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The range in which the correlation r lies –

The range in which the correlation r lies – Correct Answer [-1, 1]

CONCEPT:

Karl Pearson’s coefficient of correlation r measures numerically only linear relationship between two variables and r lies between –1 and 1.

So,

CALCULATIONS:

Karl Pearson’s coefficient of correlation r measures numerically only linear relationship between two variables and r lies between –1 and 1.

i.e r ∈

Related Questions

Which of the following statements relating to correlation and reegression are true?
1. The coefficient of correlation is independent of change of origin and scale
2. The coefficient of correlation between the two variables is the arithmetic average of the two regression coefficients
3. The probable error of the coefficient correlation is 0.6745 times of its standard error
4. Coefficient of correlation multiplied by the ratio between the standard deviations of the two variables denotes the slope of the regression line
Select the correct answer:
Which of the following statements are true? a. The correlation coefficient is dependent on the choice of both origin and scale observations. b. The correlation coefficient is dependent on the units of measurements. c. The coefficient of correlation is the square root of the coefficient of determination. d. The zero value of the correlation coefficient cannot estimate the value of the dependent variable.
Which of the following are not the property/ies of correlation coefficient? (A) r is independent of the choice of origin (B) r is independent of scale (C) r lies between –1 and +1 (D) r = + 1.0 indicates a perfectly negative correlation (E) r = –1.0 indicates a perfectly positive correlation Choose the correct answer from the options given below:
The . . . . . . . . of r (correlation) is an amount which if added to and subtracted from the average correlation co-efficient produces amounts within which the chances are even that a co-efficient of correlation from a series error selected at random will fall
The . . . . . . . . error of correlation is an amount which if added to and subtracted from the average correlation coefficient produces amounts within which the chances are even that a coefficient of correlation from a series error selected at random will fall.
Which of the following statements are true?
1. The coefficient of rank correlation has the same limits as the Karl Pearson's coefficient of correlation.
2. The coefficient of correlation is independent of the change of origin but not of scale.
3. The covariance between $$X$$ and $$Y$$ is defined as $$\frac{{\sum {xy} }}{n}$$ where, $$x = \left( {X - \overline X } \right),y = \left( {Y - \overline Y } \right)$$      and $$n = $$ no. of paired observations.
4. $${b_{xy}}$$ is called regression coefficient of $$X$$ variable on $$Y$$ variable.
5. If $${b_{xy}}$$ is 0.4 and $${b_{yx}}$$ is 1.6, coefficient of determination would be 0.8.
Select the correct answer:
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