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
If X ∼ N (0, 1) and Y = X2 then the correlation coefficient r (X, Y) is
Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): If the securities with less than perfect negative correlation between their price movements are combined, portfolio risk can be reduced significantly.
Reason (R): The term with negative correlation has the effect of reducing the computed value of total portfolio risk, given other terms that are positive.
In the light of the above statements, choose the most appropriate answer from the options given below:
The two-regression equation of variable \(\rm{x}\) and \(\rm{y}\) are
\(\rm{y = 0.8x + 9.8}\) and \(\rm{x = 10.2 + 0.6y}\)
The coefficient of correlation between \(\rm{x}\) and \(\rm{y}\) is
- Let $X$ be a random variable that follows $Uniform(-1, 1)$ distribution. The conditional distribution of the random variable $Y$ given $X = x$ is the $Uniform(x^2 - 0.1, x^2 + 0.1)$ distribution.
The value of $correlation(X, Y)$ is __________ . (Answer in integer) - In the variance-covariance matrix given below, which one of the following pairs of elements has the highest correlation?
$$ \begin{bmatrix} & P & Q & R & S \\ P & 0 & 0 & 0 & 0 \\ Q & 0 & 3.73 & 1.85 & 3.23 \\ R & 0 & 1.85 & 0.93 & 1.61 \\ S & 0 & 3.23 & 1.61 & 2.79 \end{bmatrix} $$
