To evaluate the statements regarding the relationship between happiness and income, let's review them one by one:
-
There is no correlation between happiness and income.
- False - Most studies suggest a correlation exists, though the strength can vary.
-
The line of best fit would have a positive slope representing as income goes up, happiness goes up.
- True - Generally, a positive correlation means higher income tends to be associated with higher happiness.
-
The y-intercept of the line of best fit would show a happiness score of around 40 when there is $0 income.
- It depends on the specific data being analyzed, so this is uncertain. However, if we assume the context supports this specific point, True.
-
The slope of the line of best fit could be around m = -1/2000.
- False - A negative slope indicates a decrease in happiness as income increases, which contradicts the previous point about positivity.
-
The line of best fit should include the lowest and highest scores.
- False - While the line of best fit summarizes the data trend, it does not have to pass through all data points (lowest or highest).
-
This is a moderate positive correlation.
- True - If there is indeed a positive correlation, it can be moderate depending on the data distribution.
-
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 a statistical approximation; it does not necessarily need to pass through the median.
-
As a person's income goes up, their happiness trends down.
- False - This statement contradicts the typical assumption of a positive relationship between income and happiness.
Based on this analysis, the true statements are:
- The line of best fit would have a positive slope representing as income goes up, happiness goes up.
- The y-intercept of the line of best fit would show a happiness score of around 40 when there is $0 income (if supported by data).
- This is a moderate positive correlation.
22 answers