Math Problem Statement

correct the placement of the graphs

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:

  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.


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.

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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