Check all of the statements that are true.
(9 points)
Responses
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.
As a person's income goes up, their happiness trends down.
As a person's income goes up, their happiness trends down.
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 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.
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 line of best fit should include the lowest and highest scores.
The line of best fit should include the lowest and highest scores.
It's important to note that the statements presented here aren't accompanied by a specific dataset or the context necessary to evaluate their accuracy. The line of best fit, correlation, and the other concepts mentioned relate to statistical analysis, commonly used in examining the relationships between two variables. With that in mind, I'll assess the presented statements generally:
1. The line of best fit must show the middle score of the data as being on the line.
- False. The line of best fit, also known as a regression line, is the line that best represents the data on a scatter plot, minimizing the distance between the line and all the data points. It does not necessarily pass through any specific data point, including the middle score.
2. The line of best fit would have a positive slope representing as income goes up, happiness goes up.
- This could be true or false and depends on actual data demonstrating a positive relationship between income and happiness.
3. As a person's income goes up, their happiness trends down.
- This is a statement of a negative correlation. If this were true, it would conflict with Statement 2, which asserts a positive correlation. Both statements cannot be true simultaneously.
4. There is no correlation between happiness and income.
- This statement conflicts with both Statements 2 and 3, which imply a correlation (positive or negative, respectively). Without data, we cannot determine if this statement is true.
5. The y-intercept of the line of best fit would show a happiness score of around 40 when there is $0 income.
- This could be true but depends on the actual data. The y-intercept is the point where the line crosses the y-axis, which represents the estimated value of the dependent variable (happiness) when the independent variable (income) is zero.
6. This is a moderate positive correlation.
- Without data, we cannot confirm if there is a moderate positive correlation. This statement implies there is some positive correlation, which conflicts with Statements 3 and 4.
7. The slope of the line of best fit could be around m = -1/2000.
- This implies a very slight negative slope. Without data, we cannot confirm the slope of the line of best fit.
8. The line of best fit should include the lowest and highest scores.
- False. The line of best fit does not need to include specific data points such as the lowest and highest scores. Its position is determined by the overall distribution of all data points to best represent the trend in the data.
In a real-world scenario, data must be analyzed to determine which, if any, of these statements are true.