Math Problem Statement

Which of the scatterplots shows little or no association, a negative association, a linear association, a weak or moderately strong association, and a very strong association?

Solution

Here’s an analysis of the scatterplots based on the provided options:

  1. (a) Little or no association:
    Plot (3) shows little to no association. The points are scattered randomly without any noticeable trend.

  2. (b) A negative association:
    Plot (1) shows a negative association because the points trend downward as you move from left to right.

  3. (c) A linear association:
    Plot (4) shows a clear linear association because the points form a pattern that closely aligns with a straight line.

  4. (d) A weak or moderately strong association:
    Plot (2) shows a weak or moderately strong association. The points suggest an upward trend, but they are not tightly clustered around a line.

  5. (e) A very strong association:
    Plot (4) again exhibits a very strong association, as the points are tightly clustered around a straight line.


Do you want more details or have any follow-up questions?

5 Related Questions

  1. What are the differences between positive and negative associations?
  2. How do we calculate the strength of an association numerically (e.g., correlation coefficient)?
  3. Can nonlinear associations be described using correlation coefficients?
  4. What factors can make an association weaker?
  5. How can scatterplots be used to detect outliers?

Tip

When interpreting scatterplots, always look for direction (positive/negative), form (linear/nonlinear), and strength (strong/weak).

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Math Problem Analysis

Mathematical Concepts

Scatterplots
Association Types
Correlation

Formulas

-

Theorems

Concept of Linear Correlation

Suitable Grade Level

Grades 8-10