In a p-variate distribution, all the total (order zero) correlation coefficients are equal toP*0. Let P, demote the partial correlation coefficient of order k and R, be the multiple correlationcoefficient of one variate on k other variates Prove thatk po²1(1)A-A-1 =-PxPx-11+ (k-1) poand(iii) R2

Answered: Image /qna-images/answer/3b2bb040-e5af-4da2-8407-fa4c90947a1d.jpg

Answered: in a poariate distribution, all the…

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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(b) For each pair of variables, generate the correlation coefficient r. For all pairs involving x1, compute the corresponding coefficient of determination r2. (Use 3 decimal places.) r r2 x1, x2 x1, x3 x1, x4 x1, x5 x1, x6 x2, x3 x2, x4 x2, x5 x2, x6 x3, x4 x3, x5 x3, x6 x4, x5 x4, x6 x5, x6
Q5. (a) For what range of values can the coefficient of correlation of a sample of 52 pairs be considered significantly different from zero at the 1% level of significance? (b) Do the following for the data Days after emergence, X Average dry matter Conventional, Y, Yield (g'plant) Improved, Y2 9. 35 52 170 270 49 50 71 180 91 250 270 3 10 104 Compute the coefficients of correlation between X and Y1, Yi and Y2, and X and Y2 Compute coefficients of determination between X and Y 1, and X and Y2. Interpret these coefficients. ii) iii) Test the hypothesis that the population correlation coefficient between Yi and Y: is 0.80 against the alternative that it is not. |Simple Regression & Correlation]
Q2) The following data represents the results of an experimental test, if the relation between variables take the form y=ae^(bvx) y = aeb√x X 4 7 12 15 24 y 13 10 9 7 4 * the correlation coefficient of the above (2 relation 0.9927 0.9727 0.9772 0.9977 none of all above
A computer while calculating the correlation coefficient between the variables X and Y obtained the following results: N= 30, ΣΧ-120, ΣΧ600, ΣΥ-90, ΣΥ250, ΣΧΥ-356. It was, however later discovered at the time of checking that it had copied down two pairs of observations: X Y wrongly as while the correct values are X Y 8 10 8 12 10 8 12 7. Find the correct value of correlation coefficient between X and Y.
A computer while calculating the correlation co-efficient between the variables X and Y obtained the following values. N = 25 )X= 125 SX2 = 650 2y= 100 EY2 = 460 EXY = 508 It was, however, later on discovered at the time of checking that it had copied down two pairs of observations as : X Y 14 8 While actual values were Y 12 8 Obtained the correct value of correlation coefficient between X and Y.
The following information represents the scores that 14 students obtained (X) in Test-1 and in Test-2 (y) by 14 students: Ty-876. Ey? - 65850, Ex= 854, Ex2- 64222, and Exy - 64346 The sample correlation coefficient is: O 0.943 O 0.7968 O 0.8501 O 0.8034
The following data show the number of class sessions missed during a semester of SOC221 and the final grade for a sample of 8 students selected at random. Number of Sessions Missed Final Grade (x) (y) 0 96 2 88 12 68 6 91 8…
The following results were obtained in a study of correlation coefficient between two variables X and Y : n=50, x =10, o,=3; y O, = 2; r. = 0.3. xy || However, on subsequent verification it was found that one value of X = 10 and one value of Y = 6 were inaccurate and hence weedėd out. With the remaining values how is the original value of correlation coefficient affected.
(d) Does a linear relation exist between the speed at which a ball is hit and the distance the ball travels? The variables speed at which the ball is hit and the distance the ball travels are positively associated because r is positive and the absolute value of the correlation coefficient is greater than the critical value ( ) (Round to three decimal places as needed.)
Give the formula for calculating the Kendall's partial rank correlation and Piges rank correlation coefficient between different variables like X and Y, Z and P and so on eliminating the effect of the third variable like Z, P, X etc? .
11. What is the linear correlation coefficient, r, for the scatterplot below? r = 1 r = 0 r = -1 r = -0.51

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