Step 1 :The given data is the weights of six selected cars in hundreds of pounds and their corresponding fuel efficiency in miles per gallon (mpg). The weights are [30, 30, 37, 32, 30, 29] and the fuel efficiencies are [23, 21, 18, 21, 25, 22].
Step 2 :We need to determine the correlation coefficient between the weight of a car and the fuel efficiency. The correlation coefficient, denoted by \(r\), is a measure of the strength and direction of the linear relationship between two variables.
Step 3 :Using the given data, we calculate the correlation coefficient \(r\).
Step 4 :The calculated correlation coefficient \(r\) is approximately -0.794. This indicates a strong negative correlation between the weight of a car and its fuel efficiency. This means that as the weight of a car increases, its fuel efficiency tends to decrease.
Step 5 :Final Answer: The correlation coefficient between the weight of a car and the fuel efficiency is \(\boxed{-0.794}\).