## Sunday, November 22, 2009

### Engine Displacement and Automotive Performance

I entered all of the data from the SCCOIA website into a spreadsheet and used a random number generator to pick a sample of fifty vehicles from the list of 1845. I then found the cubic inch displacement for each of the vehicles that were randomly chosen.

I made graphs of the displacement (x) and 1/4 mile times times (y), and displacement (x) and 0-60 mph times (y), then looked at the linear regression of the data. Please remember that this does not take into account the weight of the vehicles, gearing, tires, or countless other factors that change the performance of a vehicle.

Interpretation of R and R^2

The correlation coefficient of R is -.4739 for 1/4 mile times, and -0.4791 for 0-60 times. This indicates a negative linear association between the displacement of an engine and its track times. It makes sense that as the displacement gets larger, the times get smaller (quicker).

The coefficient of determination, R^2, is .2246 for 1/4 mile times and .2295 for 0-60 times. This indicates that about 22.5% - 23% of the performance times from these cars are accounted for by the displacement of the engines. This leaves 77% - 78% of the variation in the residuals.

t-Scores and P-Values

The t-scores are 28.95 (1/4 times) and 13.45 (0-60 times) and the P-values are 0.0000000000000000000000000000000048 (1/4 mile times) and 0.00000000000000000071 (0-60 times). This shows that the slope for either line is not zero.

Some interesting highlights from the random sample

The largest displacement was a 1973 Pontiac Firebird with a 455ci engine. The smallest displacement was a 1992 Geo Metro LSi with 61ci engine. The quickest 0-60 time was a 2002 Porsche 911 GT2 with 3.6 seconds. The slowest was a 1967 MG Midget III with 14.7 seconds. The quickest 1/4 mile time was the 2002 911 GT2 with 11.9 seconds. The slowest was the 1992 Geo Metro LSi with 19.4 seconds. The average car from the random sample would have a 212.28 cubic inch engine, go 0-60 in 8.02 seconds and have a 1/4 mile time of 15.91 seconds.