a) Using the listed old/new mpg ratings, find the best predicted new mpg rating for a car with an old rating of 30 mpg. b) What is the correlation coefficient r and what is the coefficient of determination r squared? c) What is the proportion of variability of the New car mpg ratings explained by the old mpg ratings based on the above data.
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.
Consider the following listed old/new mpg ratings.
Old mpg New mpg
16 15
27 24
17 15
33 29
28 25
24 22
18 16
22 20
20 18
29 26
21 19
a) Using the listed old/new mpg ratings, find the best predicted new mpg
rating for a car with an old rating of 30 mpg.
b) What is the
determination r squared?
c) What is the proportion of variability of the New car mpg ratings explained by the old mpg ratings based on the above data.
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