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Pearson's coefficient of correlation r a...

Pearson's coefficient of correlation r always follow: (a)`rle1` (b)`rlt-1` (c)`|r|le1` (d)`|r|ge1`

A

`rle1`

B

`rlt-1`

C

`|r|le1`

D

`|r|ge1`

Text Solution

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The correct Answer is:
To solve the question regarding Pearson's coefficient of correlation \( r \), we will analyze the properties of \( r \) step by step. ### Step 1: Understanding Pearson's Coefficient of Correlation Pearson's coefficient of correlation \( r \) is a statistical measure that describes the strength and direction of a linear relationship between two variables. ### Step 2: Range of \( r \) It is known that the value of \( r \) can range from -1 to +1. This means: \[ -1 \leq r \leq 1 \] ### Step 3: Analyzing the Options Now, let's evaluate the given options based on the range of \( r \): - **Option (a)**: \( r \leq 1 \) - This is true, but it does not account for the lower limit of \( r \). Therefore, it is not a complete representation of the range. - **Option (b)**: \( r < -1 \) - This is incorrect because \( r \) cannot be less than -1. - **Option (c)**: \( |r| \leq 1 \) - This is correct because it captures both the upper and lower bounds of \( r \). It states that the absolute value of \( r \) is always less than or equal to 1. - **Option (d)**: \( |r| \geq 1 \) - This is incorrect because it suggests that \( r \) can be equal to or greater than 1 in absolute value, which is not true. ### Step 4: Conclusion Based on the analysis, the correct answer is: \[ \text{(c) } |r| \leq 1 \]
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