Final answer:
The sign of the correlation coefficient (-0.56) shows a negative correlation between weight and fuel efficiency, meaning as weight increases, fuel efficiency decreases. About 31% of the variation in fuel efficiency can be explained by car weight.
Step-by-step explanation:
The numerical value for the correlation between weight and cost is not provided in the question, but the concept of correlation can be explained. A positive correlation means as one variable increases, the other does too; a negative correlation means the variables move in opposite directions.
The sign of the correlation (-0.56) between body weight and fuel efficiency for cars indicates a negative correlation. This means as the vehicle's weight increases, the fuel efficiency decreases, and vice versa. The correlation coefficient, r, measures the strength and direction of this linear relationship. Given the correlation coefficient of -0.56, we can calculate the coefficient of determination (r²) which equals 0.3136, or 31 percent. This indicates that 31 percent of the variation in fuel efficiency can be explained by the weight of the cars.