Question

the arm span and foot length were measured (in centimeters) for each of the 19 students in a statistics class. the results are displayed in the scatterplot. the equation \\( \hat { y } = - 7.61 + 0.19 x \\) is called the least - squares regression line because it passes through each data point. minimizes the sum of the squared residuals. maximizes the sum of the squared residuals. is least able to make accurate predictions for the data.

Explanation:

The least - squares regression line is defined as the line that minimizes the sum of the squared residuals. Residuals are the differences between the observed \(y\) - values (in this case, foot length) and the predicted \(\hat{y}\) - values (from the equation \(\hat{y}=-7.61 + 0.19x\)). It does not pass through each data point (as seen from the scatter - plot). Maximizing the sum of squared residuals would be a non - sensical line for prediction, and it is not the least able to make accurate predictions (in fact, it is the best - fitting line in the sense of minimizing the sum of squared errors).

Answer:

minimizes the sum of the squared residuals.