Question

r = 0.4, r = 0.9, r = -0.4, r = -1 (with scatter plots and correlation coefficients)

Explanation:

Step1: Recall Correlation Coefficient

The correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables. \( r = 1 \) is perfect positive linear, \( r = -1 \) is perfect negative linear, values close to \( \pm1 \) are strong, close to 0 are weak. Positive \( r \) means as \( x \) increases, \( y \) increases; negative \( r \) means as \( x \) increases, \( y \) decreases.

Step2: Analyze Each Graph

• Top - Left (\( r = -1 \)): Points form a perfect negative line (as \( x \) increases, \( y \) decreases).
• Top - Right: Points show a positive trend (as \( x \) increases, \( y \) increases) and the scatter is moderate - strong. \( r = 0.9 \) is a strong positive correlation, so this graph likely has \( r = 0.9 \).
• Bottom - Left: Points have no clear linear trend (scattered), so \( r \) close to 0 (maybe \( r=-0.4 \) or \( r = 0.4 \), but the negative/positive? Wait, the trend here is not clear, but if we check the other, bottom - right: also scattered, but let's match the coefficients. The top - right has a strong positive trend, so \( r = 0.9 \) fits it. The top - left is \( r=-1 \), the other two (bottom) are weak or no trend. But the question (assuming we need to match \( r = 0.9 \) to the graph) – the top - right graph has a positive, strong linear trend (points cluster closely around a positive line), so it corresponds to \( r = 0.9 \).

Answer:

The Top - Right Graph (the second graph in the top row) corresponds to \( r = 0.9 \) (or if the question was to identify which graph has \( r = 0.9 \), the answer is the Top - Right Graph).