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.

g.)For the vehicle that weighs 3000 pounds, find the residual

(y − ŷ).

(Round your answer to two decimal places.) _________

I.)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 _____

Correlation of determination _____

Find the new best fit line.  (Round your answers to four decimal places.)

ŷ = ______    x + _______

Weight	Fuel Efficiency
2695	25
2510	26
2680	29
2770	38
3000	23
3410	24
3640	20
3700	25
3880	21
3900	21
4060	20
4710	16

Answer 1

Independent variable (X) : Weight

Dependent variable (Y) : Fuel efficiency

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	2695	25	7263025	625	67375
	2510	26	6300100	676	65260
	2680	29	7182400	841	77720
	2770	38	7672900	1444	105260
	3000	23	9000000	529	69000
	3410	24	11628100	576	81840
	3640	20	13249600	400	72800
	3700	25	13690000	625	92500
	3880	21	15054400	441	81480
	3900	21	15210000	441	81900
	4060	20	16483600	400	81200
	4710	16	22184100	256	75360
Total	40955	288	144918225	7254	951695

The residual is:

(y − ŷ) = 23 - 26.52 = -3.52

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The data pair (2770, 38) is an outlier. Following table shows the calculations after removing outlier:

	X	Y	X^2	Y^2	XY
	2695	25	7263025	625	67375
	2510	26	6300100	676	65260
	2680	29	7182400	841	77720
	3000	23	9000000	529	69000
	3410	24	11628100	576	81840
	3640	20	13249600	400	72800
	3700	25	13690000	625	92500
	3880	21	15054400	441	81480
	3900	21	15210000	441	81900
	4060	20	16483600	400	81200
	4710	16	22184100	256	75360
Total	38185	250	137245325	5810	846435