Question

olympic_running contains the winning times (in seconds) in each Olympic Games sprint, middle-distance and long-distance track events from 1896 to 2016. a. Plot the winning time against the year for each event. Describe the main features of the plot. b. Fit a regression line to the data for each event. Obviously the winning times have been decreasing, but at what average rate per year? c. Plot the residuals against the year. What does this indicate about the suitability of the fitted lines? d. Predict the winning time for each race in the 2020 Olympics. Give a prediction interval for your forecasts. What assumptions have you made in these calculations?

Answer 1

The question focuses on plotting Olympic running times, fitting regression lines, predicting future values using the least-squares regression line, and interpreting percentiles in the context of running races.

Step-by-step explanation:

The student is seeking assistance with several statistical and data analysis concepts related to Olympic running times. The description of the question suggests tasks such as plotting data, fitting regression lines, analyzing residuals, predicting future values, and understanding percentiles. In one part, the question asks about fitting a regression line to Olympic running times and finding the average rate of decrease per year. The line's slope will indicate this rate. In another part, they are asked to find the correlation coefficient to assess the significance of the decrease in times.

For predicting times, the equation of the least-squares regression line can be used to estimate the times for a given year, assuming the future follows the same pattern as past data. Additionally, students are asked to interpret percentiles within the context of race times, with lower percentiles indicating faster running times.