Suppose the coefficient of correlation for two variable is r= -0.811. O 0.811 O -0.811 O 0.658 O Not enough information to determine
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
![### Understanding Coefficient of Determination
**Problem Statement:**
"Suppose the coefficient of correlation for two variables is r = -0.811. Find the coefficient of determination."
**Answer Choices:**
1. 0.811
2. -0.811
3. 0.658
4. Not enough information to determine
5. None of these
**Explanation:**
To calculate the coefficient of determination (R²), you square the coefficient of correlation (r). The coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable.
Given: \( r = -0.811 \)
Calculation:
\[ R² = r² \]
\[ R² = (-0.811)² \]
\[ R² = 0.658 \]
### Correct Answer:
The coefficient of determination is **0.658**.
This implies that approximately 65.8% of the variance in the dependent variable can be explained by the independent variable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcfef55d1-e74e-4acc-a65e-b6e34bf1c85d%2F0069e3e6-fdf9-4969-ae7f-baeb53d35c8f%2F5a3s9e_processed.jpeg&w=3840&q=75)
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