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 regression line treating weight as the explanatory variable and miles per gallon as the response variable is y=−0.0070x+44.4405. Complete parts (a) and (b) below. LOADING... 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 nothing%. (Round to one decimal place as needed.) (b) Interpret the coefficient of determination. nothing% of the variance in ▼ weight gas mileage is ▼ not explained explained by the linear model. (Round to one decimal place as needed.)
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.
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The linear correlation coefficient between the weight of a car and its miles per gallon in the city is
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