An engineer wanted to determine how the weight of a car affects gas mileage. The following data represent the weights of various cars and their gas mileages. Complete parts $($a$)$ through $($d$).$

$\backslash$table$[[$Car$,$Miles per$],[$Weight $($pounds$),,],[$A$,2655,26,],[$B$,3000,22,],[$C$,3175,22,],[$D$,3680,19,],[$E$,3590,18,]]$

critical values for the correlation coefficient

Critical Values for Correlation Coefficient

$\backslash$table$[[n,],[3,0\mathrm{.}997],[4,0\mathrm{.}950],[5,0\mathrm{.}878],[6,0\mathrm{.}811],[7,0\mathrm{.}754],[8,0\mathrm{.}707],[9,0\mathrm{.}666],[10,0\mathrm{.}632],[11,0\mathrm{.}602],[12,0\mathrm{.}576],[13,0\mathrm{.}553],[14,0\mathrm{.}532],[15,0\mathrm{.}514],[16,0\mathrm{.}497],[17,0\mathrm{.}482],[18,0\mathrm{.}468],[19,0\mathrm{.}456],[20,0\mathrm{.}444],[21,0\mathrm{.}433],[22,0\mathrm{.}423],[23,0\mathrm{.}413],[24,0\mathrm{.}404],[25,0\mathrm{.}396],[26,0\mathrm{.}388],[27,0\mathrm{.}381],[28,0\mathrm{.}374],[29,0\mathrm{.}367],[30,0\mathrm{.}361]]$

$($a$)$ Determine which variable is the explanatory variable and which is the response variable.

The explanatory variable is the miles per gallon and the response variable is the weight.

The explanatory variable is the weight and the response variable is the miles per gallon.

$($b$)$ Draw a scatter diagram of the data. Choose the correct scatter plot.

A$.$

C$.$

B$.$

D

mpg

inpy

$-.$

$2$

$($c$)$ Compute the linear correlation coefficient between the weight of a car and its miles per gallon.

$r=$

$($Round to three decimal places as needed.$)$

$($d$)$ Does a linear relation exist between the weight of a car and its miles per gallon in the city?

A$.$ There appears to be a positive linear association because $r$ is positive and greater than the critical value.

B$.$ There appears to be a neqative linear association because $r$ is positive