The winning time, in the Olympic men\'s 500-meter speed skating race over the ye

Question

The winning time, in the Olympic men's 500-meter speed skating race over the years 1924 to 2006 can be described by the following regression equation, where y is the winning time in seconds and z is the year. Y^= 272.31 - 0.12x (a) Is the correlation between the winning time and year positive or negative? Explain how you know, and explain what that means in the context of this situation. (b) In 2014, the actual winning time for the gold medal was 34.67 seconds. Use the regression equation to predict the winning time for 2014, and compare the prediction to what actually happened. (c) Explain what the slope of -0.12 indicates in terms of how winning times change from one set of Olympic games to the next. Keep in mind that Olympic games occur every four years. (d) Predict the winning time in the 2100 Winter Olympics. Why should we not use this regression equation to predict the winning time for the men's 500-meter speed skating race in the 2100 Winter Olympics?

Explanation / Answer

Here you go, Answers with details of every part mentioned below:

a. The slope is negative, hence, the points will be along the negative slope. This means that
the increasing x would lead to decreasing y. i.e. Correlation between the variables is negative

b. y^ = 272.31 - .12x

Since, x = 2014, the year mentioned , we have
y^ = 272.31 - 0.12*2014 = 30.63 seconds
but, y = 34.67 seconds, So, error = y-y^ = 30.63 - 34.67 = -4.04 seconds
We are undepredicting this by 4.04 seconds

c. This can be interpreted as with each olympics ( i.e. 4 years time - as olympics is held every 4 years), the time takes to win 500m race decreases by .12*4 = .48 seconds

So, every next olympic game, the time taken to win this event drops by .48 seconds.

d.In 2100 year, the y^ = 272.31 - .12*2100 = 20.31 seconds. 2100 year is quiet far from 2006. Being far in time we will have errors in prediction for very high no. of years, leading to inaccurate predictions. Hence, using this equation for predictions for year 2100 may not be right.

Please drop a comment in case you are satisfied with my answer

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