Answer: 1.00.

## Explanation The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. The key information given is: - When X increases by 4 units, Y increases by 1 unit - This relationship is consistent ("whenever") ### Key Concepts: 1. **Correlation coefficient (r)** ranges from -1 to +1 2. **Perfect positive correlation** (r = +1.00) means that for every unit change in X, there is a consistent, proportional change in Y 3. The correlation coefficient is not affected by the scale of the relationship, only by its consistency ### Analysis: - The statement describes a **perfect linear relationship** between X and Y - For every 4-unit increase in X, Y increases by exactly 1 unit - This is a constant ratio: ΔY/ΔX = 1/4 = 0.25 - However, correlation measures **how consistently** the relationship holds, not the slope - Since the relationship is perfectly consistent ("whenever"), the correlation is perfect ### Why not 0.25? - 0.25 would be the slope of the regression line (b = ΔY/ΔX = 1/4 = 0.25) - But correlation (r) is different from slope - Correlation measures the strength of the linear relationship, which is perfect here ### Mathematical Relationship: The correlation coefficient r is related to the slope b by: r = b × (σₓ/σᵧ) Where: - b = slope = 0.25 - σₓ = standard deviation of X - σᵧ = standard deviation of Y For a perfect linear relationship, r = ±1 regardless of the slope value. ### Conclusion: The consistent, proportional relationship described indicates a perfect positive linear correlation, so r = 1.00.

Author: LeetQuiz .