Math Problem Statement

Match these values of r with the accompanying​ scatterplots: 0.443​, 0.798​, 0.995​, 1​, and negative 0.798. LOADING... Click the icon to view the scatterplots. Question content area bottom Part 1 Match the values of r to the scatterplots. Scatterplot​ 1, requals ▼ 1 negative 0.798 0.798 0.995 0.443 Scatterplot​ 2, requals ▼ 1 negative 0.798 0.443 0.798 0.995 Scatterplot​ 3, requals ▼ 0.995 1 0.798 0.443 negative 0.798 Scatterplot​ 4, requals ▼ 0.798 0.443 1 0.995 negative 0.798 Scatterplot​ 5, requals ▼ 0.443 0.798 negative 0.798 0.995 1

Solution

To match the values of rr (the correlation coefficient) to the scatterplots, let's consider how the correlation coefficient reflects the strength and direction of the relationship between two variables:

  1. r=1r = 1: Perfect positive linear relationship (points lie on a straight line with a positive slope).
  2. r=0.995r = 0.995: Very strong positive linear relationship (points are close to a straight line with a very small amount of scatter).
  3. r=0.798r = 0.798: Strong positive linear relationship (points are somewhat scattered but generally follow an upward trend).
  4. r=0.798r = -0.798: Strong negative linear relationship (points are somewhat scattered but generally follow a downward trend).
  5. r=0.443r = 0.443: Moderate positive linear relationship (points show an upward trend but with more scatter).

Since I can’t see the scatterplots directly, I’ll give you a guideline to match these values:

  1. Scatterplot 1: If the points form a tight, upward trend or are closely packed along an upward line, r=0.995r = 0.995 or r=1r = 1 may be appropriate. If they follow a strong downward line, it could be r=0.798r = -0.798.
  2. Scatterplot 2: Look for a moderate to weak upward trend for r=0.443r = 0.443, or a strong downward trend for r=0.798r = -0.798.
  3. Scatterplot 3: If the points are very tightly clustered along an upward line, r=1r = 1 or r=0.995r = 0.995 might be a good fit. For a clear downward trend, it would likely be r=0.798r = -0.798.
  4. Scatterplot 4: If the points are tightly clustered along a perfect downward line, this would correspond to r=0.798r = -0.798.
  5. Scatterplot 5: If the points exhibit a moderate positive relationship with more scatter, it would match r=0.443r = 0.443.

If you can describe the scatterplots to me or share any visual clues, I could provide a more precise matching. Would you like to do that?


Related questions for further exploration:

  1. What is the significance of a correlation coefficient of 0 or close to 0?
  2. How does a negative value of rr affect the interpretation of a scatterplot?
  3. What is the difference between correlation and causation in statistical analysis?
  4. How does the scatter of points in a plot affect the value of rr?
  5. Can rr be interpreted the same way for different types of data (e.g., linear vs. nonlinear)?

Tip: When you look at a scatterplot, the closer the points are to forming a straight line (either upward or downward), the stronger the correlation (whether positive or negative).

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Math Problem Analysis

Mathematical Concepts

Correlation Coefficient
Scatterplots
Statistics

Formulas

r = covariance(X, Y) / (σX * σY)

Theorems

Properties of the correlation coefficient

Suitable Grade Level

Grades 9-12