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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.

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

This is a moderate positive correlation.
This is a moderate positive correlation.

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 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.

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

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.

1 answer

To assess which statements are true, we first need to understand some terms related to correlation and linear regression, specifically the line of best fit (also known as the regression line).

  1. The line of best fit should include the lowest and highest scores.
    False. The line of best fit does not need to pass through all points or include the lowest and highest scores; it minimizes the distance of all points to the line.

  2. There is no correlation between happiness and income.
    False. This statement may or may not be true, but without data analysis, we can't claim that there is no correlation. The correlation could be positive, negative, or zero.

  3. This is a moderate positive correlation.
    False (based on context). Without specific data or a correlation coefficient value, we cannot determine the strength or direction of the correlation.

  4. The slope of the line of best fit could be around m = -1/2000.
    False. A negative slope suggests that as income increases, happiness decreases.

  5. The y-intercept of the line of best fit would show a happiness score of around 40 when there is $0 income.
    False. Without specific data, we cannot determine the y-intercept's value.

  6. As a person's income goes up, their happiness trends down.
    False. This statement would indicate a negative correlation. Without specific data, we cannot make that conclusion.

  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 does not necessarily pass through the mean of the data.

  8. The line of best fit would have a positive slope representing as income goes up, happiness goes up.
    True (only if the correlation is positive). If we assume a positive relationship between income and happiness, then this statement would be true.

Based on this analysis, the only true statement, assuming a positive correlation, is:

  • The line of best fit would have a positive slope representing as income goes up, happiness goes up.

All the other statements are false based on the definitions and general principles of correlation and linear regression.