Check all of the statements that are true.

(9 points)
Responses

There is no correlation between happiness and income.
There is no correlation between happiness and income.

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.

The y-intercept of the line of best fit would show a happiness score of around 40 when there is $0 income.
The y-intercept of the line of best fit would show a happiness score of around 40 when there is $0 income.

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.

The line of best fit should include the lowest and highest scores.
The line of best fit should include the lowest and highest scores.

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.

As a person's income goes up, their happiness trends down.

1 answer

To evaluate the statements regarding the relationship between happiness and income, let's review them one by one:

  1. There is no correlation between happiness and income.

    • False - Most studies suggest a correlation exists, though the strength can vary.
  2. 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.
  3. 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.
  4. 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.
  5. 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).
  6. This is a moderate positive correlation.

    • True - If there is indeed a positive correlation, it can be moderate depending on the data distribution.
  7. 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.
  8. 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.
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