lork - Microsoft Edge tudent/PlayerHomework.aspx?homeworkld $=657389112 \&$ questionld $=1 \&$ flushed $=$ false $\& \mathrm{cld}=7545218 \& \mathrm{ce}$ ions in Math CRN 10106 miranda starling $11 / 21 / 234: 33$ 12.6b HW Question 7, 12.6.38 HW Score: $39.77 \%, 43.75$ of Part 3 of 4 110 points Points: 0 of 10 The following table shows the weights, in hundreds of pounds, for six selected cars. Also shown is the c fuel efficiency, in miles per gallon (mpg), for the car in city driving. Use the data provided in the table to a) through d). $\triangle$ \begin{tabular}{|c|l|l|l|l|l|l|} \hline Weight (hundreds of pounds) & 27 & 32 & 34 & 35 & 32 & 30 \\ \hline Fuel efficiency (mpg) & 24 & 23 & 18 & 21 & 25 & 21 \\ \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 $r=-0.522$. (Type an integer or decimal rounded to three decimal places as needed.) b) Determine whether a correlation exists at $\alpha=0.01$. Choose the correct answer below. A. A linear correlation does not exist. B. A linear correlation exists. c) Determine the equation of the line of best fit for the weight of a car and the fuel efficiency of a car. \[ y=(\square) x+(\square) \text {. } \] (Type an integer or decimal rounded to three decimal places as needed.) View an example Get more help - Clear all Reply
Solution
Step 1 ：Given the weights of the cars in hundreds of pounds as [27, 32, 34, 35, 32, 30] and the fuel efficiency in miles per gallon as [24, 23, 18, 21, 25, 21].
Step 2 ：The correlation coefficient is a measure of the strength and direction of the relationship between two variables. It ranges from -1 to 1, where -1 indicates a strong negative relationship, 1 indicates a strong positive relationship, and 0 indicates no relationship.
Step 3 ：Calculate the correlation coefficient between the weight of a car and the fuel efficiency.
Step 4 ：The correlation coefficient between the weight of a car and the fuel efficiency is calculated to be -0.5224303472635711.
Step 5 ：Round the correlation coefficient to three decimal places.
Step 6 ：Final Answer: The correlation coefficient between the weight of a car and the fuel efficiency is \( \boxed{-0.522} \).
