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. Fuel Weight Efficiency 2685 24 2560 27 2660 29 2790 38 3000 25 3410 22 3640 20 3700 25 3880 21 3900 21 4060 19 4710 15

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
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Author:Carter
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Chapter10: Statistics
Section: Chapter Questions
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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.
Fuel
Weight
Efficiency
2685
24
2560
27
2660
29
2790
38
3000
25
3410
22
3640
20
3700
25
3880
21
3900
21
4060
19
4710
15
Transcribed Image Text: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. Fuel Weight Efficiency 2685 24 2560 27 2660 29 2790 38 3000 25 3410 22 3640 20 3700 25 3880 21 3900 21 4060 19 4710 15
O Part (h)
Identify any outliers, using either the graphical or numerical procedure demonstrated in the textbook. (Select all that apply.)
no outliers
(4710, 15)
(2685, 24)
O (3700, 25)
(2790, 38)
(4060, 19)
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 is creating a curved least squares regression line.
The outlier does not lie directly on the line, but it is close.
The outlier represents a different population of vehicles compared to the rest.
The outlier lies directly on the line, so the error residual (y - ý) is zero.
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.)
ý =
X +
E Part (j)
Compare the correlation coefficients and coefficients of determination before and after removing the outlier, and explain what these numbers indicate about how the model
has changed.
The new linear model is a better fit, because the new correlation coefficient is closer to zero.
The first linear model is a better fit, because the first correlation coefficient is closer to zero.
The new linear model is a better fit, because the new correlation coefficient is farther from zero.
The first linear model is a better fit, because the first correlation coefficient is farther from zero.
O O O O o o
O O
Transcribed Image Text:O Part (h) Identify any outliers, using either the graphical or numerical procedure demonstrated in the textbook. (Select all that apply.) no outliers (4710, 15) (2685, 24) O (3700, 25) (2790, 38) (4060, 19) 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 is creating a curved least squares regression line. The outlier does not lie directly on the line, but it is close. The outlier represents a different population of vehicles compared to the rest. The outlier lies directly on the line, so the error residual (y - ý) is zero. 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.) ý = X + E Part (j) Compare the correlation coefficients and coefficients of determination before and after removing the outlier, and explain what these numbers indicate about how the model has changed. The new linear model is a better fit, because the new correlation coefficient is closer to zero. The first linear model is a better fit, because the first correlation coefficient is closer to zero. The new linear model is a better fit, because the new correlation coefficient is farther from zero. The first linear model is a better fit, because the first correlation coefficient is farther from zero. O O O O o o O O
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