Difference between coefficient of correlation and coefficient of determination.p

1. Difference between coefficient of correlation and coefficient of determination The coefficient of correlation and the coefficient of determination are closely related statistical measures used to describe the relationship between two variables. However, they have distinct meanings and interpretations: Coefficient of Correlation (r): 1. Definition: ● Coefficient of Correlation (r): It is a measure of the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship. 2. Interpretation: ● Coefficient of Correlation (r): The sign indicates the direction (positive or negative) of the relationship, and the magnitude

2. (absolute value) indicates the strength. A higher absolute value of r suggests a stronger linear relationship Coefficient of Determination (r²): 1. Definition: ● Coefficient of Determination (r²): It represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s). In the context of simple linear regression, it is the square of the coefficient of correlation (r). 2. Interpretation: ● Coefficient of Determination (r²): It ranges from 0 to 1 and is often expressed as a percentage. It indicates the proportion of the variance in the dependent variable that can be explained by the independent variable(s). Key Differences: ● Purpose: ● Coefficient of Correlation (r): Describes the strength and direction of the linear relationship. ● Coefficient of Determination (r²): Measures the proportion of variance in the dependent variable explained by the independent variable(s). ● Range: ● Coefficient of Correlation (r): Ranges from -1 to 1. ● Coefficient of Determination (r²): Ranges from 0 to 1. ● Interpretation: ● Coefficient of Correlation (r): Describes the strength and direction of the linear relationship between two variables. ● Coefficient of Determination (r²): Indicates the proportion of the variance in the dependent variable that is explained by the independent variable(s). ● Calculation: ● Coefficient of Correlation (r): Calculated using the formula for correlation. ● Coefficient of Determination (r²): Calculated by squaring the coefficient of correlation.

3. In summary, while the coefficient of correlation (r) provides information about the strength and direction of a linear relationship, the coefficient of determination (r²) specifically quantifies the proportion of variance in the dependent variable that can be explained by the independent variable(s).

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