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1. Define product-moment correlation coefficient and show that it lies between- and +1.

1. Define product-moment correlation coefficient and show that it lies between- and +1.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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4. If x' and y' are the deviations of the variables X and Y from their means, s, s are the variances of variables X and Y, correlation coefficient between variables X and Y is r and (X, Y) for i = 1, 2, n are the n values of (X, Y), then show that Hence prowa x x $2 $1 =1-12/12/2012 2n ...9 100 =−1+ Xi Xi + 2n 2n=1 $1. $₂ balles ad no
Transcribed Image Text:4. If x' and y' are the deviations of the variables X and Y from their means, s, s are the variances of variables X and Y, correlation coefficient between variables X and Y is r and (X, Y) for i = 1, 2, n are the n values of (X, Y), then show that Hence prowa x x $2 $1 =1-12/12/2012 2n ...9 100 =−1+ Xi Xi + 2n 2n=1 $1. $₂ balles ad no
In EXERCISES 1. Define product-moment correlation coefficient and show that it lies between - and +1. 2. Define scatter diagram. Give the scatter diagrams when the product-moment correlation coefficient r is zero and -1. 3. Show that the correlation coefficient of x and y is zero if x and y are independent. Is the converse also true? Give reasons for your answer. 3.3 4. If x' and y' are the deviations of the variables X and Y from their means, are the variances of variables X and Y, correlation coefficient between variables X and Y is r and (X, Y) for i = 1, 2, ..., n are the n values of (X, Y), then show that 2 1 2 ( - ) ² - - ¹ + 12 (4+4)² =-1+ 2n 2n X125 978 r=1-- Hence, prove that - 1 ≤ r ≤ 1. 13. 14. If x and y are coeficient r, fin Hence find cor 5. If ax + by + c = 0 is the relation between two variables x and y, then find the correlation coefficient between x and y. 6. If 3y - x = 4, u + 4y = 9 are the relations between variables x, y, u and v, and correlation coefficient between x and u is 0.3, then find correlation coefficient between y and v. 916 2310612noo art lo zstemes 15. If u = 2x + 5a the regression 16. Are the follo (i) The sum 0.75. (ii) If the tw is ± 0.5 (iii) The c correl 17. If regress correlatic 18. Two var y Sh Show t what is 19. Define are no 46
Transcribed Image Text:In EXERCISES 1. Define product-moment correlation coefficient and show that it lies between - and +1. 2. Define scatter diagram. Give the scatter diagrams when the product-moment correlation coefficient r is zero and -1. 3. Show that the correlation coefficient of x and y is zero if x and y are independent. Is the converse also true? Give reasons for your answer. 3.3 4. If x' and y' are the deviations of the variables X and Y from their means, are the variances of variables X and Y, correlation coefficient between variables X and Y is r and (X, Y) for i = 1, 2, ..., n are the n values of (X, Y), then show that 2 1 2 ( - ) ² - - ¹ + 12 (4+4)² =-1+ 2n 2n X125 978 r=1-- Hence, prove that - 1 ≤ r ≤ 1. 13. 14. If x and y are coeficient r, fin Hence find cor 5. If ax + by + c = 0 is the relation between two variables x and y, then find the correlation coefficient between x and y. 6. If 3y - x = 4, u + 4y = 9 are the relations between variables x, y, u and v, and correlation coefficient between x and u is 0.3, then find correlation coefficient between y and v. 916 2310612noo art lo zstemes 15. If u = 2x + 5a the regression 16. Are the follo (i) The sum 0.75. (ii) If the tw is ± 0.5 (iii) The c correl 17. If regress correlatic 18. Two var y Sh Show t what is 19. Define are no 46
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