he resulting information was used to produce two models for predicting miles per gallon in the city (mpg_city), one based on the engine displacement (in cubic inches) and a second one based the power of the engine (in horsepower).
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.
A consumer advocacy group recorded several variables on 140 models of cars.
The resulting information was used to produce two models for predicting miles per gallon in the city (mpg_city), one based on the engine displacement (in cubic inches) and a second one based the power of the engine (in horsepower).
Model 1: mpg vs engine displacement
The regression equation is
mpg_city=33.5 - 0.063*displacement
S = 3.20422
R-squared = 66.1%
Model 2: mpg vs horsepower
The regression equation is
mpg_city=32.3 - 0.0572*horsepower
S = 3.30539
R-squared = 55.1%
The variable horsepower is better because it has a higher residual standard error (S=3.30539).
The variable horsepower is better because it has a higher residual standard error (S=3.30539) and a lower R-square (55.1%).
The displacement variable is better because it has a higher R-square (66.1%).
The displacement variable is better because it has a lower estimate for the residual standard error (S=3.20422).
The displacement variable is better because it has a lower estimate for the residual standard error (S=3.20422) and a higher R-square (66.1%).
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