Question

1. match the correlation to its scatterplot by writing the value for r from the list below above the plot.

• 0.95 0.94 0.57 - 0.89 0.84 0.45

Explanation:

To solve this, we analyze the scatterplots based on the direction (positive/negative) and strength (closer to ±1 is stronger) of the linear relationship.

Step 1: Analyze negative correlations

- For strong negative (close to -1): The second plot (top middle) has a clear negative trend. Between -0.95 and -0.89, -0.95 is stronger (closer to -1), so check the scatter. If the second plot's points are more tightly clustered, it's -0.95? Wait, no—wait, the first top plot (left) has a negative trend? Wait, no, let's re-examine:

Wait, the top-left plot: points seem to have a negative trend? Wait, no, maybe I misread. Let's list the plots:

1. Top-left: Let's see the direction. If x increases, y decreases? Wait, maybe. Wait, the top-middle plot: clear negative trend, points more tightly clustered. So stronger negative: -0.95 (stronger) vs -0.89 (slightly less strong). So top-middle: -0.95? Wait, no, wait the values: -0.95 is stronger than -0.89. So the scatterplot with the most tightly clustered negative trend is -0.95, next is -0.89.

2. Top-right: positive trend, points clustered. Let's check positive values: 0.94 (strongest positive), 0.84, 0.57, 0.45.

3. Bottom plots: some with weak or no trend.

Wait, let's correct:

- Negative correlations: two values: -0.95, -0.89. The scatterplot with the strongest negative (most linear, tight) is -0.95, next -0.89.

- Positive correlations: 0.94 (strongest), 0.84, 0.57, 0.45.

Now, let's match:

- Top-middle (second top): negative, tight → -0.95.

- Top-left (first top): negative, but less tight than top-middle? Wait, no, maybe top-left is -0.89? Wait, maybe I mixed up. Let's re-express:

Strength: |r| closer to 1 is stronger.

So:

- Strong negative: -0.95 (stronger) and -0.89 (less strong).

- Strong positive: 0.94 (stronger) and 0.84 (less strong).

- Moderate positive: 0.57, 0.45.

Now, let's look at each plot:

1. Top-left: Let's see the scatter. If it's a negative trend, maybe -0.89 (since -0.95 is stronger, so top-middle is -0.95, top-left is -0.89? Wait, no, maybe top-left has a negative trend but less tight than top-middle. So top-middle: -0.95 (stronger negative), top-left: -0.89? Wait, no, maybe I got the plots wrong.

Wait, the problem has six scatterplots? Wait, the image shows six plots (2 rows, 3 columns). Let's list them as Plot 1 (top-left), Plot 2 (top-middle), Plot 3 (top-right), Plot 4 (bottom-left), Plot 5 (bottom-middle), Plot 6 (bottom-right).

Now:

- Plot 2 (top-middle): negative, tight → r = -0.95 (strongest negative).

- Plot 1 (top-left): negative, less tight than Plot 2 → r = -0.89.

- Plot 3 (top-right): positive, tight → r = 0.94 (strongest positive).

- Plot (let's say bottom-something): wait, no, let's check positive values.

Wait, maybe:

- Plot 3 (top-right): positive, tight → 0.94.

- Another positive plot: maybe Plot (top-right) is 0.94, then another positive with less tight: 0.84.

- Then 0.57, 0.45 for weaker positive.

- Bottom plots: some with weak or no trend (like bottom-left, bottom-middle, bottom-right—maybe bottom-right has a weak positive, bottom-middle no trend, bottom-left no trend).

Wait, this is getting complex, but the key is to match direction and strength.

Let's provide the standard matching (common problem):

- Top-middle (negative, tight): r = -0.95

- Top-left (negative, less tight): r = -0.89

- Top-right (positive, tight): r = 0.94

- Another positive (e.g., a plot with positive, less tight): 0.84

- Then 0.57, 0.45 for weaker.

- Bottom plots with weak or no trend: e.g., bottom-left might have r close to 0 (but we have no 0, so maybe 0.45 or 0.57, but the values given are all non-zero). Wait, the values are -0.95, 0.94, 0.57, -0.89, 0.84, 0.45.

So each plot gets one value. Let's assume:

1. Top-left: r = -0.89 (negative, moderate strength)

2. Top-middle: r = -0.95 (negative, strong strength)

3. Top-right: r = 0.94 (positive, strong strength)

4. Bottom-left: r = 0.45 (weak positive or no trend)

5. Bottom-middle: r = 0.57 (moderate positive, but scattered)

6. Bottom-right: r = 0.84 (positive, moderate-strong)

Wait, no, maybe better to use the standard approach:

- The scatterplot with the strongest negative correlation (most linear, tight) is -0.95.

- The next strongest negative is -0.89.

- The strongest positive is 0.94.

- Next positive: 0.84.

- Then 0.57, then 0.45.

So matching:

- Plot with strongest negative (tight, linear): -0.95

- Plot with next strongest negative: -0.89

- Plot with strongest positive (tight, linear): 0.94

- Plot with next positive: 0.84

- Plot with moderate positive: 0.57

- Plot with weak positive: 0.45

Assuming the plots:

- Top-middle (second top): -0.95

- Top-left (first top): -0.89

- Top-right (third top): 0.94

- Bottom-right (third bottom): 0.84

- Bottom-middle (second bottom): 0.57

- Bottom-left (first bottom): 0.45

But since the problem is to match, the key is to use the direction (positive/negative) and strength (|r| magnitude).

Answer:

To match the correlation \( r \) to each scatterplot, we analyze the direction (positive/negative) and strength (clustering of points, \( |r| \) closer to \( \pm 1 \) is stronger) of the linear relationship:

Negative Correlations (\( r < 0 \)):

• \( r = -0.95 \): Strongest negative (most linear, tightly clustered negative trend).
• \( r = -0.89 \): Strong negative (less tight than \( -0.95 \), but still linear).

Positive Correlations (\( r > 0 \)):

• \( r = 0.94 \): Strongest positive (most linear, tightly clustered positive trend).
• \( r = 0.84 \): Strong positive (less tight than \( 0.94 \), but linear).
• \( r = 0.57 \): Moderate positive (somewhat linear, looser clustering).
• \( r = 0.45 \): Weak positive (least linear, loosest clustering).

For each scatterplot:

• Top-middle (negative, tight): \( r = -0.95 \)
• Top-left (negative, less tight): \( r = -0.89 \)
• Top-right (positive, tight): \( r = 0.94 \)
• Bottom-right (positive, moderate-strong): \( r = 0.84 \)
• Bottom-middle (positive, moderate): \( r = 0.57 \)
• Bottom-left (positive, weak): \( r = 0.45 \)

(Note: The exact plot assignment depends on the visual clustering, but the key is using direction and strength. Adjust based on the scatterplots’ actual appearance.)