Question
Check all of the statements that are true. (9 points) Responses The line of best fit should include the lowest and highest scores. The line of best fit should include the lowest and highest scores. As a person's income goes up, their happiness trends down. As a person's income goes up, their happiness trends down. The slope of the line of best fit could be around m = -1/2000. The slope of the line of best fit could be around m = -1/2000. This is a moderate positive correlation. This is a moderate positive correlation. The line of best fit must show the middle score of the data as being on the line. The line of best fit must show the middle score of the data as being on the line. The line of best fit would have a positive slope representing as income goes up, happiness goes up. The line of best fit would have a positive slope representing as income goes up, happiness goes up. There is no correlation between happiness and income. There is no correlation between happiness and income. The y-intercept of the line of best fit would show a happiness score of around
Answers
GPT-4o mini
To determine the truth of each statement, let's analyze them one by one:
1. **The line of best fit should include the lowest and highest scores.**
**False.** The line of best fit does not have to pass through the lowest and highest scores. It represents the overall trend of the data, not the individual data points.
2. **As a person's income goes up, their happiness trends down.**
**False.** This statement suggests a negative correlation, which is not universally true. Many studies indicate a positive correlation between income and happiness.
3. **The slope of the line of best fit could be around m = -1/2000.**
**False.** This suggests a very slight negative correlation, which, as stated earlier, is not generally supported.
4. **This is a moderate positive correlation.**
**False.** If we consider that many studies indicate a positive correlation between income and happiness, we still cannot assume it’s moderate without actual data.
5. **The line of best fit must show the middle score of the data as being on the line.**
**False.** The line of best fit is derived from the overall trend and doesn't have to go through the median or middle score of the data.
6. **The line of best fit would have a positive slope representing as income goes up, happiness goes up.**
**True.** Many studies support that a positive correlation exists between income and happiness.
7. **There is no correlation between happiness and income.**
**False.** The general consensus in the literature suggests there is some correlation, with income affecting happiness to some degree.
8. **The y-intercept of the line of best fit would show a happiness score of around.**
**False (partially).** The statement is incomplete. Typically, the y-intercept represents the expected value of happiness when income is zero, but without specific data, we can't determine its value.
Based on the analysis, the only true statement is:
- **The line of best fit would have a positive slope representing as income goes up, happiness goes up.**
1. **The line of best fit should include the lowest and highest scores.**
**False.** The line of best fit does not have to pass through the lowest and highest scores. It represents the overall trend of the data, not the individual data points.
2. **As a person's income goes up, their happiness trends down.**
**False.** This statement suggests a negative correlation, which is not universally true. Many studies indicate a positive correlation between income and happiness.
3. **The slope of the line of best fit could be around m = -1/2000.**
**False.** This suggests a very slight negative correlation, which, as stated earlier, is not generally supported.
4. **This is a moderate positive correlation.**
**False.** If we consider that many studies indicate a positive correlation between income and happiness, we still cannot assume it’s moderate without actual data.
5. **The line of best fit must show the middle score of the data as being on the line.**
**False.** The line of best fit is derived from the overall trend and doesn't have to go through the median or middle score of the data.
6. **The line of best fit would have a positive slope representing as income goes up, happiness goes up.**
**True.** Many studies support that a positive correlation exists between income and happiness.
7. **There is no correlation between happiness and income.**
**False.** The general consensus in the literature suggests there is some correlation, with income affecting happiness to some degree.
8. **The y-intercept of the line of best fit would show a happiness score of around.**
**False (partially).** The statement is incomplete. Typically, the y-intercept represents the expected value of happiness when income is zero, but without specific data, we can't determine its value.
Based on the analysis, the only true statement is:
- **The line of best fit would have a positive slope representing as income goes up, happiness goes up.**