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Taking the lid off graphs

The last issue majorred on Trends Analysis from a qual perspective. This time Vincent Jones offers an alternative viewpoint, discussing how regression algorithms can help predict sales performance.

Qualitative researchers are adept at picking up on trends by the very nature of their work, yet clients also rely on quantitative data and its interpretation to help with their crystal ball gazing. Trend analysis is never going to be an easy subject, indeed it’s much easier to write about the past.

“The Moving Finger writes, and having writ, moves on” said Omar Khayyam. What we are left with is a fait accompli, but the very existence of this basic information is invaluable for analysts and statisticians to help gain an understanding of what might happen in the future.

This article will endeavour to show how a qualitative look at quantitative data can produce worthwhile insights. It will examine behaviour over time, so that it is possible to pick out:

  • underlying trends
  • reasons for these trends
  • how they might continue

Analysts think quantitatively, in terms of exact numbers and percentages, but they also see the benefit of looking at the broader picture. Even looking at the graph shapes can be informative.


Some data may look blatantly obvious. Take the chart, above, showing sales of a beer brand over a three and a half year period. The yearly cycle is easy to spot, with peaks over Christmas and New Year, then a dip in January as all those New Year resolutions go out of the window. Yet when we separate long-term trends from seasonality some disturbing signals emerge.

In terms of the overall picture, year-on-year sales look to be declining. There are issues here for the client to address. The first is relatively simple, it needs to ensure correct supplies for customers given seasonal shifts. The other, a longer-term trend, is not so easy to resolve but at least it is fairly easy to spot and should encourage the client to think strategically — maybe looking at alternative research for answers as to why this is happening.


Graphs are a statistician’s meat and blood, but we also see them as an art form — one that we try not to take at face value but look beneath the surface. Seasonality is one measure we use to monitor sales progress and provide a benchmark, but sales over finite periods can be just as valuable. Take a graph, above, that shows a steady increase in sales over time. It’s always tempting to give clients the good news that they’re on to a winner, yet we know that this graph might not necessarily be describing steady growth — more people buying more items over time — and instead represent a leaking bucket. The company in question might be losing eight or nine customers for every ten new customers recruited. We need to investigate further, ascertain whether this is a real problem and if so, what’s causing it, or our client will eventually run out of new customers. In other words, we can’t rely on hard data to give us the whole picture, but it might point us in the direction of further questions to ask and, potentially, solutions.

So what more shapes can we look at? Let’s look at a nicely increasing chart:


We love to see exponential growth, acknowledging that a company is providing what people really want. A typical example would be the UK sales of PCs in the 90s. Looking at the first part of this chart, an analyst might be tempted to tell the client to prepare for more of the same — but could this go on forever? No, the inevitable pattern is the tail-off in the second part of the graph. When this happens, a company may be facing hard times: its existing customers are disappearing and fewer new ones are replacing them. This is the familiar Gompertz trend curve, which occurs when a product is reaching saturation point. There seems to be very little headroom, with all the early adopters taken, and no new talent in sight.

So what are our options as analysts? Well, attacking churn rate is one possibility. Typically this type of trend includes more new customers, but we recognise that some will be lost, too. Our job would be to find out why through quantitative analysis. There might, for instance, be some pockets of population that haven’t been well targeted.

A review of the customer base might show this — but we’d need to distinguish carefully between those uninterested currently and those who just haven’t had the opportunity to try it. The client might find that by creating more headroom — by increasing brand (or product) awareness — they could open up the market for more customers.

And here’s the worst-case scenario. Continuing from the previous chart, my final one could describe the rise and fall of the Betamax market.


This product lost the war. At first it looked on to a winner, but then some bad news caused a quick step change. Competitors took advance of this and ratcheted up their sales. Some reassurance steadied the market, but not for long, and it was followed by freefall. One trend moves into another — we’re back with Omar Khayyam.

So much for the simple stuff, but this doesn’t mean that we can’t do some serious forecasting with trends. Let’s go back to that first graph. To forecast the future direction, we could develop a regression algorithm that not only has a coefficient for time as a whole, but coefficients that differ according to the month. These would represent the differential effect that each month has upon the rest of the year. We’d do this by coupling each month’s coefficient with a binary variable that has a value of 0 for every record except when the data represents the appropriate month.

Just what would we get from this? Well, we’d get a continuation of the trend line, month for month, based upon past behaviour that matches future behaviour pretty well, at least for the next few years. And if we run the regression regularly we’ll always be up to date with our predictions.

We can even improve upon this. This regression model’s errors may not be random, which is what we would like to see with classical regression. The error in the second month may relate to the error in the first month, and so on. Providing a further parameter that takes account of this month-on-month correlation, known as the autocorrelation parameter, can improve the model significantly. A recent success story with this method has been to enable a company to predict sales staff performance, by analysing the career journeys of their successful salespersons, and to set benchmarks quarter-by-quarter, benchmarks that increase as a junior becomes more experienced.

Predictions are, of course, always subject to the unpredictable — but every little bit of regression analysis helps. And for those who’d like a little more information on the quantitative aspects, a good starting point is Chris Chatfield’s ‘Analysis of Time Series’ (Chapman & Hall).


Vincent Jones
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