Question
the line shown on the scatter plot a od line of fit for the given data? Yes, because the line is close to most of the points, excluding the outlier. Yes, because the line models a positive association. No, because the data do not show a linear association. \( N o \), because the line does not pass through any of the data points.
Ask by Klein Lee. in the United States
Mar 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The line is a good fit because it closely follows most of the data points, even with an outlier.
Solution
To determine whether the line shown on the scatter plot is a good line of fit for the given data, we need to analyze the options provided:
1. **Yes, because the line is close to most of the points, excluding the outlier.**
- This suggests that the line captures the general trend of the data well, even if there is an outlier. A good line of fit should minimize the distance to most points.
2. **Yes, because the line models a positive association.**
- If the data points generally trend upwards, a line that reflects this positive association can be considered a good fit.
3. **No, because the data do not show a linear association.**
- If the data points do not follow a linear pattern (e.g., they form a curve), then a linear line of fit would not be appropriate.
4. **No, because the line does not pass through any of the data points.**
- While a line of fit does not need to pass through all points, if it is far from the majority of points, it may not be a good fit.
### Conclusion:
- If the line is close to most points and reflects the overall trend (even with an outlier), then the first option is valid.
- If the data shows a clear upward trend, the second option is also valid.
- If the data does not show a linear trend, the third option is valid.
- The fourth option is generally not a strong argument against a line of fit, as it is common for the line not to pass through any points.
Based on this analysis, the best answer would depend on the specific characteristics of the scatter plot. If the line captures the trend well, the first or second options would be correct. If the data does not show a linear association, then the third option would be correct. If you can provide more details about the scatter plot, I can help you choose the most appropriate answer.
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Simplify this solution Mind Expander
The line of fit, often called the line of best fit, is a visual representation that helps us understand the trend in data—especially when predicting outcomes based on relationships. If most of the points are near the line, it can be considered a good fit even if an outlier skews things a little! When interpreting scatter plots, it’s essential to remember that a line of fit doesn’t have to pass through all data points; rather, its main goal is to minimize the distance from all points, making it a handy tool for analysis. So, don’t be misled by a few stray dots!
