Question

4.
The following results relate to bivariate data on (x, y):
ry = 414, r= 120, y = 90, r = 600, 1 = 300, n = 30. Later or, it was known that
two pairs of observations (12, 11) and (6, 8) were wrongly taken, the correct pairs of
observations being (10,9) and (8, 10). The corrected value of the correlation coefficient is
(a) 0.752
(b) 0.768 (c) 0.846
(d) 0.953​

Answer 1

Step-by-step explanation:

Given The following results relate to bivariate data on (x, y):

∑xy = 414, ∑x = 120, ∑y = 90, ∑x^2 = 600, ∑y^2 = 300, n = 30. Later or, it was known that  two pairs of observations (12, 11) and (6, 8) were wrongly taken, the correct pairs of  observations being (10,9) and (8, 10). The corrected value of the correlation coefficient is

• Now ∑xy = 414, ∑x = 120, ∑y = 90, ∑x^2 = 600, ∑y^2 = 300, n = 30
• Question is two pairs of observations (12,11) and (6,8) were wrongly taken and we need to find the corrected value.
• Now wrong pair is (12,11) and (6,8) (these are x and y values)
•       Correct pair is (10,9) and (8,10)
• So we have corrected ∑x = n x x bar – wrong  value + corrected  value -----1
• Now x bar = ∑x / n
•                 = 120 / 30
•                  = 4
• Also y bar = ∑y / n
•                   = 90 / 30
•                   = 3
•   Substituting the values in 1 we get
•                            So ∑x = 30 x 4 – (12 + 6) + (10 + 8)
•                                     = 120 – 18 + 18
•                                     = 120  
•      Similarly for y bar we have
•            Corrected ∑y = n x y bar – wrong value + corrected value.
•                                  = 30 (3) – (11 + 8) + (9 + 10)
•                                  = 90
•   Therefore corrected ∑xy = ∑xy – wrong xy value + corrected xy value.
•                                           = 414 – [(12 x 11) + (6 x 8)] + [(10 x 9) + (8 x 10)]
•                                           = 414 – 180 + 170
•                                          = 404
•  Therefore corrected ∑x^2 = ∑x^2 – wrong x^2 value + corrected x^2 value
•                                            = 600 – (12^2 + 6^2) + (10^2 + 8^2)
•                                           = 600 – 180 + 164
•                                            = 584
• So corrected ∑y^2 = ∑y^2 – wrong y^2 value + corrected y^2 value.
•                               = 300 – (11^2 + 8^2) + (9^2 + 10^2)
•                              = 300 – 185 + 181
•                               = 296
• Now corrected correlation coefficient will be  
•                    So r = n ∑xy – ∑x.∑y / √n∑x^2 – (∑x)^2 √n∑y^2 – (∑y)^2
•                           = 30(404) – 120 x 90 / √30(584) – (!20)^2√30(296) – (90)^2
•                            = 1320 / √3120 √780
•                            = 1320 / 55.856 x 27.928
•                                = 1320 / 1559.9
•                                = 0.846

Reference link will be

https://brainly.in/question/15390083

Answer 2

Answer:

Correct Coefficient of correlation is 0.846