In multiple regression, machine learning, and predictive analytics in general, a common goal is to determine which independent variables contribute significantly to explaining the variability in the dependent variable. Unfortunately, many people fall into the same trap, classifying variable importance by comparing the smallest relative P-values. In this post, we caution modelers of biased and misleading statistics and provide alternatives to discover what predictors could be the best fit for your model.
One business strategy that is finally gaining traction in sports is dynamic pricing. Associated with a poor connotation to users of Uber and Lyft, dynamic pricing, which is also referred to as surge pricing, is a pricing strategy in which businesses set their prices for products or service based on current market demands. This real-time pricing strategy is not a new concept. Travel-related industries such as hotels, rental cars, and airlines have employed this technique for years, as well as more recently in the energy market and sports businesses.
In 2014, Cubs single-game ticket prices at Wrigley Field were set through dynamic pricing, which helped more accurately price tickets for individual games and provides fans with more price options. However, with football season finally back, we decided to look at how a dynamic pricing structure could work for an NFL team. Back in April, the Buffalo Bills announced a new dynamic ticket pricing model for all Bills home games in the 2017 regular season that will adjust ticket prices to better reflect demand throughout the season. With this precedent established, we decided to see how this economic strategy would work for the Houston Texans.
So the lovable kiwi above is a GOOD fruit to help keep you FIT. Can you guess what we are discussing this week? Yup, model goodness-of-fit!
Just because we are able to fit a regression model to a data set does not mean that it is the right model to use. It is imperative to assess the goodness-of-fit of a regression model with determined metrics and graphical displays. What actions then constitute an analysis of goodness-of-fit for a regression model? What can go wrong in the interpretation of the results and the use of a regression model that would be deemed to “fit poorly”? Today, we tackle what makes a regression model well fitting. One quick caveat, this post deals only with models fitted using OLS regression, not maximum likelihood.