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The regression lines will be perpendicular to each other if the coefficient of correlation r is equal to

The regression lines will be perpendicular to each other if the coefficient of correlation r is equal to Correct Answer 0

Concept:

Properties of regression line and correlation coefficient:

  • If the correlation coefficient rxy = 0, then the two lines of regression are perpendicular to each other.
  • If the correlation coefficient rxy = + 1, then the two lines of regression are parallel to each other.

 

Calculation:

Properties of regression line and correlation coefficient:

  • If the correlation coefficient rxy = 0, then the two lines of regression are perpendicular to each other.
  • If the correlation coefficient rxy = + 1, then the two lines of regression are parallel to each other.
  • Hence, r = 0. And option (4) is correct.

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:
Consider the following statements: 1) If the correlation coefficient rxy = 0, then the two lines of regression are parallel to each other. 2) If the correlation coefficient rxy = + 1, then the two lines of regression are perpendicular to each other. Which of the above statements is/are correct?
Which of the following statements is false?  1. When value of correlation coefficient is one, the two regression lines coincide 2. The regression coefficients are independent of the change of origin and of scale 3. The sign of the regression coefficients are always the same 4. The square of the coefficient of correlation is called coefficient of determination 
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:
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.
Assertion (A): If regression coefficient of X on Y is greater than one, regression coefficient of Y on X must be less than one.
Reason (R): The geometric mean between two regression coefficients is the coefficient of correlation.
Assertion (A): If regression coefficient of X on Y is greater than one, regression coefficient of Y on X must be less than one.
Reason (R): The geometric mean between two regression coefficients is the co-efficient of correlation.
On the basis of the above, choose the appropriate answer :
The statement concern psychrometric chart. 1. Constant relative humidity lines are uphill straight lines to the right 2. Constant wet bulb temperature lines are downhill straight lines to the right. 3. Constant specific volume lines are downhill straight lines to the right. 4. Constant enthalpy lines are coincident with constant wet bulb temperature lines. Which of the statements are correct?
Statement I The product of coefficient of correlation, standard deviation of variable 'X' and Standard deviation of variable 'Y' gives the measure of covariance between X and Y variables.
Statement II The product of coefficient of correlation between X and Y variables and the ratio between standard deviation of X variable to standard deviation of Y variable measures the slope of the regression line of X on Y variable.
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.