Friday, August 23, 2019

Median-based Trend Analysis – despite being Industry Standard – must be Statistically Challenged

(Click on the image to enlarge)

Ryan, a new college graduate with co-concentrations in Economics and Math, is interviewing for the Market Data Analyst position with a major Research firm.

Question # 1
Interviewer: These two graphs are derived off the same housing market and reflect the same time period. Why do they look so dissimilar? In order to keep the conversation more professional, let’s address the Monthly Median Sale Price as the Champion or Champ and the Monthly Median Sale Price per Square Feet as the Challenger.

Ryan: This dissimilarity proves that an industry standard Champ must always be validated or statistically challenged. A prudent market analyst must not take a set of established assumptions for granted; instead, such assumptions should be subjected to frequent tests and validations.

Question # 2
Interviewer: Why do you think that is important? What’s wrong with a time-tested Champ? Why do you need to introduce an untested Challenger?

Ryan: The Challenger helps identify any on-going shifts in the market; for example, when the prospective buyers are gradually moving towards smaller homes, the demand pattern shifts. The Champ will not capture and reflect that shift in the demand pattern, but the Challenger definitely will. That is why the Champ must be meaningfully challenged.

Question # 3
Interviewer: Why is the double top bearish? Shouldn't the double bottom be bearish as well?

Ryan: A double top is bearish because it fails to break out of the congestion, generally trending downward. A double bottom, on the other hand, is bullish as it’s a breakout event with an up-sloping linear trend and potential for new highs.  

Question # 4
Interviewer: Explain the difference between the two in more quantitative terms.

Ryan: After peaking at $320,000, the Champ remains sideways, congesting between $300,000 and $310,000. The Challenger trend is almost diametrically opposite with an extremely bullish up-sloping double bottom, even eclipsing the prior high of $180/SF. The moving average is confirming the breakout as well.

Question # 5
Interviewer: If you have to show one of the two graphs to our clients, which one would you choose and why?

Ryan: Obviously, the Challenger graph, as it captures and depicts the underlying fundamentals of the market.  

Question # 6
Interviewer: Is there a missing piece in this presentation that would explain as to why these two solutions are diverging? If so, how would you present that data?

Ryan: Yes, the Monthly Median Home Size (SF) is missing. The movement of SF would explain why they are diverging. I would use a simple table showing all three monthly data variables, without having to show these two-dimensional graphs.   

Question # 7
Interviewer: Why do you think the bullish R-squared is so much higher than its bearish counterpart?

Ryan: Because that’s the right trendline for that slope of the curve. The bearish one does not demonstrate a linear trend so the resulting R-squared is low.

Question # 8
Interviewer: In that case, what type of trendline would you fit and how much difference would that make?

Ryan: I would fit a polynomial trendline of the 6th order, expecting fairly similar results.   
Interviewer: Give me a minute and let me check it out. Yes, you are right; it’s 0.794. That’s great data visualization. Congrats!

Question # 9
Interviewer: Would you use the median-based analysis in business decision-making? If not, how would you improve upon it?

Ryan: The median-based analysis is necessary (for quick and dirty analysis) but not sufficient in taking business decisions. I would use an extended percentile data curve like the 5th to 95th, without the outliers.   

Interviewer: Did you learn data analysis and modeling on your own?

Ryan: No. My mom is a consulting Economist so I get to learn a lot from her.

Interviewer: So, who do we hire – you or your mom?

Ryan: Got to be me because it’s BOGO.

Thank you,

Sid Som, MBA, MIM
Homequant, Inc.   

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