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"he 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= -0.972. The least-squares regress veight as the explanatory variable and miles per gallon as the response variable is y= -0.0070x + 44.4405. Complete parts (a) and (b) below. E Click the icon view the data table. a) What proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per gallon? "he 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) Interpret the coefficient of determination. - X % of the variance in Round to one decimal V is V by the linear model. Data Table Full data eot

"he 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= -0.972. The least-squares regress veight as the explanatory variable and miles per gallon as the response variable is y= -0.0070x + 44.4405. Complete parts (a) and (b) below. E Click the icon view the data table. a) What proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per gallon? "he 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) Interpret the coefficient of determination. - X % of the variance in Round to one decimal V is V by the linear model. Data Table Full data eot

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 \( r = -0.972 \). The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is \( \hat{y} = -0.0070x + 44.4405 \). 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 \(\ 94.5 \%\). (Round to one decimal place as needed.) (b) Interpret the coefficient of determination. \(\ 94.5 \% \) of the variance in gas mileage is explained 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 | 18 | | Car 2| 3,984 | 17 | | Car 3| 3,530 | 20 | | Car 4| 3,175 | 22 | | Car 5| 2,580 | 26 | | Car 6| 3,730 | 18 | | Car 7| 2,605 | 25 | | Car 8| 3,772 | 17 | | Car 9| 3,310 | 20 | | Car 10| 2,991 | 25 | | Car 11| 2,752 | 26 | **Explanation:** The task asks for the proportion of variability in miles per gallon that can be explained by the car's weight. The coefficient of determination, denoted as \( r^2 \), represents this proportion. It is derived from the linear correlation coefficient \( r \), where \( r^2 = (-0.972)^2 \approx 0.945 \), which equals 94.5%. This indicates that 94.5% of the variability in gas
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 \( r = -0.972 \). The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is \( \hat{y} = -0.0070x + 44.4405 \). 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 \(\ 94.5 \%\). (Round to one decimal place as needed.) (b) Interpret the coefficient of determination. \(\ 94.5 \% \) of the variance in gas mileage is explained 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 | 18 | | Car 2| 3,984 | 17 | | Car 3| 3,530 | 20 | | Car 4| 3,175 | 22 | | Car 5| 2,580 | 26 | | Car 6| 3,730 | 18 | | Car 7| 2,605 | 25 | | Car 8| 3,772 | 17 | | Car 9| 3,310 | 20 | | Car 10| 2,991 | 25 | | Car 11| 2,752 | 26 | **Explanation:** The task asks for the proportion of variability in miles per gallon that can be explained by the car's weight. The coefficient of determination, denoted as \( r^2 \), represents this proportion. It is derived from the linear correlation coefficient \( r \), where \( r^2 = (-0.972)^2 \approx 0.945 \), which equals 94.5%. This indicates that 94.5% of the variability in gas
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