Question

R$^2$ is the notation for

• A. The coefficient of correlation
• B. The coefficient of determination
• C. The coefficient of variation
• D. The coefficient of regression

Hint:

\( R^2 \) (Coefficient of Determination) shows the percentage of variation explained by the model.
For example, an \( R^2 \) value of 0.85 means that 85% of the variation in the dependent variable is explained by the independent variables in the model.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In regression analysis, it is important to measure how well the regression line fits the observed data.
The standard metric used to represent this goodness-of-fit is denoted by the symbol \( R^2 \) (or \( r^2 \)).

Step 2: Detailed Explanation:
Let us clarify the notations used for different statistical coefficients:
- Coefficient of correlation (\( r \)): Measures the linear strength and direction between two variables.
- Coefficient of determination (\( R^2 \)): Measures the proportion of the total variation in the dependent variable (\( y \)) that can be explained by the independent variable (\( x \)) in the regression model.
It takes values between 0 and 1 (or 0% to 100%).
- Coefficient of variation (CV): Measures the relative dispersion of data and is calculated as \( \text{CV} = \frac{\text{Standard Deviation}}{\text{Mean}} \times 100\% \).
- Coefficient of regression (\( b \)): Represents the slope of the regression line, indicating the change in \( y \) per unit change in \( x \).
Therefore, \( R^2 \) is the standard notation for the coefficient of determination.

Step 3: Final Answer:
\( R^2 \) is the notation for the coefficient of determination.