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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The accompanying data represent the weights of various domestic cars and their gas mileages in the city. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is \( r = -0.984 \). The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is \( \hat{y} = -0.0066x + 43.3954 \). Complete parts (a) and (b) below.

(a) What proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per gallon?

The proportion of the variability in miles per gallon explained by the relation between weight of the car and miles per gallon is \(\square\)%.

(Round to one decimal place as needed.)

(b) Interpret the coefficient of determination.

\(\square\%\) of the variance in \(\square\) is \(\square\) by the linear model.

(Round to one decimal place as needed.)

**Data Table**

| Car   | Weight (pounds), \( x \) | Miles per Gallon, \( y \) |
|-------|--------------------------|---------------------------|
| Car 1 | 3,765                    | 19                        |
| Car 2 | 3,984                    | 18                        |
| Car 3 | 3,530                    | 21                        |
| Car 4 | 3,175                    | 23                        |
| Car 5 | 2,580                    | 27                        |
| Car 6 | 3,730                    | 18                        |
| Car 7 | 2,605                    | 26                        |
| Car 8 | 3,772                    | 18                        |
| Car 9 | 3,310                    | 21                        |
| Car 10| 2,991                    | 24                        |
| Car 11| 2,752                    | 25                        |

**Note:**

- The correlation coefficient \( r = -0.984 \) indicates a strong negative linear relationship between the weight of the car and the miles per gallon.
- The least-squares regression line equation is given as \( \hat{y} = -0.0066x + 43.3954 \), where \( \hat{y} \) is the predicted miles per gallon and \( x \) is the car’s
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Transcribed Image Text:The accompanying data represent the weights of various domestic cars and their gas mileages in the city. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is \( r = -0.984 \). The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is \( \hat{y} = -0.0066x + 43.3954 \). Complete parts (a) and (b) below. (a) What proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per gallon? The proportion of the variability in miles per gallon explained by the relation between weight of the car and miles per gallon is \(\square\)%. (Round to one decimal place as needed.) (b) Interpret the coefficient of determination. \(\square\%\) of the variance in \(\square\) is \(\square\) by the linear model. (Round to one decimal place as needed.) **Data Table** | Car | Weight (pounds), \( x \) | Miles per Gallon, \( y \) | |-------|--------------------------|---------------------------| | Car 1 | 3,765 | 19 | | Car 2 | 3,984 | 18 | | Car 3 | 3,530 | 21 | | Car 4 | 3,175 | 23 | | Car 5 | 2,580 | 27 | | Car 6 | 3,730 | 18 | | Car 7 | 2,605 | 26 | | Car 8 | 3,772 | 18 | | Car 9 | 3,310 | 21 | | Car 10| 2,991 | 24 | | Car 11| 2,752 | 25 | **Note:** - The correlation coefficient \( r = -0.984 \) indicates a strong negative linear relationship between the weight of the car and the miles per gallon. - The least-squares regression line equation is given as \( \hat{y} = -0.0066x + 43.3954 \), where \( \hat{y} \) is the predicted miles per gallon and \( x \) is the car’s
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