Final answer:
The coefficient of determination, or r², is a measure of the proportion of the variation in the dependent variable that can be explained by the independent variable. In this case, the coefficient of determination is 0.3136 or approximately 31%, indicating the strength of the relationship between body weight and fuel efficiency in the sample of cars.
Step-by-step explanation:
The coefficient of determination, also denoted as r², is a measure of the proportion of the variation in the dependent variable that can be explained by the independent variable in a linear regression model. It represents the strength of the relationship between the two variables.
In this case, the coefficient of determination, also known as r², is the square of the correlation coefficient, or r, which is given as -0.56. Therefore, r² = (-0.56)² = 0.3136. This means that approximately 31% of the variation in fuel efficiency can be explained by the relationship between body weight and fuel efficiency in the sample of 2,012 model cars.
It appears that you're referring to the coefficient of determination (2r 2) in the context of linear regression, which represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s)