Suppose you are doing research on whether maternal income affects newborn birth
ID: 1134478 • Letter: S
Question
Suppose you are doing research on whether maternal income affects newborn birth weights. To analyze the question, you have data on 10 observations. The table below shows 8 observations with maternal income in the thousands (mi) and the mother’s newborn baby’s birth weight (wi) in grams.
(a) You need to estimate the equation ˆwi = ˆ 0 + ˆ 1mi but you do not have a computer. Calculate ˆ 0 and ˆ 1 by hand and show your work in a table.
(c) Based on the estimates, if a mother’s income is $25,000, what do you expect her baby’s birth weight to be?
m 20 18 30 52 40 25 35 45 w 4200 3200 3500 3600 3400 3200 2800 3300Explanation / Answer
m w (m-mbar) (w-wbar) (m-mbar)(w-wbar) (m-mbar)2 (w-wbar)2 20 4200 -13.125 800 -10500 172.2656 640000 18 3200 -15.125 -200 3025 228.7656 40000 30 3500 -3.125 100 -312.5 9.765625 10000 52 3600 18.875 200 3775 356.2656 40000 40 3400 6.875 0 0 47.26563 0 25 3200 -8.125 -200 1625 66.01563 40000 35 2800 1.875 -600 -1125 3.515625 360000 45 3300 11.875 -100 -1187.5 141.0156 10000 Total -4700 1024.875 1140000 a) 1= [(m-mbar)(w-wbar)]/(m-mbar)2 1 = -4700/1024.875 1 = -4.58593 0 = wbar-1 *mbar 0 = 3400+4.58*33.125 0 =3551.71 b) R = [(m-mbar)(w-wbar)]/(m-mbar)2(w-wbar)2 R =-4700/[(1024.85)*(1140000)]^0.5 R = [(m-mbar)(w-wbar)]/[(m-mbar)2(w-wbar)2]0.5 R2 =(4700/34181.24)2 =0.0189 c) weight= 3551.71 -25*4.58 weight = 3437.21 gram
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