The coefficient of correlation is independent of
Show Hint
- Change of scale only
- Change of origin only
- Both change of scale & origin
- No change
The Correct Option is C
Solution and Explanation
The coefficient of correlation, often denoted as \( r \), is a measure of the linear relationship between two variables. It is calculated as:
\[ r = \frac{n(\Sigma xy) - (\Sigma x)(\Sigma y)}{\sqrt{[n \Sigma x^2 - (\Sigma x)^2][n \Sigma y^2 - (\Sigma y)^2]}} \]
Where \( x \) and \( y \) are the two variables, and \( n \) is the number of data points.
The important point to note is that the coefficient of correlation is **independent** of both the scale (i.e., the units of the variables) and the origin (i.e., the reference point for measuring the variables). This means that the coefficient of correlation will remain the same if you change the units of measurement or shift the origin of the data.
Thus, the correct answer is option (C): Both change of scale & origin.
Top Questions on Statistics
Scores obtained by two students P and Q in seven courses are given in the table below. Based on the information given in the table, which one of the following statements is INCORRECT?
- For the following ten angle observations, the standard error of the mean angle is given as __________ arcsecond (rounded off to 2 decimal places).
25°40'12'' 25°40'14'' 25°40'16'' 25°40'18'' 25°40'09''
25°40'15'' 25°40'10'' 25°40'13'' 25°40'15'' 25°40'18'' - Two adjacent angles \( A \) and \( B \) have been observed with the following mean values and correlation matrix \( \rho \):
\[ \bar{A} = 10^\circ 20'10'' \pm 10'', \quad \bar{B} = 25^\circ 35'15'' \pm 20'' \]
\[ \rho = \begin{bmatrix} 1.0 & 0.6 \\ 0.6 & 1.0 \end{bmatrix} \]
The standard deviation of the sum of the estimated angles \( A + B \) will be \underline{\hspace{2cm}} arcseconds (rounded off to 2 decimal places). - The covariance matrix, \( \Sigma \), for the planar coordinates of a surveyed point is given as:
\[ \Sigma = \begin{bmatrix} 25 & 0.500 \\ 0.500 & 100 \end{bmatrix} \ \text{(in mm}^2\text{)} \]
The coefficient of correlation is \underline{\hspace{1cm}} (rounded off to 2 decimal places). - The residual error in a measurement comprises a bias of \( +0.08 \, {m} \) and a random component given by the following density function: \[ f(x) = \frac{1}{0.15 \sqrt{2\pi}} \exp\left( -\frac{x^2}{2 \cdot (0.15)^2} \right) \] For this system, the mean square error (MSE) is \underline{{2cm} m (rounded off to 2 decimal places).}
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