Let’s analyze each statement to identify which ones are true:

1. Statement A: "A line of best fit with a positive gradient shows a positive correlation."

   • This is true. A positive gradient in a line of best fit indicates that as one variable increases, the other also tends to increase, which is the definition of positive correlation.

2. Statement B: "The line of best fit must go through at least one point on the scatter graph."

   • This is not necessarily true. A line of best fit is drawn to best represent the trend of the data, minimizing the distance from all points, but it does not need to pass through any specific data points.

3. Statement C: "The line of best fit must go through every point on the scatter graph."

   • This is false. The line of best fit is typically an approximation that minimizes the distances (errors) to the points and does not need to go through each individual point.

4. Statement D: "The line of best fit must go through the origin of the scatter graph."

   • This is not necessarily true. The line of best fit goes through the origin only if it is required by the context or data structure (e.g., when both variables are expected to be zero together), but generally, it does not have to go through the origin.

5. Statement E: "There can be a different number of points above and below the line of best fit."

   • This is true. The line of best fit minimizes the overall deviation, but it’s possible for there to be more points on one side than the other.

True Statements: A and E

Would you like further explanation on any of these points?

Here are some additional questions related to this topic:

1. What does a negative gradient in a line of best fit indicate?
2. How is the line of best fit calculated in linear regression?
3. Why might a line of best fit not pass through any points in a dataset?
4. In what situations is it important for the line of best fit to pass through the origin?
5. How does the presence of outliers affect the line of best fit?

Tip: When creating a line of best fit, it’s essential to understand the context of the data to interpret the correlation accurately.