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= - 0.977. The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is y = - 0.0061x + 41.3297. 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

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= - 0.977. The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is y = - 0.0061x + 41.3297. 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

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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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

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= - 0.977. The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is
-0.0061x +41.3297. Complete parts (a) and (b) below.
V =
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
is
by the linear model.
(Round to one decimal place as needed.)
Data Table
Full data set
Miles per
Miles per
Weight
(pounds), x
Weight
(pounds), x
Car
Car
Gallon, y
Gallon, y
1
3,765
19
Car
2,605
25
Car 2
3,984
18
Car 8
3,772
18
Car 3
3,530
20
Car 9
3,310
20
Car 4
3,175
22
Car 10
2,991
24
Car 5
2,580
26
Car 11
2,752
25
Car 6
3,730
18
Print
Done
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