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This scatterplot shows the relationship between vertical drop of slope (in feet) and adult weekend lift ticket price for various ski resorts in the Middle Atlantic states, as of November 2004.24
a. Looking at the scatterplot, which of these is your best guess for the mean vertical drop of the slopes: 600, 1,000, 1,400, or 1,800?
b. Looking at the scatterplot, which of these is your best guess for the standard deviation of vertical drop of the slopes: 3, 30, 300, or 3,000?
c. Looking at the scatterplot, which of these is your best guess for the mean lift ticket price: $10, $20, $30, or $40?
d. Looking at the scatterplot, which of these is your best guess for the standard deviation of lift ticket price: $0.15, $1.50, $15, or $150?
e. Which one of these best describes the situation?
There is no relationship between vertical drop and lift ticket price at these resorts.
There is a slight tendency for ski resorts with more of a vertical drop to charge more for a lift ticket.
There is a moderately strong relationship between vertical drop and price of a lift ticket at these resorts.
Knowing the vertical drop, we can predict lift ticket price almost exactly for these resorts.
f. Blue Knob’s slope has a vertical drop of 1,025 feet. Use the regression equation to predict the lift ticket price there.
g. In fact, the lift ticket price at Blue Knob was $40. Is this relatively expensive or inexpensive for the size of the drop there?
h. What is the size of the residual in your prediction in part (f), if the actual price was $40?
i. Is this residual size quite a bit smaller than usual, fairly typical, or quite a bit larger than usual for this regression?
j. The y-intercept is about 20, predicting a lift ticket price of $20 for a downhill ski resort whose slopes have a vertical drop of zero. How often would this actually be the case: never, occasionally, or frequently?
k. If vertical drop had been measured in meters instead of feet, would the value of the correlation r increase, decrease, stay the same, or change in a way that is unforeseeable?
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