In a race the probability that tom wins is the probability that mathew wins is and the probability that

es) as a function of time (in minutes). Who wins the race? How do you know? Imagine you were watching the race and had to announce it over the radio, write a little story describing the race.

mile at an average of 62.3 mi/h (27.8 m/s) on a track of planks set over railroad ties in the draft of a Long Island Railroad train. In 1985, a record was set for this type of “motor pacing” by Olympic cyclist John Howard who pedaled at 152.2 mi/h (68.04 m/s) in the wake of a race car at Bonneville Salt Flats. The race car had a modified tail assembly designed to reduce the air drag on the cyclist. Assume that the mass of bicycle plus rider is 72.3 kg in each case.

there was no Age and/or Sex entered) has been created. It is called Newmarket_Cleaned.csv. Data file: Newmarket_Cleaned.csv (Links to an external site.) . Direct HTTP link: https://unh.box.com/shared/static/p8x4xlbean3rlslmfskfu74fe89yjui8.csv Please use it for this problem. Consider the “Model 4” developed in class, which contained Age, Age^2, and Sex as independent variables. First re-create this model with the cleaned dataset (you will need to create the Age^2 column; you can verify your model summary against the one from class), and then proceed with this problem. Make the necessary changes to the model to incorporate Year as a categorical explanatory variable (you may need to change how R interprets the variable, before running this model). Does the year of the race seem to be related to mean finishing time, after taking into account the other variables in Model 4? Use the 0.05 significance level. Explain your work/logic, and key output to support your answer. Using the updated model, after accounting for age and sex, what is the expected difference in finishing times for runners from 2008 versus runners from 2004? Using the updated model, after accounting for age and sex, what is the expected difference in finishing times for runners from 2014 versus 2011? In the above, the directions are to treat Year as a categorical variable. Explain how the regression model would be different if it instead were treated as a numeric variable. What are the assumptions being made about the effect of Year in the two different approaches?