Subjects statistics

Line Of Fit 692309

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **Stating the problem:** We are given a scatter plot with points approximately at (1,3), (1,4), (2,3), (2,4), (3,4), (4,6), (5,7), (6,7), (7,8), (8,9), (9,10), and (10,10). We need to identify which graph shows a line that fits this data well. 2. **Understanding line of fit:** A line of fit (or regression line) is a straight line that best represents the data points on a scatter plot. It usually minimizes the distance from all points to the line (least squares method). 3. **Observing the data:** The points show a positive correlation, increasing roughly from bottom left to top right. 4. **Analyzing the given graphs:** - The first graph (top-left) has points that do not match the original data well and the line fits points roughly but not the original data points. - The second graph (bottom-left) has points closer to the original data and the line passes through points from about (1,3) to (9,10), matching the positive trend. - The third graph (top graph) shows a line from (0,0) to (10,2), which is too flat compared to the data. - The middle graph (center) shows a regression line from about (1,2) to (10,10), which fits the data well. - The bottom graph (bottom-left) shows a line starting near (0,3) to (10,8), which is less steep than the data trend. 5. **Conclusion:** The middle graph (center position) best fits the data points given, as its regression line closely follows the increasing pattern from (1,3) to (10,10). Final answer: The graph in the center position shows the line that fits the data best.