To determine which statements are true, let's analyze each one based on general knowledge about the relationships between happiness and income, as well as the properties of a line of best fit:
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This is a moderate positive correlation.
- True (if the data suggests happiness increases with income).
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The y-intercept of the line of best fit would show a happiness score of around 40 when there is $0 income.
- True (if the data shows that happiness at zero income is indeed around 40).
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The line of best fit would have a positive slope representing as income goes up, happiness goes up.
- True (if there is a positive correlation between income and happiness).
-
The line of best fit must show the middle score of the data as being on the line.
- False (the line of best fit averages the data and does not have to pass through the median).
-
As a person's income goes up, their happiness trends down.
- False (this contradicts the positive correlation described).
-
The slope of the line of best fit could be around m = -1/2000.
- False (if there is a positive correlation, the slope should be positive).
-
There is no correlation between happiness and income.
- False (if previous statements suggest a correlation exists).
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The line of best fit should include the lowest and highest scores.
- False (the line of best fit does not have to pass through these points; it is based on minimizing the distance to all points).
Based on this analysis, the true statements are:
- This is a moderate positive correlation.
- The y-intercept of the line of best fit would show a happiness score of around 40 when there is $0 income.
- The line of best fit would have a positive slope representing as income goes up, happiness goes up.