📚 What is Positive Linear Association?
Positive linear association means that as one variable increases, the other variable tends to increase as well. Think of it like this: the more you study, the higher your grades tend to be!
- 📈 Upward Trend: On a scatter plot, the points generally move upwards from left to right.
- ➕ Positive Slope: The line of best fit has a positive slope. This means the 'm' in the equation $y = mx + b$ is greater than 0.
- 🔢 Example: The relationship between hours studied and test scores. More study hours usually lead to higher test scores.
🧠 What is Negative Linear Association?
Negative linear association means that as one variable increases, the other variable tends to decrease. Imagine the relationship between time spent playing video games and your grade in math. More gaming might (unfortunately!) lead to a lower grade.
- 📉 Downward Trend: On a scatter plot, the points generally move downwards from left to right.
- ➖ Negative Slope: The line of best fit has a negative slope. In the equation $y = mx + b$, 'm' is less than 0.
- 🌡️ Example: The relationship between temperature and the number of coats people wear. As the temperature rises, the number of coats worn decreases.
| Feature |
Positive Linear Association |
Negative Linear Association |
| Definition |
As one variable increases, the other tends to increase. |
As one variable increases, the other tends to decrease. |
| Slope of Line of Best Fit |
Positive (m > 0) |
Negative (m < 0) |
| Scatter Plot Trend |
Points move upwards from left to right. |
Points move downwards from left to right. |
| Example |
Hours studied vs. Test Score |
Temperature vs. Coats Worn |
💡 Key Takeaways
- ✅ Positive: Variables move in the same direction.
- ❌ Negative: Variables move in opposite directions.
- 🌱 Linear: The relationship can be approximated by a straight line.