The question asks about the range of multiple correlation. Let's first understand what multiple correlation is.
Definition: Multiple correlation is a statistic that measures the strength and direction of a linear relationship between one dependent variable and two or more independent variables simultaneously.
Range of Multiple Correlation (R): The multiple correlation coefficient (\( R \)) is a square root of the coefficient of determination and ranges from \(0\) to \(1.0\). This means:
- A value of \(0\) indicates no linear relationship between the dependent and independent variables.
- A value closer to \(1.0\) indicates a stronger linear relationship.
Explanation of Options:
- Option 1: $-0.50$ to $+0.50$ - This range is incorrect as it does not correspond to any usual statistical range for correlation coefficients.
- Option 2: $-1.00$ to $+1.00$ - This range corresponds to simple (bivariate) correlation coefficients, not multiple correlation.
- Option 3: Zero to $1.00$ - This is the correct range for the multiple correlation coefficient as explained above.
- Option 4: There is a fixed range for bivariate correlation, but not for multiple correlation - This statement is incorrect. Multiple correlation also has a fixed range from zero to one.
Conclusion: Based on the above explanation, the correct answer is Zero to $1.00$, indicating that the multiple correlation coefficient ranges from 0 to 1.
Important Questions from Correlation Analysis
The value of simple correlation coefficient lies in the interval:
Which option is correct for the correlation ratio E 2?
Let θ be the angle made by the line of regression of Y on X. If σ Y= 2σ X and the correlation coefficient between X and Y is 0.3, the value θ equals
The multiple correlation coefficient R 1,23 as compared to any simple correlation coefficients between the distinct variable X 1 ,X 2, and X 3is
The coefficients of the regression β X|y and β Y|x , are known, The coefficient of correlation equals:
