I re-ran the analysis of my ski speeds discussed in an earlier post. The model looks like this:
lm(formula = mph ~ season_days + temp, data = ski) Residuals: Min 1Q Median 3Q Max -1.76466 -0.20838 0.02245 0.15600 0.90117 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 4.414677 0.199258 22.156 < 2e-16 *** season_days 0.008510 0.001723 4.938 5.66e-06 *** temp 0.027334 0.003571 7.655 1.10e-10 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.428 on 66 degrees of freedom Multiple R-squared: 0.5321, Adjusted R-squared: 0.5179 F-statistic: 37.52 on 2 and 66 DF, p-value: 1.307e-11
What this is saying is that about half the variation in my ski speeds can be explained by the temperature when I start skiing and how far along in the season we are (season_days). Temperature certainly makes sense—I was reminded of how little glide you get at cold temperatures skiing to work this week at -25°F. And it’s gratifying that my speeds are increasing as the season goes on. It’s not my imagination that my legs are getting stronger and my technique better.
The following figure shows the relationship of each of these two variables (season_days and temp) to the average speed of the trip. I used the melt function from the reshape package to make the plot:
melted <- melt(data = ski, measure.vars = c('season_days', 'temp'), id.vars = 'mph') q <- ggplot(data = melted, aes(x = value, y = mph)) q + geom_point() + facet_wrap(~ variable, scales = 'free_x') + stat_smooth(method = 'lm') + theme_bw()
Last week I replaced by eighteen-year-old ski boots with a new pair, and they’re hurting my ankles a little. Worse, the first four trips with my new boots were so slow and frustrating that I thought maybe I’d made a mistake in the pair I’d bought. My trip home on Friday afternoon was another frustrating ski until I stopped and applied warmer kick wax and had a much more enjoyable mile and a half home. There are a lot of other unmeasured factors including the sort of snow on the ground (fresh snow vs. smooth trail vs. a trail ripped up by snowmachines), whether I applied the proper kick wax or not, whether my boots are hurting me, how many times I stopped to let dog teams by, and many other things I can’t think of. Explaining half of the variation in speed is pretty impressive.