Question
The multiple correlation ranges between :
The correct answer is
Zero to $1.00$
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.
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Important Questions from Correlation Analysis
- 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?
$$ \begin{bmatrix} & P & Q & R & S \\ P & 0 & 0 & 0 & 0 \\ Q & 0 & 3.73 & 1.85 & 3.23 \\ R & 0 & 1.85 & 0.93 & 1.61 \\ S & 0 & 3.23 & 1.61 & 2.79 \end{bmatrix} $$ - Consider 62 pair of observations $(x_i, y_i)$, i = 1, …., 62, obtained from the distribution of $(X, Y)$. The Pearson correlation coefficient ($R$) of these observations is 0.27.
Which one of the following statements is CORRECT for a significance level $\alpha = 0.05$ and $t_{0.025,60} = 2.0$?
Hint: Test statistic $t = \frac{R\sqrt{n - 2}}{\sqrt{1 - R^2}}$ - Let $X = \cos \theta$ and $Y = \sin \theta$, where $\theta$ is a random variable uniformly distributed over $(0, 2\pi)$. Which of the following options is/are CORRECT?
Hint: $\text{cov}(X, Y) = E[(X - E(X)) (Y - E(Y))]$ - Arrange the following correlation coefficients in descending order in terms of their strength of relationship, as defined by common variance :
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