Question

6. More Mentos, more mess? When Mentos are dropped into a newly opened bottle of Diet Coke, carbon dioxide is released from the Diet Coke very rapidly, causing the Diet Coke to be expelled from the bottle. Using 16-ounce (2-cup) bottles of Diet Coke, two statistics students dropped either 2, 3, 4, or 5 Mentos into a randomly selected bottle, waited for the fizzing to stop, and measured the number of cups remaining in the bottle.64 Then, they subtracted this measurement from the original amount in the bottle to calculate the amount of Diet Coke expelled (in cups). The scatterplot shows the relationship between y = amount expelled (in cups) and x = number of Mentos, along with the least-squares regression line. The standard deviation of the residuals for this model is s= 0.067. Interpret this value.

Answer 1

The standard deviation of the residuals is a measure that can be interpreted as how well the given set of data points fit with the model (the model is the regression line).

In this case, the value gives us an idea of how much the amount of Diet Coke expelled (in cups) could vary from the expected amount expelled according to the model.

It is like a measure of the error of the regression line's predictions.