For a statistics class project at a large northeastern university, a student examined the relationship between the following two variables:
x = body weight (in pounds)
y = time to chug a 12- ounce beverage (in seconds)
We'll leave it to you to imagine the beverage. The student collected data from 13 individuals, and those data are in the following table. (This dataset is named chugtime on the website for this book.)
a. Draw a scatterplot of the measurements. Characterize the relationship between chug time and body weight.
b. The heaviest person appears to be an outlier. Do you think that observation is a legitimate observation, or do you think an error was made in recording or entering the data?
c. Outliers should not be thrown out unless there's a good reason, but there are several reasons why it may be legitimate to conduct an analysis without them (for instance, see part (e)). Delete the data point for the heaviest person, and determine a regression line for the remainder of the data.
d. Use the regression line from part (c) to estimate the chug time for an individual who weighs 250 pounds. Do you think this time could be achieved by anybody?
e. Sometimes the relationship between two variables is linear for a limited range of x values and then changes to a different line or curve. Using this idea, draw a sketch that illustrates what you think the actual relationship between weight and chug time might be for the range of weights from 100 to 300 pounds.
f. Discuss plausible reasons why the heaviest person appears to be an outlier with regard to his combination of weight and chug-time measurements.