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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**Educational Website 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 \( r = -0.983 \). The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is \( \hat{y} = -0.0075x + 46.5061 \). Complete parts (a) through (c) 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 ______%. (Round to one decimal place as needed.)

**(b)** Construct a residual plot to verify the requirements of the least-squares regression model. Choose the correct graph below.

- **A**: A horizontal residual plot
- **B**: A residual plot with a pattern
- **C**: A random residual plot
- **D**: A diagonal residual plot

**(c)** Interpret the coefficient of determination and comment on the adequacy of the linear model.

\[ \text{__}% \text{ of the variance in } y \text{ is } \_\_\_\_ \text{ by the linear model. The least-squares regression model appears to be } \_\_\_\_, \text{ based on the residual plot. \newline (Round to one decimal place as needed.)}\]

**Data Table:**

| Car   | Weight (pounds), \( x \) | Miles per Gallon, \( y \) |
|-------|--------------------------|--------------------------|
| Car 1 | 3,765                    | 18                       |
| Car 2 | 3,984                    | 17                       |
| Car 3 | 3,530                    | 21                       |
| Car 4 | 3,175                    | 23                       |
| Car 5 | 2,550                    | 21                       |
| Car 6 | 3,730                    | 18                       |
| Car 7 | 2,605                    | 26                       |
| Car 8 | 3,772                    | 17                       |
| Car 9 | 3,310                    | 21                       |
| Car
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Transcribed Image Text:**Educational Website 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 \( r = -0.983 \). The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is \( \hat{y} = -0.0075x + 46.5061 \). Complete parts (a) through (c) 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 ______%. (Round to one decimal place as needed.) **(b)** Construct a residual plot to verify the requirements of the least-squares regression model. Choose the correct graph below. - **A**: A horizontal residual plot - **B**: A residual plot with a pattern - **C**: A random residual plot - **D**: A diagonal residual plot **(c)** Interpret the coefficient of determination and comment on the adequacy of the linear model. \[ \text{__}% \text{ of the variance in } y \text{ is } \_\_\_\_ \text{ by the linear model. The least-squares regression model appears to be } \_\_\_\_, \text{ based on the residual plot. \newline (Round to one decimal place as needed.)}\] **Data Table:** | Car | Weight (pounds), \( x \) | Miles per Gallon, \( y \) | |-------|--------------------------|--------------------------| | Car 1 | 3,765 | 18 | | Car 2 | 3,984 | 17 | | Car 3 | 3,530 | 21 | | Car 4 | 3,175 | 23 | | Car 5 | 2,550 | 21 | | Car 6 | 3,730 | 18 | | Car 7 | 2,605 | 26 | | Car 8 | 3,772 | 17 | | Car 9 | 3,310 | 21 | | Car
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