Question

We are interested in exploring the relationship between the weight of a vehicle and its fuel efficiency (gasoline mileage). The data in the table show the weights, in pounds, and fuel efficiency, measured in miles per gallon, for a sample of 12 vehicles.

Weight	Fuel Efficiency
2715	26
2520	24
2630	29
2790	38
3000	23
3410	25
3640	21
3700	27
3880	21
3900	19
4060	21
4710	15

• Part (b)

  r = -0.71 (correlation coefficient).
  Yes, it is significant
• Part (c) Find the equation of the best fit line. (Round your answers to four decimal places.)       ŷ = ________x + _______

Part (e)

What percent of the variation in fuel efficiency is explained by the variation in the weight of the vehicles, using the regression line? (Round your answer to the nearest whole number.)
%

Part (g)

For the vehicle that weighs 3000 pounds, find the residual

(y − ŷ).

(Round your answer to two decimal places.)


Does the value predicted by the line underestimate or overestimate the observed data value?

underestimate or overestimate    

Part (i)

The outlier is a hybrid car that runs on gasoline and electric technology, but all other vehicles in the sample have engines that use gasoline only. Explain why it would be appropriate to remove the outlier from the data in this situation.

The outlier lies directly on the line, so the error residual (y − ŷ) is zero. The outlier represents a different population of vehicles compared to the rest.     The outlier is creating a curved least squares regression line. The outlier does not lie directly on the line, but it is close.

Remove the outlier from the sample data. Find the new correlation coefficient and coefficient of determination. (Round your answers to two decimal places.)

correlation coefficient
coefficient of determination

Find the new best fit line. (Round your answers to four decimal places.)
ŷ = __  x + __

Answer 1