Asked by mani
Check 3 statements that are true.
The line of best fit would have a positive slope.
The line of best fit should have the same number of points above and below it
The slope of the line of best fit could be around - 1/2000
The y-intercept of the line of best fit would be around 45.
There is no correlation between happiness and income.
As a person's income goes up, their happiness trends down
As a person's income goes up, their happiness increases as well in a moderate, positive trend
The line of best fit must pass through at least 2 points on the scatter plot
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All Answers 1
Answered by
GPT-5 mini
AI
I can’t reliably pick the three true statements without seeing the scatterplot or the data (or at least a description of the trend). Could you upload the scatterplot or give the slope/correlation or a short description (e.g., "points slope upward moderately")?
Meanwhile, here are quick rules to help you decide which statements are true once you have the plot or data:
- The sign of the slope (positive or negative) is determined by the overall direction of the points: if they trend upward left→right the slope is positive; downward means negative.
- The least-squares regression line does not have to pass through any particular data points (it can pass through 0, 1, 2, or more points by chance). So “must pass through at least 2 points” is not generally true.
- The regression line does not need to have the same number of points above and below it. However, the sum of the residuals (signed vertical distances) for the least-squares line is zero, which does not imply equal counts.
- The slope magnitude (for example, −1/2000) and the y-intercept (for example, ~45) are numeric estimates you must compute/estimate from the plot or regression output.
- “No correlation” vs. “moderate positive/negative trend”: check the scatter or compute the correlation coefficient. If r ≈ 0 there’s no linear correlation; if r is noticeably positive (e.g., 0.3–0.7) that’s a moderate positive trend; if r is negative, the trend is down.
If you upload the scatterplot or give the data (or summary statistics), I’ll pick the three true statements for you and show the reasoning.
Meanwhile, here are quick rules to help you decide which statements are true once you have the plot or data:
- The sign of the slope (positive or negative) is determined by the overall direction of the points: if they trend upward left→right the slope is positive; downward means negative.
- The least-squares regression line does not have to pass through any particular data points (it can pass through 0, 1, 2, or more points by chance). So “must pass through at least 2 points” is not generally true.
- The regression line does not need to have the same number of points above and below it. However, the sum of the residuals (signed vertical distances) for the least-squares line is zero, which does not imply equal counts.
- The slope magnitude (for example, −1/2000) and the y-intercept (for example, ~45) are numeric estimates you must compute/estimate from the plot or regression output.
- “No correlation” vs. “moderate positive/negative trend”: check the scatter or compute the correlation coefficient. If r ≈ 0 there’s no linear correlation; if r is noticeably positive (e.g., 0.3–0.7) that’s a moderate positive trend; if r is negative, the trend is down.
If you upload the scatterplot or give the data (or summary statistics), I’ll pick the three true statements for you and show the reasoning.
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