MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Concept explainers

Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
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Please label each part

 

SUBPART

**Exploring Weight and Fuel Efficiency in Vehicles** 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 (lbs) | Fuel Efficiency (mpg) | |--------------|-----------------------| | 2685 | 24 | | 2560 | 27 | | 2660 | 29 | | 2790 | 38 | | 3000 | 25 | | 3410 | 22 | | 3640 | 20 | | 3700 | 25 | | 3880 | 21 | | 3900 | 21 | | 4060 | 19 | | 4710 | 15 | In this study, we aim to determine how the weight of a vehicle affects its fuel efficiency. Typically, lighter vehicles tend to have better fuel efficiency, but this data set will help us analyze specific trends and outliers in a small sample of vehicles.
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Transcribed Image Text:**Exploring Weight and Fuel Efficiency in Vehicles** 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 (lbs) | Fuel Efficiency (mpg) | |--------------|-----------------------| | 2685 | 24 | | 2560 | 27 | | 2660 | 29 | | 2790 | 38 | | 3000 | 25 | | 3410 | 22 | | 3640 | 20 | | 3700 | 25 | | 3880 | 21 | | 3900 | 21 | | 4060 | 19 | | 4710 | 15 | In this study, we aim to determine how the weight of a vehicle affects its fuel efficiency. Typically, lighter vehicles tend to have better fuel efficiency, but this data set will help us analyze specific trends and outliers in a small sample of vehicles.
**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) - [ ] (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 (\( y - \hat{y} \)) 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.) - \( \hat{y} = \) [______]x + [______] --- **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.
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Transcribed Image Text:**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) - [ ] (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 (\( y - \hat{y} \)) 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.) - \( \hat{y} = \) [______]x + [______] --- **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.
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