Chart A: Boston Marathon winning times (only men). Comparing Linear, Nonlinear (piecewise) and Exponential regression forecasting techniques. The piecewise model uses splines in the period 1950-1980. Forecasting periods: 10. Prediction interval: 95%

Table 1: Comparing Modeling Techniques: Performance Measures.

From the table below, we can see that the model that best captures nonlinear patterns in this time series data is the piecewise (nonlinear) regression: The highest adjusted R-squared coefficient means that this model is able to explain 88.4% of the variability in the data, against 79.5% of the plain linear and 80.2% of the exponential counterparts.

# A tibble: 3 x 16
  Event  .model r_squared adj_r_squared  sigma2 statistic  p_value    df log_lik
  <fct>  <chr>      <dbl>         <dbl>   <dbl>     <dbl>    <dbl> <int>   <dbl>
1 Men's~ Linea~     0.795         0.793 2.11e+1      365. 3.85e-34     2   -282.
2 Men's~ Expon~     0.802         0.800 1.03e-3      380. 8.48e-35     2    195.
3 Men's~ Piece~     0.884         0.880 1.22e+1      234. 6.83e-43     4   -254.
# ... with 7 more variables: AIC <dbl>, AICc <dbl>, BIC <dbl>, CV <dbl>,
#   deviance <dbl>, df.residual <int>, rank <int>

Source of the data: Department of Econometrics and Business Statistics at Monash University, Australia