World Cup Women’s 10k Classic Nordic Ski Race

The times and ranks of skiers taken at four different distance points (1.3, 4.3, 7.5, and 10k) in a 10k classic race in Trondheim, Norway.

Motivation

The International Ski and Snowboard Federation (FIS), organizes and records a series of events such as the World Cup which exists for all disciplines of FIS such as Nordic Skiing. World Cup races occur every weekend between January and March, with events hosted in different countries. These events consist of multiple different races, held in different disciplines and distances. Nordic skiing is split up into two different techniques, classic and skate, all race weekends have a mixture of skate and classic technique races. The race in this dataset is a womens’ 10k classic race set in Trondheim, Norway. In long distance pieces like 10ks there is often a lot of discussion about pacing. Racers’ times are recorded at different distance intervals throughout the course. I think it is interesting to look at how well racers’ times at different distances predict their rank at the end of the race. I think especially the first time is most interesting to see with regard to the final rank, to see if the same racers who have top times in the first distance have good ranks at the end of the race.

Data Preparation

init-nordicw10k.qmd

Data

Each row of the dataset represents a skier in the womens’ 10k classic ski race in Trondheim. There are 61 racers in the dataset and 20 variables.

W10kTro_2257.csv

Variable	Description
Bib	The bib number of the skier, which also represents the order they started in.
Name	The name of the skier.
NSA	The nation a skier is representing.
Rank1	The rank or placement of skiers at the first distance interval.
Time1	The skier’s time at the first distance interval, measured in minutes.
Diff1	The difference of time between each skier and the first place racer, at the first distance interval, measured in seconds.
Dist1	The distance of the first interval, measured in kilometers.
Rank2	The rank or placement of skiers at the first distance interval.
Time2	The skier’s time at the first distance interval, measured in minutes.
Diff2	The difference of time between each skier and the first place racer, at the second distance interval, measured in seconds.
Dist2	The distance of the second interval, measured in kilometers.
Rank3	The rank or placement of skiers at the third distance interval.
Time3	The skier’s time at the third distance interval, measured in minutes.
Diff3	The difference of time between each skier and the first place racer, at the third distance interval, measured in seconds.
Dist3	The distance of the third interval, measured in kilometers.
Rank4	The rank or placement of skiers at the fourth distance interval.
Time4	The skier’s time at the fourth distance interval, measured in minutes.
Diff4	The difference of time between each skier and the first place racer, at the fourth distance interval, measured in seconds.
Dist4	The distance of the fourth interval, measured in kilometers.
Event	The FIS code assigned to the event.

Questions

1. Create a simple linear regression model of Time4 predicted by Time1. Check the conditions for the model, to assess its variance, linearity, and normality.

2. Find the correlation between Time1 and Rank4. Is there a strong correlation and if so, is it positive or negative?

3. Make a model of Rank4 predicted by Bib. Interpret the coefficient of Bib.

4. Use an ANOVA for means test to decide if there is a considerable difference in the mean time for each time interval. First, perform the test by constructing a one-way ANOVA model for means by hand. Then, check it by running it through R.

References

results{target = “_blank”}