Question

(c) Compute the sample correlation coefficient r for each of the following data sets and show that r is the same for both. (Use 3 decimal places.)

Answer 1

Solution - Given that, Find the correlation coefficient or c.) 24 2 Tu no sis 45 25 7 | u | 28 | 49 | 16 2 2 4 4 4 181 {x=18 Ey= 11 {xy=77/{x: 134 Ey?:45] - nEny -(Ex) (Ey) Correlation coefficient (8): VnCE2")-(Ex)" ✓n Cey")-(ey)" 3(77)-(18)(11) 13 (134) -(13)*. 13(us)-(10) : - .231-198 T78.ru 33 - 33.036 X-0.998 ii) I y Ixy ă 1 y xnn 7 1.2 orno s - ∞ 4 1 4 45 | 25 Ex:11 Ey= 18 {2y = 77 23:45 | Ey² = 134]

Correlation coefficient (o): - nexy -(Ex) Cey) Nacex") = (2x)" Jacęga)- czyja 3(77) - (1) (18) √3cus)-(1137 | 3 (134) = (18) 231-198 ja .578 33 · 33.036 7 20.998 ♡ Given that, Significance level (&)-0.05. Sample size(n): 5. lo y lal y l xy 3 | 60 q 3600 180 6 | 95 | 36 9025 570 140 144 119600 1680 184 289 33856 3128 22 114 484 30276 | 3828 2x360 Sy=6535x8 962 4y=96357|Say: 9386. Correlation coefficient (8) .. nexy - ({x) Cey) Incex")_(8x)2 Incey)-(eyr 519386) (60)(653) 5(962)-(60) /5196357)-(653)?

46930 - 39180 ✓ 1210 155376 7750 (34.785)(235.32) 7750 8185.60 820.926 Critical & Significance level@)-0.05 samples (n) = 5 Coiticalooss 201878. 67 Given that, x 1004 y ny HO 40160 97500 975 992 65 935 1008016 1600 950625 10.000 984064 4225 874225 21025 944784 4624 857476 22201 {2=5619190 / Ey= 63675 145 68 926 Ex=5804 Ey= 567 912 .64480 135575 66096 137974 Exy=541185 (५१ Correlation coefficient 6). Correlation collicent or nɛay (Ex) Cey) Incex")-(ex Sney")-(EY)

60541785) -(5804)(567) V6(5619190) – (5804)”. V6C63175) – (567) 3250710 - 3290868 √28724 560561 -40158 (169.481) (246.091) -40158 41707.7488 18 = -0.963 Critical oi- Signififance level (&)-0.01 sample (n) = G. Criteal y eleron = Critical o..16 30.917