Hello Canisius Math department! I hope everyone had a good Easter weekend. Today, I get the chance to share with you something I’ve worked very hard on. I previously completed my undergraduate thesis on alternate regression techniques in the presence of multicollinearity.

In many fields of study there exist questions of cause and effect. What causes interest rates to rise? Can real estate prices be forecasted? What affects agriculture positively and negatively, and what can be done? In all of these problems, multicollinearity may be present. By definition, multicollinearity is the presence of a near linear combination, or dependence, between two or more explanatory variables in regression analysis. Imagine you’re trying to forecast the sales of your food truck during the summer. You correctly assume that nicer weather will bring more customers, so weather is one explanatory variable. As you ponder what else affects sales, you think about events. If there’s a festival or market going on, that would bring more customers as well, so events becomes a second variable. However. when the weather is nicer, that would impact the number of people at the events, or even the events themselves!

In the common regression method of Ordinary Least Squares, presence of multicollinearity causes serious problems which impact the results of the study. Alternative methods to approach this problem are Ridge and Lasso regression. After explaining the problems with Ordinary Least Squares, we will walk through these remedies and discuss the advantages and drawbacks of using each one. I hope you enjoy!

https://drive.google.com/open?id=1bXlHmphbvdX4Wuw8fv5sz7eu6amdv7AF

This is a thorough, informational presentation that was very well put together. My first introduction to multicollinearity was studying linear regression in one of my psychology courses. We knew how to identify multicollinearity, but we did not look at it from a mathematical standpoint. You provide a very nice example of linear regression by OLS and the problem surrounding multicollinearity. I like how you included an example about finding the scalar k for Ridge Regression. Also, I was finally able to understand the mathematics behind VIF, even though we used tolerance (1/VIF) to identify multicollinearity. Overall, this was a great presentation that easily helps the reader understand this complex topic.

Great slides! They are shown in a nicely organized manner and each layout made sense. Multicollinearity is not an easy topic and I applaud you not just presenting it for 480 but doing it for your thesis. Great work. I liked how you built up the presentation by using a simple example from multiple linear regression based on factors that have a statistically significant relationship on sales for a company, then went into matrices and Ridge Regression. Great idea and great work.

Olivia, this is a great presentation. You made a complicated idea easily understood for people who have not studied it much or even at all. There was just enough background information so we could understand the concepts. It was very organized and I like how you used separate boxes to distinguish the definitions. It is important to understand definitions when learning about multicollinearity, otherwise the concepts might never be understood. I wish we could have seen this in person so you could explain even further. Great job!

This was a fantastic presentation, and the flow of it really helped for understanding of a complex topic. It was very interesting to see subtopics of other classes I’m taking/have taken combined in order to show the results. I additionally appreciated all the additional resources you mentioned, as I anticipate seeking some of those out as I prepare for 480 and thesis.

Wonderful presentation!! You did a great job at taking a complex topic and making it easier to understand for those that may not have as much background in the topic. The way you put your presentation together made it easy to follow and comprehend. The work that you put into this has really paid off, good work!

This was extremely well put together! You can tell not only that you know your stuff, but that you put this in a way that made it much more intuitive to understand. I really like how you would explain the complexities of the mathematics in just a few simple sentences that were digestible to someone with little experience in stats. In fact, I have a stats quiz tomorrow morning and you just helped me study!

Wow! Your presentation was very impressive! You were able to effectively pack a ton of information into one presentation that was very nicely put together. I found your topic very interesting, and your presentation clearly demonstrates your strong understanding of this topic. I really appreciated your example with the grocery store, since it gave me a good idea of the purpose of multicollinearity before you went into how it all works. It is very obvious how much effort you put into this presentation. You should be very proud! Amazing job!

This is awesome stuff. I can’t really remember what we did for multicollinearity in Econometrics, but it definitely wasn’t this. All these crazy methods for fixing statistical issues, especially in regression, are all really cool to me. Excellent work! You really know what you’re talking about. The math behind this stuff is pretty complex. Very impressive.

I like your presentation. Because I am interested in machine learning especially data pre

diction model so your presentation is especially curious for me. I knew just linear regression with one variable so multicollinearity is new to me. If we can set up several variables such as time and weather in the slide, the prediction model would be more accurate. That is not only interesting but useful way. Great job!!

Great work, the presentation was very impressive and jam-packed with information. I have never had the chance to study statistics so a lot of this felt like Greek to me, but it was refreshing to have the English descriptions of what was going on in conjunction with the stats of it all. I figured modeling was complex, but I hadn’t figured that the techniques would be so linear-algebraic.

Great presentation, and congrats!