Question 1: Plot the points (1, 2), (2, 4), (3, 6), and (4, 8) on the grid. Describe the trend you observe.

Answer: The points form an upward trend, indicating a positive correlation.

Question 2: Calculate the approximate line of best fit for the points: (1, 3), (2, 5), (3, 7).

Answer: Line: y = 2x + 1

Question 3: Identify whether the following scatter graph shows a positive, negative, or no correlation: A graph with data points trending upwards from left to right.

Answer: Positive

Question 4: On a scatter plot, a student notices a cluster of points at low x-values but high y-values. What does this suggest about the data?

Answer: It suggests variability or potential outliers; not necessarily a positive correlation.

Question 1: A scientist plots the height of a plant against the number of days. The points show an increasing trend. Explain how this indicates a positive correlation and what this suggests about the relationship between height and days.

Answer: An increasing trend indicates that as days increase, the plant's height tends to increase, showing a positive correlation and a likely causal relationship.

Question 2: Given a scatter plot with a clear upward trend but with some scattered points, how can you determine if the correlation is strongly positive?

Answer: If most points follow an upward trend closely with few outliers, the correlation is strongly positive.

Question 3: Describe a situation in real life where a positive correlation might be misleading or incorrect to assume.

Answer: Assuming that ice cream sales cause drowning incidents because both increase in summer; the correlation is coincidental, not causal.

Question 1: A company records the number of hours employees work and their productivity scores. The data shows that higher hours worked generally lead to higher productivity. How does this reflect positive correlation? What are some potential misconceptions?

Answer: It suggests a positive correlation between hours worked and productivity, but misconceptions include assuming causation without considering fatigue or diminishing returns.

Question 1: Construct a scatter graph with points that clearly show a weak positive correlation, then explain why the correlation is considered weak.

Answer: A scatter graph with points mostly forming an upward trend but with many scattered points away from the trend line indicates a weak positive correlation.

Question 2: Identify a common mistake students make when interpreting positive correlation and explain how to avoid it.

Answer: Mistake: assuming correlation implies causation. To avoid it, remember correlation does not prove cause-effect relationships.

Question 1: A student draws a scatter plot with a slight downward trend and claims it shows a positive correlation. What is wrong with this interpretation?

Answer: The trend is downward; it shows a negative correlation, so claiming positive is incorrect.

Question 2: A data set shows a perfect upward line, but a student thinks there is no correlation. What mistake did they make, and how can they correct it?

Answer: They might think the data is random or no correlation exists; correction involves recognizing that a perfect line indicates a strong positive correlation.

Question 3: If some points in a scatter plot are far from the main trend line, how does this affect the strength of the correlation?

Answer: It weakens the strength of the positive correlation because of outliers or variability.