Board Thread:Game Discussion/@comment-31526827-20191027014218/@comment-27170954-20191102175157

Thanks for posting the coefficients.

Yes, negative coefficients just mean larger values have a negative influence on the dependent variable (PR). Increasing acceleration from 2.2 sec to 2.3 should reduce PR. So should an increase in braking. Perfectly logical.

Standard Error is one way to see how well the model fits the observed data. It relates the regression equation to actual data. Smaller is better. Standard Error can be used to approximate the prediction interval – 51.7 is the point estimate, the 95% prediction interval is approximately ±2 x SE, or between 41.7 and 61.7. This means there is a 95 % chance the PR would fall in this range.

Calculation of the real prediction interval is much more complicated – and the interval widens as you deviate from the middle. I don’t even remember how to do it without looking at my old textbooks. It’s been a while…

There is much more to regression than just using the data analysis tool. There are several assumptions about linearity, normality, homoscedasticity, multicollinearity, etc… that would need to be verified before it could be said that 51.7 is a reasonable estimate.

It is easy to see that the independent variables are NOT linearly related to the dependent – make some scatter plots of PR vs. the 4 performance characteristics. There are also groups of cars where the performance parameters stand out from the group – the F1-type cars and the Aussie Supercars for example. There are also probably variables in the PR we can’t see – things FM has not disclosed. Things like this make the standard error larger and complicate estimation. Transforming the data and maybe controlling for certain car types might yield a narrower prediction interval. Really, you cold spend days building a model for this.