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Correlation Coefficient Formula:
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The correlation coefficient (R) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, where -1 indicates perfect negative correlation, +1 indicates perfect positive correlation, and 0 indicates no linear correlation.
The calculator uses the formula:
Where:
Explanation: This formula calculates the correlation coefficient from the coefficient of determination obtained through linear regression analysis on TI-84 calculators.
Details: The correlation coefficient is essential in statistics for understanding relationships between variables, making predictions, and determining the reliability of linear models in research and data analysis.
Tips: Enter the coefficient of determination (R²) value obtained from your TI-84 linear regression analysis. The value must be between 0 and 1 inclusive.
Q1: What is the difference between R and R²?
A: R measures the strength and direction of linear relationship, while R² represents the proportion of variance in the dependent variable explained by the independent variable.
Q2: How do I get R² on TI-84?
A: Use the STAT menu, perform linear regression (LinReg), and R² will be displayed in the results along with other regression statistics.
Q3: Can R be negative?
A: Yes, R can range from -1 to +1. Negative values indicate inverse relationships, positive values indicate direct relationships.
Q4: What does R = 0.8 mean?
A: R = 0.8 indicates a strong positive linear relationship between the variables, meaning as one variable increases, the other tends to increase as well.
Q5: When should I use this calculation?
A: Use this when you have R² from linear regression analysis and need to determine the actual correlation coefficient for interpretation and reporting.