Which line fits the data graphed below?
Check the final answer first, then review the worked steps.
Problem
Which line fits the data graphed below?
Answer
B
Step-by-step solution
- Analyze the scatter plot: The graph displays a set of blue data points and three lines labeled A, B, and C. The goal is to determine which of these lines best represents the trend of the data points.
- Examine Line A: Line A is a downward-sloping line (negative slope). It passes through the upper left portion of the data cloud and extends to the lower right. Many data points are far from this line, particularly those in the lower left and upper right sections.
- Examine Line B: Line B is an upward-sloping line (positive slope). It starts in the lower left and moves towards the upper right. This line appears to pass through the general trend of the data points, with points scattered relatively evenly above and below it.
- Examine Line C: Line C is a horizontal line (zero slope) at $y=6$. This line does not capture the overall trend of the data, as the points clearly show an upward movement from left to right.
- Determine the best fit: A line of best fit should minimize the distance between the line and the data points. Line B shows the most consistent relationship with the data, indicating a positive correlation. The points are clustered around Line B, suggesting it is the most representative line for the given data.