People who responded to a July 2004 Discovery Channel poll named the 10 best rol

Question

People who responded to a July 2004 Discovery Channel poll named the 10 best roller coasters in the United States. Among the data collected for these coasters were the length of the initial drop (in feet) and the duration of the ride (in seconds). A regression to predict duration from drop has r = 0.35, the regression analysis gives the model: duration-hat = 91.033 + 0.242 drop a) What are the variables in this regression and what are their units? b) What is that symbol above duration and why is it there? c) What units does the slope have? d) Give an interpretation of the slope. e) A new roller coaster advertises an initial drop of 200 feet. How long would you predict the ride lasts? f) Another coaster with a 150-foot initial drop advertises a 2-minute ride. Is this longer or shorter than you’d expect? By how much? Explain.

Explanation / Answer

a) What are the variables in this regression and what are their units?

Answer : length of the initial drop (in feet) and the duration of the ride (in seconds)

b) What is that symbol above duration and why is it there?

Answer : hat since duration is a predicted variable.

c) What units does the slope have?

Answer : feet

d) Give an interpretation of the slope.

Answer : As duration increases by 1 second the drop will increase by 0.242 feet.

e) A new roller coaster advertises an initial drop of 200 feet. How long would you predict the ride lasts?

Answer : duration-hat = 91.033 + 0.242 *200 = 139.433 seconds

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