Given a set of data points, the least squares regression line is calculated to best fit the data. Which of the following values is the most likely approximate slope of the line of best fit if the data shows a strong negative linear relationship?

• A. $-5.5$
• B. $-4.5$
• C. $-2.0$
• D. $-1.0$

Answer: (C)

Verified step by step guidance

1. Understand that the slope of the least squares regression line represents the rate of change of the dependent variable with respect to the independent variable.
2. Recognize that a strong negative linear relationship means the slope should be a negative number with a relatively large absolute value, indicating a steep downward trend.
3. Compare the given slope options: -5.5, -4.5, -2.0, and -1.0, noting that more negative values correspond to steeper negative slopes.
4. Consider that extremely large negative slopes (like -5.5 or -4.5) might be too steep depending on the context, while smaller negative slopes (like -1.0) indicate a weaker negative relationship.
5. Conclude that the slope closest to -2.0 balances being negative and moderately steep, which aligns with a strong negative linear relationship without being excessively steep.