The difference between an introvert and extrovert mathematicians is:

An introvert mathematician looks at his shoes while talking to you.

An extrovert mathematician looks at your shoes

A Study of Influences on Birth Weight

Math 540, Spring 2006By: Jennifer Wright

Patrick GassAnna Tivy

Introduction to Data Set

• phbirth.xls – This data set involves several variables for mothers and their babies in Philadelphia. These variables include the mother’s race and education level, if she smoked, and the baby’s gestation period (weeks) and birth weight (grams). Total sample size 1115.

black educ smoke gestate grams

1 12 1 20 284

1 0 1 26 994

0 17 0 42 3486

1 12 1 43 4690

1 16 0 39 4830

Range: gestation 20 – 43 (5 - 10 months), grams 284 – 4830 (0.6 – 10.7lbs) , education 0 - 17

Sample of Data

Full Data Plot(w/o education)

Characteristics:

(1) Blacks have more premature births

(2) Gestation is measured in weeks not days

(3) Many points in one graph

(4) Somewhat linear, bunching

(5) If there was more premature

← 9 months

CenteredNot Centered

What does centering tell us?

Non-Black/Non-Smokers (00) 3498 145

Non-Black/Smokers (01) 3111 169

Black/Non-Smokers (10) 3156 157

Black/Smokers (11) 2880 158

*0 1

Non-Black/Non-Smokers (00) -2247 145

Non-Black/Smokers (01) -3481 169

Black/Non-Smokers (10) -2945 157

Black/Smokers (11) -3494 158

0 1

1. (01) Have more premature births than (00).

2. (01) also has lighter babies overall compared to (00).

Non-Black/Non-Smokers (00)

vs. Non-Black/Smokers (01)

01

00

1.(1

0) h

ave

mor

e pr

emat

ure

birt

hs t

han

(00)

.

2.(1

0) a

lso

has

light

er b

abie

s ov

eral

l com

pare

d to

(00

).

Non-Black/Non-Smokers (00)

vs. Black/Non-Smokers (10)

00

10

Full Model Selection

Model Dependent variable

Intercept Educ Gestate # of parameters

R-sq. Mallow’s C(p)

1 grams -3480.6 22.7 165.3 3 0.4985 3

2 grams -3245.4 166.4 2 0.4929 13.4643

3 grams 2779.6 35.9 2 0.0141 1075.29

Residuals:

• There seems to be curvature

• Heteroscedasticity in the plot with gestation.

• Possibly due to premature babies

- Have less variance

- Less points

Analysis of Non-Black/Smoking (01)

Model # of regressors C(p) R-square Variables in model

1 1 1.0049 0.5392 ge

2 2 3.0000 0.5392 ed ge

3 1 110.9292 0.0003 ed

Mallow’s suggests we only use gestation in the model for this group.

Multicollinearity

– No notable collinearity between the regressors. VIF’s ~ 1.

gey 1693481ˆ

97 subjects, 9%

4 groups

Points of Interest

Leverage

Residuals

DFFITS

89

89

89

Negative

Predicted vs. Data

y = 168.75x - 3480.5

-200

800

1800

2800

3800

4800

19 24 29 34 39

gestation (weeks)

gra

ms

bw

Predicted bw

Linear (Predicted bw)

89

15

Removing point 89 causes a slight drop in R^2

There wasn’t a strong reason to remove points.

Similar analyses where performed on all 4 groups.

Back to Full Data Set

Somewhat exponential

Transformations

)()( 10 geLnbbbwLn

More of a homoscedastic behavior

This transformation is not an improvement. More transformations could be tried.

MSE = 634 (Transform)

MSE = 451 (Linear)

Conclusion

• Black mothers have a higher chance of having premature delivery.

• Smoking does have an affect on the weight of babies.

- Smoking has less affect on the weight of babies in black mothers.

- Non-Black mothers who smoked are going to have a lower weight

baby.

• The weight of a baby depends on the gestational age.

• Education level of mother doesn’t affect the weight of baby.

You are not allowed to ask questions

Just Kidding!!