Do heavier cars really use more gasoline? Suppose a car is chosen at random. Letxbe the weight of the car (in hundreds of pounds), and letybe the miles per gallon (mpg).

x2946334723403452y2819261329172114

Complete parts (a) through (e), givenx=304,y=167,x²=12,244,y²=3757,xy=5944,andr0.9285.

(a)

Draw a scatter diagram displaying the data.

A scatter diagram has a horizontal axis labeled "x(weight of the car (in hundreds of pounds))" with values from 23 to 52 and a vertical axis labeled "y(miles per gallon)" with values from 13 to 29. The scatter diagram has 8 points. A pattern goes up and right from(23, 13)to(52, 29).

A scatter diagram has a horizontal axis labeled "x(weight of the car (in hundreds of pounds))" with values from 23 to 52 and a vertical axis labeled "y(miles per gallon)" with values from 13 to 29. The scatter diagram has 8 points. A pattern goes down and right from(23, 29)to(52, 13).

A scatter diagram has a horizontal axis labeled "x(weight of the car (in hundreds of pounds))" with values from 13 to 29 and a vertical axis labeled "y(miles per gallon)" with values from 23 to 52. The scatter diagram has 8 points. A pattern goes up and right from(13, 23)to(29, 52).

A scatter diagram has a horizontal axis labeled "x(weight of the car (in hundreds of pounds))" with values from 13 to 29 and a vertical axis labeled "y(miles per gallon)" with values from 23 to 52. The scatter diagram has 8 points. A pattern goes down and right from(13, 52)to(29, 23).

(b)

Verify the given sumsx,y,x²,y²,xy, and the value of the sample correlation coefficientr. (Round your value forrto four decimal places.)

x=y=x²=y²=xy=r=

(c)

Findx, andy. Then find the equation of the least-squares line=a+bx. (Round your answers to four decimal places.)

x=y==+x

(d)

Graph the least-squares line. Be sure to plot the point (x,y) as a point on the line.

A graph containing a trend line and a point has a horizontal axis labeled "x(weight of the car (in hundreds of pounds))" with values from 13 to 29 and a vertical axis labeled "y(miles per gallon)" with values from 23 to 52. The trend line enters the window in the first quadrant, goes down and right, passes through the approximate point(14.5, 47.5),passes through the approximate point(27.8, 27.7),and exits the window in the first quadrant. The approximate point(20.9, 38)is plotted on the trend line.

A graph containing a trend line and a point has a horizontal axis labeled "x(weight of the car (in hundreds of pounds))" with values from 13 to 29 and a vertical axis labeled "y(miles per gallon)" with values from 23 to 52. The trend line enters the window in the first quadrant, goes up and right, passes through the approximate point(13.5, 26.4),passes through the approximate point(27.6, 48.6),and exits the window in the first quadrant. The approximate point(20.9, 38)is plotted on the trend line.

A graph containing a trend line and a point has a horizontal axis labeled "x(weight of the car (in hundreds of pounds))" with values from 23 to 52 and a vertical axis labeled "y(miles per gallon)" with values from 13 to 29. The trend line enters the window in the first quadrant, goes up and right, passes through the approximate point(26, 13.5),passes through the approximate point(49, 27.6),and exits the window in the first quadrant. The approximate point(38, 20.9)is plotted on the trend line.

A graph containing a trend line and a point has a horizontal axis labeled "x(weight of the car (in hundreds of pounds))" with values from 23 to 52 and a vertical axis labeled "y(miles per gallon)" with values from 13 to 29. The trend line enters the window in the first quadrant, goes down and right, passes through the approximate point(26, 27.8),passes through the approximate point(49, 14.5),and exits the window in the first quadrant. The approximate point(38, 20.9)is plotted on the trend line.

(e)

Find the value of the coefficient of determinationr². What percentage of the variation inycan beexplainedby the corresponding variation inxand the least-squares line? What percentage isunexplained? (Round your answer forr²to four decimal places. Round your answers for the percentages to two decimal place.)

r²=explained%unexplained%

(f)

Suppose a car weighsx=33(hundred pounds). What does the least-squares line forecast fory= miles per gallon? (Round your answer to two decimal places.)

mpg