Question

sort the following scatterplots under the correct correlation. positive correlation negative correlation no correlation

Explanation:

Step1: Recall Correlation Types

- Positive Correlation: As \( x \) increases, \( y \) increases (upward trend).
- Negative Correlation: As \( x \) increases, \( y \) decreases (downward trend).
- No Correlation: Points have no clear trend.

Step2: Analyze Each Scatterplot

1. **First Scatterplot (Top):**
As \( x \) (horizontal) increases, \( y \) (vertical) decreases. So, **Negative Correlation**.
2. **Second Scatterplot (Second from Top):**
As \( x \) increases, \( y \) decreases? Wait, no—wait, check axes. Wait, \( x \) and \( y \) axes: Wait, no, let's recheck. Wait, second plot: As \( x \) (horizontal) increases, \( y \) (vertical) seems to have no clear trend? Wait, no, maybe I misread. Wait, third plot: Let's list all four:
- Top (1st): \( x \) up, \( y \) down → Negative.
- 2nd: Points cluster with \( x \) up, \( y \) maybe no trend? Wait, no—wait, the third plot (third from top): As \( x \) increases, \( y \) increases? Wait, no, third plot: \( x \) (horizontal) increases, \( y \) (vertical) increases? Wait, no, let's look at the y-axis. Wait, the third plot (third from top) has \( x \) from 0 - 9 (bottom axis) and \( y \) from 0 - 9 (side). Wait, third plot: When \( x \) is small (left), \( y \) is large (top); when \( x \) is large (right), \( y \) is small (bottom). Wait, no—wait, the fourth plot (bottom): Let's re-express:

- **1st Scatterplot (Top):** Downward trend ( \( x \) ↑, \( y \) ↓ ) → Negative Correlation.
- **2nd Scatterplot (Second):** Points are scattered with no clear trend? Wait, no—wait, second plot: \( x \) (horizontal) increases, \( y \) (vertical) seems to have a slight downward? No, maybe I messed up. Wait, the problem has four scatterplots, to sort into Positive, Negative, No Correlation.

Wait, let's correct:
- **Positive Correlation:** 3rd plot (third from top): As \( x \) increases, \( y \) increases (upward trend).
- **Negative Correlation:** 1st plot (top) and maybe 2nd? Wait, no—wait, 2nd plot: Let's see, 2nd plot: \( x \) (horizontal) increases, \( y \) (vertical) decreases? No, 2nd plot: When \( x \) is 1, \( y \) is 2; \( x=2 \), \( y=2 \); \( x=3 \), \( y=3 \); no, maybe 2nd plot has no trend? Wait, no—let's use the standard:

- **Positive Correlation:** Scatterplot where points trend upward ( \( x \) ↑, \( y \) ↑ ).
- **Negative Correlation:** Scatterplot where points trend downward ( \( x \) ↑, \( y \) ↓ ).
- **No Correlation:** Points are random, no trend.

So:
- **Positive Correlation:** The third scatterplot (third from top) – as \( x \) increases, \( y \) increases.
- **Negative Correlation:** The first scatterplot (top) – as \( x \) increases, \( y \) decreases.
- **No Correlation:** The second and fourth? Wait, no, the fourth plot (bottom): Let's see, fourth plot: Points are clustered in a vertical band? No, fourth plot: \( x \) (horizontal) increases, \( y \) (vertical) has no clear trend (points are scattered vertically? No, fourth plot: \( x \) from 0 - 9, \( y \) from 0 - 9. Points are in the middle, no clear up/down. Wait, maybe:

- **Positive Correlation:** Third scatterplot (third from top) ( \( x \) ↑, \( y \) ↑ ).
- **Negative Correlation:** First scatterplot (top) ( \( x \) ↑, \( y \) ↓ ).
- **No Correlation:** Second and fourth? Wait, no, the second scatterplot (second from top): Let's check again. Second plot: Points are spread with \( x \) from 0 - 9, \( y \) from 0 - 9. No clear trend? Wait, maybe the second plot is No Correlation, and the fourth is also No? No, the problem has three categories: Positive, Negative, No. So four scatterplots, so one category may have two.

Wait, the user’s image has four scatterplots and three categories: Positive, Negative, No. So:

- **Positive Correlation:** The third scatterplot (third from top) (trend upward: \( x \) increases, \( y \) increases).
- **Negative Correlation:** The first scatterplot (top) (trend downward: \( x \) increases, \( y \) decreases).
- **No Correlation:** The second and fourth scatterplots (points have no clear upward/downward trend).

Answer:

• Positive Correlation: The third scatterplot (third from the top).
• Negative Correlation: The first scatterplot (top).
• No Correlation: The second and fourth scatterplots (second from top, bottom).