A line of fit is a straight line drawn through a scatter plot that best represents the general trend of the data. It doesn't necessarily pass through every point but aims to minimize the overall distance between the line and the data points. This line is helpful in visualizing the relationship between the variables rep...
Visualizing the Scatter Plot
Before we delve into finding the best line of fit, let's visualize the given data points: (1, 7), (2, 5), (3, 3), (3, 7), (4, 1), (5, 5), (6, 3), and (9, 3). Imagine plotting these points on a coordinate plane. You'll notice that the data points don't perfectly align in a straight line, but they exhibit a general downward trend.
The Goal: Minimize Distance
Our goal is to find a line that minimizes the overall distance between the line and all the data points. This means the line should be as close as possible to most of the points, with roughly an equal number of points above and below the line.
Evaluating the Answer Choices
Let's examine the answer choices provided:
* **(2, 5) and (6, 3):** If we draw a line through these two points, it seems to roughly follow the downward trend of the data. Many of the points lie near this line, and it does a decent job of representing the overall relationship.
* **(2, 5) and (4, 1):** This line would have a steeper slope than the previous option. While it passes through two points, it doesn't seem to capture the general trend of the data as effectively.
* **(1, 7) and (9, 3):** This line would have a more gradual slope than the first option. Although it captures the downward trend, it seems to be too far from many of the data points, making it a less accurate representation.
* **(1, 7) and (5, 5):** This line, like the previous one, has a more gradual slope. While it passes through two points, it doesn't appear to follow the overall trend of the data as well as other options.
Conclusion
Based on a visual assessment, the line passing through **(2, 5) and (6, 3)** appears to be the best line of fit for the given data. It captures the general downward trend, minimizes the overall distance to the points, and provides a good representation of the relationship between the variables.
Important Considerations
It's important to note that finding the best line of fit can be subjective to some degree, particularly when dealing with relatively small datasets. More sophisticated methods like regression analysis can provide a more statistically accurate line of fit. These methods use mathematical formulas to minimize the overall distance between the line and the data points, providing a more precise and objective representation of the relationship between variables.