Define 'Pearson correlation coefficient'.

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∻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.⚹◊What is the formula for calculating the Pearson correlation coefficient between two variables $X$ and $⍭ Generate me a similar question◊

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