Most roller coasters get their speed by dropping down a steep initial incline, s

Question

Most roller coasters get their speed by dropping down a steep initial incline, so it makes sense that the height of that drop might be related to the speed of the coaster. Below is a scatterplot of top speed and largest drop for 108 roller coasters around the world along with regression output. Simple linear regression results: Dependent Variable: Speed Independent variable: Drop Speed = 35.24402 + 0.19865676 Drop Sample size: 108 R (correlation coefficient) = 0.93686836 R-sq = 0.87772233 Estimate of error standard deviation: 4.896213 a. Find and interpret the correlation coefficient. b. Suppose the height of the drop was recorded in meters. Find the correlation coefficient in this case. c. Suppose that the speed of the coaster is the predictor variable and the height of the drop is the response. Find the correlation coefficient in this case. d. The Top Drill Dragster seems to be an outlier. Based on the scatterplot, would you consider this observation to be a regression outlier or an influential point?

Explanation / Answer

(a) According to the given output, the correlation coefficient is R=0.9369.

(b) The correlaton coefficient does not change with change of scale, so the correlation remains same as R=0.9369

(c) The correlation coefficient for x and y is same as that of y and x, so it still remains R=0.9369

(d) Based on the scatterplot, it is not an outlier but just an influential point as it lies in the close approximity of the regression line drawn.

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