Question: Use the worksheet Rollercoaster fall 08.MTW. Is there a relationship between the Height of the tallest hill and the maximum Speed?

a) Give a scatterplot of speed (y-axis) and height (x-axis). Describe the relationship between speed and height by describing the form, direction and scatter of this scatterplot.

b) Determine the simple linear regression line to predict maximum speed by height of tallest hill.

c) What percent of variation in maximum speed can be explained by this regression equation?

d) Test the null hypothesis \[{{H}_{0}}:{{\beta }_{1}}=0\] against the alternative hypothesis \[{{H}_{a}}:{{\beta }_{1}}\ne 0\]. Give the test statistic, p-value, decision and conclusion describing what this test means.

e) A certain rollercoaster has the tallest hill at 200 feet. What would be the predicted maximum speed of this rollercoaster?

f) Give a 95% prediction interval for the prediction of this rollercoaster.