Question

Statistics

Posted 4 months ago

`Define 'Pearson correlation coefficient'.`

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Answer from Sia

Posted 4 months ago

Solution by Steps

step 1

Define the Pearson correlation coefficient: The Pearson correlation coefficient, denoted as $r$, is a measure of the linear correlation between two variables $X$ and $Y$. It is the ratio of the covariance of the two variables to the product of their standard deviations

step 2

The formula for the Pearson correlation coefficient is: $r = \frac{\sum_{i=1}^{n}(X_i - \bar{X})(Y_i - \bar{Y})}{\sqrt{\sum_{i=1}^{n}(X_i - \bar{X})^2}\sqrt{\sum_{i=1}^{n}(Y_i - \bar{Y})^2}}$ where $\bar{X}$ and $\bar{Y}$ are the means of the $X$ and $Y$ variables, respectively, and $n$ is the number of data points

step 3

Interpretation of $r$: The value of $r$ ranges from -1 to 1. A value of 1 implies a perfect positive linear relationship, -1 implies a perfect negative linear relationship, and 0 implies no linear relationship between the variables

Answer

The Pearson correlation coefficient $r$ is a measure of the linear relationship between two variables, calculated using the formula provided.

Key Concept

Pearson correlation coefficient

Explanation

The Pearson correlation coefficient quantifies the degree of linear relationship between two variables, with values ranging from -1 to 1.

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