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Regression Analysis

Blog posts and articles about regression analysis techniques applied to Lean and Six Sigma quality improvement projects.

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
In Blind Wine Part I, we introduced our experimental setup, which included some survey questions asked ahead of time of each participant. The four questions asked were: On a scale of 1 to 10, how would you rate your knowledge of wine? How much would you typically spend on a bottle of wine in a store? How many different types of wine (merlot, riesling, cabernet, etc.) would you buy regularly (not as... 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
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
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
If betting wasn't allowed on horse racing, the Kentucky Derby would likely be a little-known event of interest only to a small group of horse racing enthusiasts. But like the Tour de France, the World Cup, and the Masters Tournament, even those with little or no knowledge of the sport in general seem drawn to the excitement over its premier event—the mint juleps, the hats...and of course,... Continue Reading
In April 2012, I wrote a short paper on binary logistic regression to analyze wine tasting data. At that time, François Hollande was about to get elected as French president and in the U.S., Mitt Romney was winning the Republican primaries. That seems like a long time ago… Now, in 2014, Minitab 17 Statistical Softwarehas just been released. Had Minitab 17, been available in 2012, would have I... 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
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
If you regularly perform regression analysis, you know that R2 is a statistic used to evaluate the fit of your model. You may even know the standard definition of R2: the percentage of variation in the response that is explained by the model. Fair enough. With Minitab Statistical Software doing all the heavy lifting to calculate your R2 values, that may be all you ever need to know. But if you’re... 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
“Turnovers are like ex-wives. The more you have, the more they cost you.” – Dave Widell, former Dallas Cowboys lineman It doesn’t take witty insight from a former NFL player to realize how big an impact turnovers can have in a football game. Every time an announcer talks about “Keys to the Game,” winning the turnover battle is one of them. And as Cowboys fans know all too well, an ill-timed... 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
I know we lost by 2 touchdowns, but if only you had given Peterson 3 more carries we would have won! Last week, ESPN ran an article about why the running game still matters. They used statistics to show that the more you run the football in the NFL, the more likely you are to win the game. Specifically, if you have a running back who gets at least 20 carries, you win about 70% of the... Continue Reading
by Matthew Barsalou, guest blogger I recently moved, and right after finishing the less-than-joyous task of unpacking I decided to take and break and relax by playing with Minitab Statistical Software.   As a data source I used the many quotes I received from moving companies. I'd invited many companies to look around my previous home, and then they would provide me an estimate with the price... Continue Reading
In my previous post, I highlighted recent academic research that shows how the presentation style of regression results affects the number of interpretation mistakes. In this post, I present four tips that will help you avoid the more common mistakes of applied regression analysis that I identified in the research literature. I’ll focus on applied regression analysis, which is used to... Continue Reading
As Halloween is almost here, I'm ready to check out some Halloween statistics. You can have a lot of fun with Minitab on Halloween. The National Retail Foundation (NRF) released the results of their Halloween Consumer Spending Survey last month. The basics are easy to summarize: Because we have Minitab, we can dig a little deeper into the data. The NRF gives some information about the proportion... Continue Reading