https://file.aiquickdraw.com/mathbot/file/1726805245817axj11pb8.jpg

In the image, we need to correct the placement of the scatter plots according to whether the y-intercept of the least-squares regression line is meaningful or not. Here's the correct placement:

### **Meaningful y-intercept value:**
1. **Scatter plot A** (Fruit fly weight vs. length)  
   - A meaningful y-intercept because a length of 0 suggests no fly, leading to a weight of 0.
2. **Scatter plot B** (Wind speed vs. crane level)  
   - A meaningful y-intercept because at a wind speed of 0, the crane height would also be relevant.
3. **Scatter plot D** (Iris petal length vs. petal width)  
   - A meaningful y-intercept since a petal length of 0 would suggest no width.

### **Not meaningful y-intercept value:**
1. **Scatter plot C** (Old Faithful's eruption duration vs. waiting time)  
   - A y-intercept is not meaningful because a waiting time of 0 wouldn't imply a meaningful relationship in this context.
2. **Scatter plot E** (Tree height vs. volume)  
   - A y-intercept is not meaningful because a tree cannot have 0 height and still have a volume.
3. **Scatter plot F** (Medicine dose vs. red blood cell count)  
   - A y-intercept is not meaningful because no dose would imply no effect, and thus the y-intercept doesn't make sense here.

Let me know if you need further clarification or details.

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Here are 5 related questions:
1. What is the meaning of the y-intercept in a linear regression?
2. How do we interpret the slope of a least-squares regression line?
3. Why might a y-intercept not be meaningful in some real-world scenarios?
4. How does correlation influence the shape of a regression line?
5. What is the difference between a positive and negative y-intercept in context?

**Tip:** Always examine the context of a scatter plot to determine whether the y-intercept makes sense within the real-world data being modeled.

Explore how to correctly classify scatter plots based on whether the y-intercept of the least-squares regression line is meaningful or not. This example includes real-world scenarios such as wind speed vs. crane level, tree height vs. volume, and medicine dose vs. red blood cell count. Suitable for Grades 9-12 students learning linear regression.

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