Question

omsidered the varinhles soke and parity In the problems e at a time, in modeling birth weights of babies. A moare realistic approch to modeling infint weights consider all possibly related variables at once. Other variables of interest include length of pregnacy in days (gextation, mother's age in years (age), mther's height in inches (height), and rther's pregnancy weight in pounds (weight). Below are three oservations frarn this data set hw gestation parlty height welght 10m smoke 1 120 0 2 113 282 3 54 135 . .. .. 1736 117 297 65 174 Tbe summary table below shows the results of a regrcasion model for predicting the average birth wcight of babics based on all of the variables included in thc data sct. Std. Error tvalue Pr) Estimate (Intereept) -8041 14.35 5,60 0.0000 D44 -3.33 o 07 15.2 gestation 1 13 2.9: parity 0,0033 -0.01 0,09 -0.10 0.9170 age ht weiaht smoke 0.05 00 199 00471 -840 0,95 8.8 0,0000) :equation af he regression line. a) Write t bwt.- xheight + x parity x gestation weight + x ace smoke bi Intepret the coefficient for gestation: the hirth weiht of the baby for each additional day of premancy, all else held constant The model predicts a ounce inrnease c) Interpret the caefticient for sge ouIce docrease in the birth weight of the baby fur ach additional year in olher'ss age, all else held conslant The mdel predicts a e) The coefficient for parity is different than in the linear model in the previous exercise. Why might there be a difference? Parity might be correlated with ome of the other variables in the model, which introduces collinearity and complicates model estimation. Parity is not significant and should have bocn removed from the multiple regression model t) Calculate the residual for the tirst observation in the data set The actual birth weight of the bahy unces (Raund to the nearest tenth.) The predicted birth weight of the baby ounces, (Round to the ncarest tenth.) Tbe residual = | ounces Subrait

Answer 1

a).equation of regression line:-

bwt -80.41(0.44) (1.15) height +(0.05) gestation 1.33)* parity (-0.01) age + weight+(-8.40) *smoke

b).interpretation of coefficient for gestation:-

the model predicts a 0.44 ounce increase in the birth weight of the baby for each additional day of pregnancy,all else held constant.

c).interpretation of coefficient for age:-

the model predicts a 0.01 ounce decrease in the birth weight of the baby for each additional year in mother's age,all else held constant.

e).the correct option is:-

parity might be correlated with one of the other variable of the model,which indicates collinearity and complicates model estimation.( 1st option)

[interpretation for your clarification:-

the 2 nd option is not true because p value of parity=0.0033<common alpha level of 0.05 . this indicates that it is statistically significant.]

f).the actual birth weight of the baby is: 120 ounces

the predicted birth weight of the baby be:-

for first obs in data set:

gestation=384 , parity=0 , age=27 , height=62 , weight=100 ,smoke=0

so our predicted birth weight be:-

= (-80.41)+(0.44*384)+(-1.33*0)+(-0.01*27)+(1.15*62)+(0.05*100)+(-8.40*0)

=164.58 ounces

= 164.6 ounces

the residual is:-

=(observed value - predicted value)

= (120-164.6)ounces

= - 44.6 ounces

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