Question

A small study is conducted involving 10 infants to investigate the association between gestational age at birth, measured in weeks, and birth weight, measured in grams.: Cured Not Cured Drug 1 37 13 Drug 2 88 21 Total 125 34 Total 50 109 159 Table 1: Gestational age: 34.7, 36, 29.3, 40.1, 35.9, 40.8, 38.3, 37, 41.2, 39.8. Birth weight: 1895, 2030, 1440, 2835, 3115, 4013, 3174, 3625, 2289, 2845. . Find the correlation coefficient r of the gestational age at birth and birth weight. (5 points) Test He: p=0 vs. H:p#0 at 5% level of significance. Here p is the population correlation coefficient between the two variables. Use P(tz > 2.36) = 0.025. (5 points) • Construct a regression line Y = Bo + B1X + €, where Y, X are gestational age at birth and birth weight respectively. What are the best estimates of Bo and B.? (10 points) • Test H, : B = 0 vs. H: B170 at 5% level of significance. (5 points) • Compute the coefficient of determination, R. (5 points)

Answer 1

page - 0 Answer & Given data bet we take x = birth weight y - Gestational age Birth weight Gestational age 34.7 3895 36 2030 1440 2835 29.3 yo. 1 35.9 3115 40.8 4013 38.3 3174 37 3625 2289 42 2845 34,8 ey = 373.1 Total Ex = 27261

page:- © ga nery - Ency v (nen? (Eus') (n2y+-cey) from the given data n =0 Ezy = 87261 X 373.1 1033498 Ex = 24261 Ey = 373.1 Ex? - (27261)* – 80178691 Ery?= (373.1)* = 14037.41 The volues are substitude in s

page:- 10५ [033५१४ - (27861 9 73.1) [loy 80785१) - (226137/10५ १५०32. ५10- (373.15 10334980 - 1014107१.। (8078590) - (४०।१854)] १५०, 3३५.1) -1५०37. ५) 1638११.१ 58623789/11०.५१ 1638११.१ 168618558787 163899.9 26195.५५36 0.625686 10- 62577

page Given data Ho: P=0 VS HP 70 test Statistic, (to) We know the from the truestion and by giren data y = 0.6257 n=o. The values Stub stude the to 0.6257 X/10-2 Ti-co.6257² - 0.6257x ve 1 -0.39150049 0.6257 x 2.828 10.6085

page - $ 6.76975 Jo.6085 Ho > 2.26871 df = ne = 10-2 we have p (te > 2.36) = 0.025 i critical values are - 2.360f + 2.36 Rejection region is -2.36 to = 2.2687 to do it talls we not tals in rejection region in ace plence region fail to reject. Ho Cie Aceppt Ho)

page:- Given data Y = Bot Bix+E B = [nɛny - Eu. Ey) nex ² (Exj2 n =10 Eny = 4033498 from the Autio © gxon data Eu = 27861 Ey - 373.1 ERE - 80178691 Substitude the values in 'B! 10 X 1033498 - 27261 X 373.1 10 x(2726133 - (242613? 10 334980. - 272614 373.1 10 X 80178695.- 80178691

page- 10334980 - 10170791 801786910 - 80178691 163899.9 58623789 IB, = 0.002796 Bi = 0.0028 ..... sounding to u deumal Bo = y a bit ģ ey - 3431 10 T = EN = 27261 n 10 .Ę = 37.31 ī - 27.26.1 Bo = 37.31 - (0.0028 x 27a6.1) 37.31 - 7.63308 - 29.677,

page- JY = 29.677 +0.0028 x The given Estimates of ßo fß, sou least Square Estimates and they are the best estimetes of Bo fße Given data Ho: Br=0 vs Hi! B140 to = ßi vtn-a Secco Sere) = ney?- LE y-j - 6.(ne xy - (E1) (84) NEwe CExg2 1170.49 -0.0028 X163899.9 58623789 88.946985 58603789

page-① Secên) = 0.001232 to = 0.0028 0.001932 to = 2.273 Since df=8, 20.02:3 2.36 Crictical values are - 2.36€ to - 2.273.2.36 we fail to reject Ho e Accept to pr (neny - Ex. cy j? [n {u? (eng' J [ney - (Ey!) a ge from the question ① R = (0.6257)2 77:750.6257) R? = 0.3915 ie 39.15% of the vanition in yis Explained by a