Question

On a graph, points are scattered all over the graph.
Determine if there is a correlation and slope for the scatterplot.
positive correlation, positive slope
negative correlation, negative slope
negative correlation, positive slope
no correlation

Answer 1

To determine the correlation and slope for a scatterplot, you should follow these steps:

1. **Visual Inspection**:
- Look for a pattern in the scattering of points.
- If the points tend to rise from left to right, there is a positive correlation (and a positive slope).
- If the points tend to fall from left to right, there is a negative correlation (and a negative slope).
- If the points are scattered randomly without any discernible pattern, there is no correlation.

2. **Statistical Analysis**:
- You can calculate the correlation coefficient (e.g., Pearson's r) to quantify the strength and direction of the correlation. Values near 1 indicate a strong positive correlation, values near -1 indicate a strong negative correlation, and values near 0 indicate no correlation.
- If you are finding a slope, you can perform a linear regression analysis to find the best-fit line and determine the slope.

Based on these observations, use the following guidelines for conclusion:

- **Positive correlation & positive slope**: If points show an upward trend.
- **Negative correlation & negative slope**: If points show a downward trend.
- **Negative correlation & positive slope**: This situation is contradictory and should not occur.
- **No correlation**: If points show no clear pattern.

If you provide more specific information or a description of the scatterplot, I could give you a more tailored analysis!