Question

Use the tables to create scatter plots and determine which scatterplot shows a non - linear association.

X 50 46 80 59 78 64 68 53 70 68

Y 35 30 75 45 70 50 55 36 62 67



X 50 46 98 59 78 64 68 53 70 72

Y 75 71 90 55 70 100 90 25 40 76



X 50 46 90 59 78 64 68 53 70 72

Y 75 71 100 80 90 82 85 77 87 89



X 50 46 80 59 78 64 68 53 70 68

Y 90 100 57 80 60 75 72 82 70 67

Answer 1

To determine which scatterplot shows a non-linear association, we can analyze the relationships depicted by the pairs of \(X\) and \(Y\) values from each table. I'll summarize them and provide insights about their potential linearity.

1. **First dataset:**
- **X:** 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
- **Y:** 35, 30, 75, 45, 70, 50, 55, 36, 62, 67

This set appears to maintain a generally positive trend but has scattered points suggesting some non-linearity. This requires plotting for visual confirmation.

2. **Second dataset:**
- **X:** 50, 46, 98, 59, 78, 64, 68, 53, 70, 72
- **Y:** 75, 71, 90, 55, 70, 100, 90, 25, 40, 76

This dataset has a wider range in \(Y\) values, but it also seems to include varying trends, indicating potential non-linearity.

3. **Third dataset:**
- **X:** 50, 46, 90, 59, 78, 64, 68, 53, 70, 72
- **Y:** 75, 71, 100, 80, 90, 82, 85, 77, 87, 89

The points here seem to form a clear upward trend, suggesting a linear relationship.

4. **Fourth dataset:**
- **X:** 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
- **Y:** 90, 100, 57, 80, 60, 75, 72, 82, 70, 67

In this case, the \(Y\) values fluctuate widely without a clear linear progression, hinting at possible non-linearity.

### Summary:

Based on this analysis:
- The **third dataset** shows a linear relationship due to the closely aligned upward trend observed from the points.
- The **first and second datasets** may show potential non-linearity but would require final plots for exact determination.
- The **fourth dataset** displays a clear non-linear association due to significant variability in \(Y\) values without consistent patterns.

In conclusion, the scatterplots for the **first**, **second**, and **fourth datasets** may depict non-linear associations, with the **fourth dataset** being the clearest example. To confirm these findings visually, plotting each set on graphing software would be most effective.