Question

4. Heights of Presidents and Runners-Up data set: determine correlation coefficient r, determine of the correlation is significant. Winner 69.5 73 73 74 74.5 74.5 71 71 a correlation coefficient r = Runner-up 72 69.5 70 68 74 74 73 76 b. significant (yes or no)? 5. Casino Size and Revenue data set: determine correlation coefficient r, determine if the correlation is significant Size 160 227 140 144 161 147 141 a. correlation coefficient Revenue 189 157 140 127 123 106 significant (yes or no).

Answer 1

since coeff then ③ Her Rei we . If (x4), (3 ). Pland) is our data set then the correlation coefficient de or simply p is given by the formula nano of obseruation en & (&: - 50) (9:- 9 where = t žr. {:-)}{(4-9)} Ja tu & y; Here is the heights of Presidents are a denoted by x;'s & heights of Runners-up are denoted by ds. n=8 (because & sets of exi, Y;)'s are given to us) Nowe the formula of a can be simplified as the following pa y – nisłą | 12 – nữ) } Su - 6)^ Calculations for finding r a X; ; X;? y;? 3; ; Calculations are 69.5 72 (69.52 (72)2 69.5872 done using 73 69.5 (43)² (69.573 73x69.5 calculator (70)2 74 68 325x580.5 74.5 74 674.5) (74)? 74.5874 or x = 72.5625 74.5 79 74-5674 j = 1x576.5 71 73 (71)² (73121 7176 1702 1762 / 71876 ar j = 72.0625 580.5 576.5 42146.75 41595.2541824.5 73 73x70 74868 this In to the dat 71x73 The 41824.5 - (8 x 72.5625872 boz ✓ 42146.75 – 18 4472.562573}] 41595-25-432(72.0625) P = -0.22

given) since the values differs from o hence the correlation coefficient is significant. (If its value is close to o then we say it is not significant Here xi's are the casino sires & gi's are the Revenue values. Using some formula as before we calculate & Here n=7 (7 sets of observations X; I Y I x2 1 X:4, 160 189 I (160)2 I (189)2 160x 189 227 157 (227)2 (157) 227x157 140 140 (140)2 140) 140x140 144 127 (144)3 | (127) 144x127 123 (161)2 (123)? 1618123 147 106 (147² (106)² 147X106 141 101 (141) (101)2 1120 943 184876 132665 153393 161 1418101 & Here a = 1120 2160 j = 943 = 134.714 P. 153393 - (7x160x134.714) [184876 – 47*(160)2}][132665 - {7x (134714)?}] -p20.4456 which is not at alle close to o Hence this pualue is also significant In last question of your pictures we are to determine the regression equation of you x from the same data set. Hence I am doing this before. The regression equation of y an x is given by ộ = atba where a=g-bê . &b= con(x,y) ab [7; 4; - n5ý E9;? - 7130)? Here b = 153393-7x 160x134.714 [184876 – 47*(60123]

:.ba_2913.33 0 .4428 5676 a=y-bă = 134.714-(0.4428% 160) = 63.866 Regression dire is given by ŷ = 63.866 +(0.4428°32) None if sire x=100 then y= 63.866+ (0.4428x100) y = 108.146 y u 108 rounded to hearest integer) I The equation for regression line is ý = -3.22+1.028 where a represents the Is score of the twin that was born first The best predicted Ios of a twin who was born second given that the first born twin has an IS of Ilo is ĝ =-3.22 +(1.02 X 110) = 108.98 ③ Here the regression tire is 9 = 3.46 +1.01x, where x represents the sugar content. The best predicted calorie content for cereal with 0.40 gram of sugar per gram of cereal is. ŷ = 3.46+(1.01X0.40) = 3.864 ③ The regression line of y an x is given by ŷ a+bx where b= {aily; - hlatif) [x² – na)? on & a=ý bă log as sin DEL Ans *

a &b: calculations for y; x;? finding 2:4; here n = 5 s = 12 = 2.4 } = 12 = 2.4 NW us N - - io N N mo Onslo 25 7.2 -0.643 35 a 15 12 12 140 36 : b= 36 - 5*(2.4)2 [40 - {5^(2.412}] i. a = ū-ba = 2.4-10.643x214) = 26., 0.857 .. The reo equation of regression line is. ŷ = 0.857 +0.643% Using some formula we solue for a &b Xi Yi here n=5 jo onroe 2 = 15 = 3 j = 2 3 = 4.2 62 1 21 185 b. [Xiy-n (.() [x;? - n(² - 62 – 65*34.2) 85-45x(3)} = -0.025 40 a= g- b ă SHI = 402 +0.025*3) = 4.275 .. The regression equation of you x is given by = 4.275 - 0.0252 RL