Section 12.6
Question $10,12.6 .38$
HW Scors: $70.17 \%, 10.53$ of 15 points
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The following table shows the weights, in hundreds of pounds, for six selected cars. Also shown is the corresponding fuel efficiency, in miles per gallon (mpg), for the car in city driving. Use the data provided in the table to complete parts a) through d).
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline Weight (hundreds of pounds) & 30 & 30 & 37 & 32 & 30 & 29 \\
\hline Fuel efficiency (mpg) & 23 & 21 & 18 & 21 & 25 & 22 \\
\hline
\end{tabular}
(i) Click the icon to view the correlation coefficient, $r$, for various values of $n$ and $\alpha$
a) Determine the correlation coefficient between the weight of a car and the fuel efficiency.
The correlation coefficient between the weight of a car and the fuel efficiency is $r=\square$.
(Type an integer or decimal rounded to three decimal places as needed.)
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Answer
Final Answer: The correlation coefficient between the weight of a car and the fuel efficiency is \(\boxed{-0.794}\).
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 \(\boxed{-0.794}\).
