If (x,y) is the relationship and r(x,y) = 0.5, then which of the following statements is correct?
Understand the Problem
The question appears to be asking about various statistical methods and concepts, particularly focusing on correlation coefficients and their interpretations. It seeks to determine the appropriate correlation type and its implications based on given values and scenarios.
Answer
The correlation coefficients are: - \( r(X, Y) = 0.5 \) (Moderate Positive) - \( r(X, Y) = 0.7 \) (Strong Positive) - \( r(X, Y) = 0.9 \) (Very Strong Positive) - \( r(X, Y) = 0.0 \) (No Correlation)
Answer for screen readers
The interpretations of the respective correlation coefficients are:
- ( r = 0.5 ): Moderate positive correlation
- ( r = 0.7 ): Strong positive correlation
- ( r = 0.9 ): Very strong positive correlation
- ( r = 0.0 ): No correlation
Steps to Solve
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Identify the Question The problem asks about several correlation scenarios and their respective coefficients.
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Analyze the Given Correlations We have the following given values related to different situations:
- ( r(X, Y) = 0.5 )
- ( r(X, Y) = 0.7 )
- ( r(X, Y) = 0.9 )
- ( r(X, Y) = 0.0 )
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Determine the Characteristics of Correlations
- ( r = 1 ): Perfect positive correlation
- ( r = -1 ): Perfect negative correlation
- ( r = 0 ): No correlation
- ( 0 < r < 1 ): Positive correlation
- ( -1 < r < 0 ): Negative correlation
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Applying Correlation Interpretation For each correlation value:
- ( r = 0.5 ): Moderate positive correlation
- ( r = 0.7 ): Strong positive correlation
- ( r = 0.9 ): Very strong positive correlation
- ( r = 0.0 ): No correlation
- Answer the Relevant Questions From the context, relate the type of correlation to the given questions about specific scenarios (like marks, observations, etc.), indicating their potential relationships.
The interpretations of the respective correlation coefficients are:
- ( r = 0.5 ): Moderate positive correlation
- ( r = 0.7 ): Strong positive correlation
- ( r = 0.9 ): Very strong positive correlation
- ( r = 0.0 ): No correlation
More Information
Correlation coefficients describe the strength and direction of a linear relationship between two variables. The closer the correlation coefficient is to 1 or -1, the stronger the relationship.
Tips
- Misinterpreting the value: Confusing the strength of the correlation with its direction (positive or negative).
- Ignoring context: Failing to consider the specific context of the variables when analyzing correlation.
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