Question

a set of data is collected, pairing the number of games a team plays to the number of errors committed. using the least-squares regression method, which is the line of best fit? line a line b line c line d

Explanation:

Step1: Recall Least-Squares Regression

The least - squares regression line (line of best fit) minimizes the sum of the squared vertical distances between the data points and the line. Visually, it should pass through the "middle" of the data points, balancing the distances above and below the line.

Step2: Analyze Each Line

• Line a: This line has a very steep slope. The data points are not evenly distributed around it; most points are below it, so it is not the line of best fit.
• Line b: Observe the data points (the blue dots). Line b seems to pass through or be very close to the middle of the data points. The vertical distances from the data points to line b are relatively balanced in terms of being above and below the line.
• Line c: This line has a shallower slope than what would be appropriate for the trend of the data points. The data points are mostly above this line, so it does not represent the best fit.
• Line d: This line is almost horizontal, which does not match the positive trend of the data (as the number of games increases, the number of errors generally increases). So it is not the line of best fit.

Answer:

line b