Question 1: Plot the points for the data where as the number of hours studied decreases, the test scores decrease. Use the point (x, y) notation. For example, (2, 80).

Answer: (1, 70), (2, 60), (3, 50), (4, 40)

Question 2: Calculate the correlation coefficient (rough estimate) for the following data: (x: 1, 2, 3, 4), (y: 80, 60, 40, 20). Is it positive or negative?

Answer: Approximately -1, negative

Question 3: A student claims that plotting a downward trend always means a perfect negative correlation. Is this true? Explain briefly.

Answer: No, a downward trend indicates negative correlation, but it may not be perfect (not exactly -1).

Question 4: Identify and correct the mistake in this statement: 'All scatter graphs with points going down from left to right show negative correlation.'

Answer: Some downward trends are due to random data, not true negative correlation.

Question 5: Plot the points for the data: (x: 1, 2, 3, 4), (y: 80, 60, 40, 20). Draw the line that best fits the data.

Answer: Line passing through (1, 80) and (4, 20), with negative slope.

Question 6: Given the data points (x: 1, 2, 3, 4), (y: 90, 70, 50, 30), what is the general trend? Is it positive or negative?

Answer: Negative trend

Question 7: A scatter graph shows a downward trend, but some points are far from the line. What mistake might students make when interpreting this?

Answer: They might think there's a perfect negative correlation; however, outliers can weaken the correlation.

Question 8: Construct a scatter plot with points that show a moderate negative correlation. Describe the pattern briefly.

Answer: Points generally trend downward, but some are closer or farther from the line.

Question 9: Explain why a data set with a lot of variation around the trend line might still have a negative correlation.

Answer: Because most points tend to decrease as x increases, despite some outliers or variability.

Question 10: Identify the common mistake in the following statement: 'A negative slope always means negative correlation.'

Answer: A negative slope indicates negative correlation, but data may not be strongly correlated.

Question 11: A student draws a scatter graph with points scattered randomly but notices a slight downward trend. What misconception might they have?

Answer: They might think there is a negative correlation when the data is actually random; correlation requires a pattern.