Question

Listed below are heights (in inches) and weight (in pounds) of randomly selected adult females subjects from the California Health Interview Survey

3) Listed below are heights (in inches) and weight (in pounds) of randomly selected adult female subjects from the California Health Interview Survey. Height 67 64 65 61 68 61 61 65 59 70 59 63 66 64 Weight 140 228 160 130 140 135 118 135 162 201 110 150 215 125 (a) Use a 0.05 significance level to test for a linear correlation between height and weight. (b) Find the equation of the straight line that best fits the sample data. Does this equation appear to be good for predicting the weight of an adult female given her height? Explain why or why not. (c) Predict the weight of an adult female who is 62.5 inches tall. 152

Answer 1

Le 2 x be height (in inches), be weight lin pounds) a = 0.05 significance level have to test for a linedes correlation (r) between height & weight. here, D=14 here, a=0.05 we 7 Ssay Issoc. ssy Here. Exi=893 X= Exi 893 63.7857 n ý = {yi Eyi=2199 153.5 2149 14 here, Ssay Sse ssy {(x-7)(y-7) Elx-X2 ECY-Y)2 CS Starts with CMS

(x-7) 2 (4-7) 2 (x-7)(y-7) 10.332 182.250 -43.393 10.046 1.474 7.760 17.760 7.760 7.760 1-474 5550.280 42.250 552.250 182.250 15.964 7.893 65.464 -56.893 slo 536 342.250 1260.250 22.903 38.617 98.893 +22.464 -40.679 295.179 208.179 2-750 136.179 -6.107 342. 230 72.250 2256.250 1892.250 12.250 3782.250 812:20 17281.500 22.903 0.617 40 903 00046 Total 144.357 7/2.500 Ssay 712.500 144.357 ssy = 17281.500 ssa = .. ssay 0-4511. 15524.ssy 712.500 146.357x17281.500 : 1020.4511 tо е want to Hoi There is no test , linear and weight comelation between height it. Ho : NS cs

linear comelation between HI: There is weight. ic. Hii rto height and Test statistic tcal is given by tna under Ho 0.4511 √ 14-2 Ji-20.451192 1.7509 here, tal, in-2 toos, 12 2.1788 ccrtical value Decisian criteria: we reject Ho I tcally to12,0-2 at at significance level if here, je. 1.750g <2.1788 tcal < to 12,n.2. at 54. significance level. we allept Mo conclusion: There is no and weight. linear correlation between height 6 we know that ; fitted linear regression Ý = Bot Bit equcation is given by where, BO is estimate of eine y-intercept of regression CS

Bi - estimate of Glope of regression dine Bo= Bo 7- Bir BIE Ssxy ssa Now Ssxy = 712.500 ssa - 144.357 B,= 4.9357 712.500 144.357 B = - 160.3 2.3. The equation of the straight eine that best fits sample data is the ŷ = -161.3259 + 409357130 her height is no comelution The equation not appears to be good for predicting the weight of an adult female given since, from * there between height 9 weight of female. ③ bene to predict the weight of an adult female we have who is je for x = 625 inches tall. 62.5 ů = -161.3259 +4.9357a - 161.3259 4.9357 (62.5) 147.1541. pounds 147.1540) pounds -7 CS