Question 1: Plot the points (1, 2), (2, 4), (3, 6), and (4, 8) on the grid. Describe the type of correlation shown.

Answer: The points form a straight line with positive slope, indicating positive correlation.

Question 2: Calculate the gradient of the line passing through (2, 3) and (5, 6).

Answer: 1

Question 3: A scatter graph shows data points with a clear upward trend. What does this indicate about the relationship between the two variables?

Answer: There is a positive correlation between the variables.

Question 4: Plot the data points: (1, 1), (2, 3), (3, 5), (4, 7). What is the approximate equation of the line of best fit?

Answer: y = 2x - 1

Question 5: A set of data shows the following points: (2, 4), (3, 6), (4, 8), (5, 10). Calculate the correlation coefficient to determine the strength of the positive relationship.

Answer: Approximately 1 (perfect positive correlation)

Question 6: In a real-world scenario, an increase in hours studied is associated with higher test scores. Explain whether this suggests a positive correlation and why.

Answer: Yes, because as hours studied increase, test scores tend to increase, indicating positive correlation.

Question 7: Construct a scatter plot showing a positive relationship between the number of hours exercised per week and fitness level. Use any data points you choose.

Answer: Students will draw points trending upwards; specific points will vary.

Question 8: A teacher records students' heights and their scores in a physical endurance test. The data shows a positive trend. What might be a reason for this relationship?

Answer: Heavier or taller students may generally have more strength, leading to better endurance scores.

Question 9: Identify and correct the mistake in this statement: 'A positive correlation means that as one variable decreases, the other also decreases.'

Answer: Incorrect; positive correlation means both variables increase together.

Question 10: Using the data points (1, 2), (2, 4), (3, 6), (4, 8), calculate the coefficient of determination (R²) to assess the fit of the line.

Answer: R² = 1 (indicating a perfect fit)

Question 11: Explain why positive correlation does not imply causation with an example.

Answer: For example, ice cream sales and drowning incidents both increase in summer, but one does not cause the other.

Question 12: Identify the common mistake in interpreting a scatter plot showing a strong positive trend: assuming causation. Why is this incorrect?

Answer: Correlation does not prove that one variable causes the other; there may be other factors involved.