analysis course at Penn State. Now, before you begin making certain assumptions—because as any statistician will tell you, assumptions are important in regression—you should know that I have no teaching experience whatsoever, and I’m not much older than the students I addressed. I’m just 5 years removed from my undergraduate days at Virginia Tech,... Continue Reading
If you use ordinary linear regression with a response of count data, if may work out fine (Part 1), or you may run into some problems (Part 2). Given that a count response could be problematic, why not use a regression procedure developed to handle a response of counts? A Poisson regression analysis is designed to analyze a regression model with a count response. First, let's try using Poisson... Continue Reading
My previous post showed an example of using ordinary linear regression to model a count response. For that particular count data, shown by the blue circles on the dot plot below, the model assumptions for linear regression were adequately satisfied. But frequently, count data may contain many values equal or close to 0. Also, the distribution of the counts may be right-skewed. In the quality field,... Continue Reading
Ever use dental floss to cut soft cheese? Or Alka Seltzer to clean your toilet bowl? You can find a host of nonconventional uses for ordinary objects online. Some are more peculiar than others. Ever use ordinary linear regression to evaluate a response (outcome) variable of counts?  Technically, ordinary linear regression was designed to evaluate a a continuous response variable. A continuous... Continue Reading
In 2007, the Crayola crayon company encountered a problem. Labels were coming off of their crayons. Up to that point, Crayola had done little to implement data-driven methodology into the process of manufacturing their crayons. But that was about to change. An elementary data analysis showed that the adhesive didn’t consistently set properly when the labels were dry. Misting crayons as they went... Continue Reading
In regression analysis, overfitting a model is a real problem. An overfit model can cause the regression coefficients, p-values, and R-squared to be misleading. In this post, I explain what an overfit model is and how to detect and avoid this problem. An overfit model is one that is too complicated for your data set. When this happens, the regression model becomes tailored to fit the quirks and... Continue Reading
Imagine a multi-million dollar company that released a product without knowing the probability that it will fail after a certain amount of time. “We offer a 2 year warranty, but we have no idea what percentage of our products fail before 2 years.” Crazy, right? Anybody who wanted to ensure the quality of their product would perform a statistical analysis to look at the reliability and survival of... Continue Reading
If you want to use data to predict the impact of different variables, whether it's for business or some personal interest, you need to create a model based on the best information you have at your disposal. In this post and subsequent posts throughout the football season, I'm going to share how I've been developing and applying a model for predicting the outcomes of 4th down decisions in Big... Continue Reading
Statisticians say the darndest things. At least, that's how it can seem if you're not well-versed in statistics.  When I began studying statistics, I approached it as a language. I quickly noticed that compared to other disciplines, statistics has some unique problems with terminology, problems that don't affect most scientific and academic specialties.  For example, dairy science has a highly... Continue Reading
Just 100 years ago, very few statistical tools were available and the field was largely unknown. Since then, there has been an explosion of tools available, as well as ever-increasing awareness and use of statistics.   While most readers of the Minitab Blog are looking to pick up new tools or improve their use of commonly-applied ones, I thought it would be worth stepping back and talking about one... Continue Reading
Previously, I’ve written about how to interpret regression coefficients and their individual P values. I’ve also written about how to interpret R-squared to assess the strength of the relationship between your model and the response variable. Recently I've been asked, how does the F-test of the overall significance and its P value fit in with these other statistics? That’s the topic of this post! In... Continue Reading
In my previous post, I showed you that the coefficients are different when choosing (-1,0,1) vs (1,0) coding schemes for General Linear Model (or Regression).  We used the two different equations to calculate the same fitted values. Here I will focus on showing what the different coefficients represent.  Let's use the data and models from the last blog post: We can display the means for each level... Continue Reading
Since Minitab 17 Statistical Software launched in February 2014, we've gotten great feedback from many people have been using the General Linear Model and Regression tools. But in speaking with people as part of Minitab's Technical Support team, I've found many are noticing that there are two coding schemes available with each. We frequently get calls from people asking how the coding scheme you... Continue Reading
If you’ve checked out What’s New in Minitab 17, you’ve had the chance to see that Conditional Formatting leads the list. If you’ve been reading the Minitab blog, you’ve had the chance to see demonstrations with Marvel’s Avengers and the Human Development Index. But you might not have had a chance to see that you can highlight large standardized residuals from a regression model and that the... Continue Reading
In previous posts, I discussed the results of a recycling project done by Six Sigma students at Rose-Hulman Institute of Technology last spring. (If you’re playing catch up, you can read Part I and Part II.) The students did an awesome job reducing the amount of recycling that was thrown into the normal trash cans across all of the institution’s academic buildings. At the end of the spring... Continue Reading
By Erwin Gijzen, Guest Blogger In my previous post, we assessed the out-of-spec level for a process with capability analysis and visualized process variability using a control chart. Our goal is to reduce variability, but when a process has a multitude of categorical and continuous variables, identifying root causes can be a huge challenge. Analyzing covariance—using the statistical technique... Continue Reading
by Erwin Gijzen, Guest Blogger People who work in quality improvement know that the root causes of quality issues are hard to find. A typical production process can contain hundreds of potential causes. Additionally, companies often produce products with multiple quality requirements, such as dimensions, surface appearance, and impact resistance. With so many variables, it’s no wonder many companies... Continue Reading
This week I'm at the American Society for Quality's World Conference on Quality and Improvement in Nashville, TN. The ASQ conference is a great opportunity to see how quality professionals are tackling problems in every industry, from beverage distribution to banking services.  Given my statistical bent, I like to see how companies apply tools like ANOVA, regression, and especially... Continue Reading
Banned! In February 2015, editor David Trafimow and associate editor Michael Marks of the Journal of Basic and Applied Social Psychology declared that the null hypothesis statistical testing procedure is invalid. They promptly banned P values, confidence intervals, and hypothesis testing from the journal. The journal now requires descriptive statistics and effect sizes. They also encourage large... Continue Reading