Paolo Gironi - notes on data analysis, SEO, statistics and retro computing

Multiple Regression Analysis, Explained Simply

Does content length help ranking? Do backlinks bring traffic? Do faster pages convert better?
Taken one at a time, these questions almost always get the same lazy answer: “yes, a bit”. The trouble is that in the real world factors never arrive one at a time. Long pages also tend to attract more links; pages with more links are often the most carefully made, and maybe the slowest too. Everything moves together, and the question that really matters is a different one: which of these factors weighs on traffic net of the others?

We saw, talking about correlation, that we can measure how much two variables move together; and with simple linear regression that we can use one to predict the other.
But one correlation at a time is blind to the tangle: it risks handing the same medal to a factor and to its companion, without being able to tell them apart. It is the doorway to a trap we already know, Simpson’s paradox: an association that flips sign or vanishes as soon as we account for a third variable. Multiple regression is the tool that tackles precisely this head-on — many causes together, each measured while holding the others fixed.

The Data: The 4 Scales of Measurement

A question: how many times have we seen — or made — the mistake of calculating the average SERP position for a set of keywords and then using that number as if it were any other piece of data?
The average position is 4.3, keyword A is at 3 and keyword B at 7, “on average we are fourth”.
The problem is that a ranking position is not a number: it is ordinal data. The distance between position 1 and position 3 is not the same as between 3 and 5, and averaging numbers that do not have an interpretable distance — that is truly a meaningless operation.

Before performing any calculation on data, we must ask ourselves: what type of data is this? The answer determines everything we can — and cannot — do downstream. The answer comes from a classification that, although dating back to 1946, remains the foundation of every respectable statistical analysis: the 4 scales of measurement by Stanley Smith Stevens.

The scale of measurement does not serve to describe data: it serves to establish which operations are meaningful on that data. The more information a scale contains, the greater the number of statistical analyses we can apply. This is the criterion that makes Stevens’ classification so powerful and enduring in practice.

Correlation and Simple Linear Regression: the Line, Pearson’s r and R²

The hotter it gets, the more ice cream sells: we all suspect as much. But by how much? If tomorrow the thermometer reads 27 degrees, how many ice creams should we get ready? And, moving onto our own ground: if we raise the campaign budget, how many extra conversions can we expect?

Concepts such as the mean or the standard deviation describe one variable at a time. Questions like these, instead, require us to look at two variables together: that is the job of correlation and simple linear regression, two of the most widely used (and most misunderstood) tools in data analysis.

Time Series Analysis and Forecasting in R

What is meant by a time series?

A time series consists of values observed over a set of sequentially ordered periods. This, for those who do SEO, is already an element of utmost interest.

Website traffic data, considered over a time sequence, is in fact an example of a time series.

Time series analysis is a set of methods that allow us to derive significant patterns or statistics from data with temporal information.

In very general terms, we can say that a time series is a sequence of random variables indexed in time.

The purpose of analyzing a time series can be descriptive (consider decomposing the series to remove seasonality elements or to highlight underlying trends) or inferential, with the latter including forecasting values for future time periods that have not yet occurred.

The Chi-Square Test: Goodness of Fit and Test of Independence

Desktop 5.5% CTR, mobile 2.5%. A difference that looks huge: but is it real, or could it vanish with another month of data?
To answer with numbers rather than gut feeling there is one of the most widely used tests of all, the chi-square test (χ²).

The chi-square test was proposed by Karl Pearson in 1900, and it is widely used to estimate how effectively the distribution of a categorical variable represents an expected distribution (in this case, we talk about the “Goodness of Fit Test”) or to estimate when two categorical variables are independent of each other (and then we talk about the “Test of Independence”).

Such is the importance and widespread use of this test that it was listed by the magazine Scientific American among the 20 most important scientific discoveries of the 20th century.