I replicated your findings. The R-Square for the #1 team for the years 1974-2013 is 0.1173. As a biochemist, you should know that that is not good at all. Plus, as I've suspected above, if you restrict the sample to the years 1985-2013, the coefficient of the time variable actually becomes negative. This means that for these years, dominance has actually gone down.Moxie wrote: Well then I challenge you to do your own research, create your own chart, and paint a prettier picture. As a former biochemist, I am quite comfortable discussing my data, and listening to criticism. I can do without the trash talk. I'll admit that I am not an expert in statistic, but at least I am making some attempt to define the situation, rather than just talking a bunch of $h!T. This is F1 Technical after all.; am I to be the only one to undertake a technical analysis of the competition itself? I am open to collaboration.
I refer you to the thread "Statistical Analysis of F1 Competition"
This chart uses the same data, but shows the standard deviation from the linear regressions
https://drive.google.com/file/d/0BzuAgI ... sp=sharing
On the other hand, if you extend the sample all the way to 1958-2013 (there was no WCC before), the R-Square value is 0.0308. That is downright terrible. Your sample selection biased the results in favor of the point you were making (and as I mentioned, even then it is very weak).
To the uninitiated: Regression via ordinary least squares fits a line to the data by minimizing the distance between said line and each data point. The distance between the line and a point is called a residual. You want this (or to be more precise, the sum of squared residuals) to be as small as possible. As a diagnostic tool to determine if the regression result are actually valid and the model fits the data, you use an indicator called R-Square. It's the relation of Explained Sum of Squares to the Total Sum of Squares. It is one of the simplest diagnostic tools and not the only thing that's important, but for such a ridiculously simple type of regression such as this one it's more than sufficient. It's bounded between 0 and 1. 1 is perfect, zero means that your model explains nothing. So a value of 0.0308 means the model is virtually useless. Even in the social sciences good models have an R-Square of at least 0.4-0.6. In the physical sciences this is far higher.