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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?

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? Correct Answer Neither 1 nor 2

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:

  • 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.


So, statement (1) & statement (2) both are wrong.

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 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.
Which of the following statements are true? (i) Angles forming a linear pair are supplementary. (ii) Angles forming a linear pair can both be acute angles. (iii) Two lines parallel to the same line are parallel to each other. (iv) Two lines perpendicular to the same line are perpendicular to each other.
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 following are the conditions for selecting list of a suitable candidates to be called for interview after the written test for the recruitment is conducted/organized for management - level persons for a multi - national company. For providing accounting services and sales the candidate must (a) be holding a graduation in basic science with 65% or above or B.E. degree with 55% and above marks (b) have passed the written test with 70% or above marks (c) the age must be in the group 25 to 30 years as on 1/4/18 (d) have experience in an accounting firms for three years and diploma in accounting with 60% or above marks (e)  be presently drawing CTC of 6 Lakhs per annum and above In case the applicant who satisfies all other terms above except 1) at (a) above, then be referred as Junior Accountant 2) at (d) & (e) above then be referred as Trainee - Accountant Satisfying all the above with experience of 5 years then the referred as senior-Accountant Satisfying all the above criteria (a - e) with CA/ICWA/MBA (Finance) then be referred as manager (Accounts) Read all the above information and answer the following question Praveen has done his Masters in physics. He has no experience in accounting neither diploma. He is ready to be on training for accounting after joining. For which position he may be referred
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The following are the conditions for selecting list of a suitable candidates to be called for interview after the written test for the recruitment is conducted/ organized for management-level persons of a multi-national company. For providing accounting services and sales the candidates must (a) be holding a graduation in basic science with 65% or above or B. E degree with 55% and above marks (b) have passed the written test with 70% or above marks (c) the age must be in the group 25 to 30 years as on 1/4/18 (d) have experience in an accounting firms for three years and diploma in accounting with 60% or above marks (e) be presently drawing CTC of 6 Lakhs per annum and above In case the applicant who satisfies all other terms above except 1) at (a) above, then be referred as Junior Accountant 2) at (d) & (e) above then be referred as Trainee-Accountant Satisfying all the above with experience of 5 years then be referred as senior-Accountant Satisfying all the above criteria (a-e) with CA/ ICWA / MBA (Finance) then be refereed as manager (Accounts) Read all the above information and answer the following question Shravani has passed H. SC with 72% of marks. She has done diploma in accountancy with 62% of marks. She was working with an organization in the field of accounting in the field of accounting from 4 years and was drawing CTC of 6.5 Lakhs presently. She is 28yrs as on July 2018. She may referred for the position of: