Final answer:
The coefficient of determination measures the proportion of the variation in one variable explained by the linear relationship with another variable.
Step-by-step explanation:
The coefficient of determination (r²) measures the proportion of the variation in one variable that can be explained by the linear relationship with another variable. In this case, the coefficient of determination of the expanded data set can be calculated using the formula r² = (r)² where r is the correlation coefficient. Given that the coefficient of determination is the square of the correlation, or r², we can calculate it by squaring the correlation coefficient. So for this data set, r² = (-0.56)² = 0.3136 ≈ 0.31 or 31 percent. This means that approximately 31 percent of the variation in fuel efficiency can be explained by the car's weight.