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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 r , is a measure of the linear correlation between two variables X X and Y 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=i=1n(XiXˉ)(YiYˉ)i=1n(XiXˉ)2i=1n(YiYˉ)2 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 Xˉ \bar{X} and Yˉ \bar{Y} are the means of the X X and Y Y variables, respectively, and n n is the number of data points
step 3
Interpretation of r r : The value of r 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 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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