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 (the correlation coefficient) to the scatterplots, let's consider how the correlation coefficient reflects the strength and direction of the relationship between two variables:
- : Perfect positive linear relationship (points lie on a straight line with a positive slope).
- : Very strong positive linear relationship (points are close to a straight line with a very small amount of scatter).
- : Strong positive linear relationship (points are somewhat scattered but generally follow an upward trend).
- : Strong negative linear relationship (points are somewhat scattered but generally follow a downward trend).
- : 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:
- Scatterplot 1: If the points form a tight, upward trend or are closely packed along an upward line, or may be appropriate. If they follow a strong downward line, it could be .
- Scatterplot 2: Look for a moderate to weak upward trend for , or a strong downward trend for .
- Scatterplot 3: If the points are very tightly clustered along an upward line, or might be a good fit. For a clear downward trend, it would likely be .
- Scatterplot 4: If the points are tightly clustered along a perfect downward line, this would correspond to .
- Scatterplot 5: If the points exhibit a moderate positive relationship with more scatter, it would match .
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:
- What is the significance of a correlation coefficient of 0 or close to 0?
- How does a negative value of affect the interpretation of a scatterplot?
- What is the difference between correlation and causation in statistical analysis?
- How does the scatter of points in a plot affect the value of ?
- Can 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
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