Question 1: Plot the points (1, 5), (2, 3), (3, 1), and (4, -1) on the grid. Describe the trend you observe.

Answer: As x increases, y decreases, indicating a negative correlation.

Question 2: Calculate the correlation coefficient (r) for the data points: (1, 10), (2, 8), (3, 6), (4, 4).

Answer: -1

Question 3: A scatter graph shows height vs. number of hours spent watching TV. The points tend to slope downward. What does this indicate about their relationship?

Answer: There is a negative correlation; as hours watching TV increase, height tends to decrease or less growth.

Question 4: Construct a scatter plot with the following data: (-1, 4), (-2, 3), (-3, 2), (-4, 1). What pattern do you observe?

Answer: Points decrease in y as x decreases; negative correlation.

Question 5: Given points (-2, 7), (-3, 4), (-4, 1), determine if they show a negative correlation and justify your answer.

Answer: Yes, as x decreases, y decreases, indicating negative correlation.

Question 6: A data set shows that when x increases from 1 to 5, y decreases from 10 to 2. Describe the nature of the correlation and what it suggests.

Answer: It shows a negative correlation; as x increases, y decreases.

Question 7: Plot the points (0, 3), (1, 1), (2, -1), (3, -3). What does the trend suggest?

Answer: The points show a downward trend, indicating negative correlation.

Question 8: Find the equation of the line of best fit for the points (2, 10), (4, 6), (6, 2).

Answer: y = -2x + 14

Question 9: Explain a real-world scenario where negative correlation might be observed and how it is useful.

Answer: Example: In medicine, as dosage increases, side effects may decrease, or vice versa; understanding this helps optimize treatments.

Question 10: Identify the common mistake: a student draws a scatter plot with points that form a upward-sloping line when asked for negative correlation. How should they correct this?

Answer: They should plot points where y decreases as x increases, showing a downward trend.

Question 11: A student claims that a perfect negative correlation means all points lie exactly on a downward-sloping line. Is this true? Explain.

Answer: Yes, a perfect negative correlation means all points lie exactly on a line with negative slope.