Does a correlation of -0.70 or +0.50 give a larger...

Does a correlation of $-0.70$ or $+0.50$ give a larger coefficient of determination? We say that the linear relationship that has the larger coefficient of determination is more strongly correlated. Which of the values shows a stronger correlation?

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Key Concepts

Coefficient of Determination

The coefficient of determination, often represented as R², measures the proportion of the variance in one variable that is predictable from the other variable. It is computed by squaring the Pearson correlation coefficient, thus removing any sign and emphasizing the magnitude of the linear relationship. This concept is central in regression analysis and helps determine how well the data fits a statistical model.

Pearson Correlation Coefficient

The Pearson correlation coefficient quantifies the linear relationship between two variables and ranges from -1 to +1. The sign indicates the direction (positive or negative), while the magnitude indicates the strength of the relationship. It is a foundational concept in statistics used to assess the degree of association between two continuous variables.

Squaring the Correlation

Squaring the Pearson correlation coefficient is a crucial step because it converts the correlation into the coefficient of determination. This process eliminates any influence of the sign, meaning both positive and negative correlations contribute equally when evaluating the strength of the linear association. The resulting value, R², allows for a more straightforward comparison of the strength of different correlations.

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