Math Problem Statement
correct the placement of the graphs
Solution
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:
- 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.
- 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.
- 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:
- 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.
- 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.
- 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.
Here are 5 related questions:
- What is the meaning of the y-intercept in a linear regression?
- How do we interpret the slope of a least-squares regression line?
- Why might a y-intercept not be meaningful in some real-world scenarios?
- How does correlation influence the shape of a regression line?
- 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.
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Math Problem Analysis
Mathematical Concepts
Linear Regression
Scatter Plots
Least-Squares Regression
Y-Intercept
Formulas
y = mx + b (linear equation for least-squares regression)
Theorems
Least-Squares Regression Theorem
Suitable Grade Level
Grades 9-12
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