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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= - 0979 The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is y = -0.0066x+ 43.3079. Complete parts (a) and (b) below. E Click the icon to 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? 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) Interpret the coefficient of determination. % of the variance in V is by the linear model. (Round to one decimal place as needed.)

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= - 0979 The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is y = -0.0066x+ 43.3079. Complete parts (a) and (b) below. E Click the icon to 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? 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) Interpret the coefficient of determination. % of the variance in V is by the linear model. (Round to one decimal place as needed.)

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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Certainly! Here's the transcription suitable for an educational website: --- ### Understanding Correlation and Causation #### Correlation and Causation: The Stork Example - **Remember the stork example?** Correlation does not always imply causation. Correlations may be caused by another variable, often referred to as a lurking or confounding variable. #### Example Study - In June 1957, the Associated Press reported the results of a study conducted by the National Canners Association showing a high correlation between canned applesauce and incidents of polio. #### Historical Data - **The Real Cause of Polio!** - A graph, titled "Typhoid Rate in Canned Sales, 1910" illustrates two lines. One indicates the incidence of typhoid cases (per 100,000 people, vertical axis, from 0 to 80) which decreases from 1910 to 1957. - The other line shows canned sales (in thousands of cases, from 0 to 30,000), which increases over the same period. - The graph may suggest a relationship between these variables, but further analysis is needed to determine causation. ### Linear Regression and Data Interpretation #### Data Analysis of Domestic Cars and Gas Mileage - 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 \( r = -0.979 \). - The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is given by: \[ \hat{y} = -0.0066x + 43.3079 \] - **Tasks to Complete:** 1. **(a)** What proportion of the variability in miles per gallon is explained by the relationship between the weight of the car and miles per gallon? - Calculate this percentage to one decimal place. 2. **(b)** Interpret the coefficient of determination. - Determine the percentage of the variance in the data that is explained by the linear model. ---
Transcribed Image Text:Certainly! Here's the transcription suitable for an educational website: --- ### Understanding Correlation and Causation #### Correlation and Causation: The Stork Example - **Remember the stork example?** Correlation does not always imply causation. Correlations may be caused by another variable, often referred to as a lurking or confounding variable. #### Example Study - In June 1957, the Associated Press reported the results of a study conducted by the National Canners Association showing a high correlation between canned applesauce and incidents of polio. #### Historical Data - **The Real Cause of Polio!** - A graph, titled "Typhoid Rate in Canned Sales, 1910" illustrates two lines. One indicates the incidence of typhoid cases (per 100,000 people, vertical axis, from 0 to 80) which decreases from 1910 to 1957. - The other line shows canned sales (in thousands of cases, from 0 to 30,000), which increases over the same period. - The graph may suggest a relationship between these variables, but further analysis is needed to determine causation. ### Linear Regression and Data Interpretation #### Data Analysis of Domestic Cars and Gas Mileage - 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 \( r = -0.979 \). - The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is given by: \[ \hat{y} = -0.0066x + 43.3079 \] - **Tasks to Complete:** 1. **(a)** What proportion of the variability in miles per gallon is explained by the relationship between the weight of the car and miles per gallon? - Calculate this percentage to one decimal place. 2. **(b)** Interpret the coefficient of determination. - Determine the percentage of the variance in the data that is explained by the linear model. ---
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