the difference between an introvert and extrovert mathematicians is: an introvert mathematician...
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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!!