The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. The results are displayed in the scatterplot

Question

The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. The results are displayed in the scatterplot

The equation ŷ = 17.4 + 0.5x is called the least-squares regression line because it

A.is least able to make accurate predictions for the data.

B.makes the strongest association between weight and height.

C.minimizes the sum of the squared distances from the actual y-value to the predicted y-value.

D. maximizes the sum of the squared distances from the actual y-value to the predicted y-value

Answer 1

The correct answer is C. The equation ŷ = 17.4 + 0.5x is called the least-squares regression line because it minimizes the sum of the squared distances from the actual y-value to the predicted y-value. In other words, it is the line that best fits the data points in the scatterplot by minimizing the total squared distance between each data point and the line. This line is often used to make predictions about new data that fall within the range of the observed data. Therefore, option C is the correct answer.