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7-1-weight_vs_age.md

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Think Stats Chapter 7 Exercise 1 (weight vs. age)

Exercise 7.1 Using data from the NSFG, make a scatter plot of birth weight versus mother’s age. Plot percentiles of birth weight versus mother’s age. Compute Pearson’s and Spearman’s correlations. How would you characterize the relationship between these variables?

Scatter plot of birth weight vs. mother's age:

Code:

import thinkstats2
import thinkplot
import nsfg
import numpy as np
import math
% matplotlib inline

preg = nsfg.ReadFemPreg()
live = preg[preg.outcome == 1]
df = live.dropna(subset=['agepreg', 'totalwgt_lb'])

weights = df.totalwgt_lb
ages = df.agepreg
thinkplot.Scatter(ages, weights)
thinkplot.Show(xlabel = "Age of mother in years", ylabel = "Birthweight in pounds")

Output: Scatter Plot

Plot percentiles of birth weight vs. mother’s age:

Code:

#arange makes an array of bins from first # up to but not including
#the second number, with increments of third number
bins = np.arange(5, 50, 5)

#digitize gives the index of the bin that contains each value
indices = np.digitize(df.agepreg, bins)

#groupby creates groups based on indices
groups = df.groupby(indices)

#computes mean age of each bin
age_group = []
for i, group in groups:
    age_mean = group.agepreg.mean()
    age_group.append(age_mean)
    
#computes Cdf for each bin
cdf_group = []
for i, group in groups:
    cdfs = thinkstats2.Cdf(group.totalwgt_lb)
    cdf_group.append(cdfs)

#Sets up graph to take three plots
thinkplot.PrePlot(3)

#For each percentile:
for percent in [75, 50, 25]:
    #Calculates value at each percentile for each bin
    weight_values = [cdf.Percentile(percent) for cdf in cdf_group[1:-1]]
    label = "%dth" % percent
    thinkplot.Plot(age_group[1:-1], weight_values, label = label)

thinkplot.Config(legend=label, loc = "lower right")
thinkplot.Show(xlabel = "Age of mother in years", ylabel = "Birth weight in pounds")

Output: Percentiles of birth weight vs mother's age

Compute Pearson's and Spearman's correlations:

Code:

print "Pearson's correlation is: %f" % thinkstats2.Corr(ages, weights)
print "Spearman's correlation is: %f" % thinkstats2.SpearmanCorr(ages, weights)

Output: Pearson's correlation is: 0.068834 Spearman's correlation is: 0.094610

How can you characterize the relationship between age of the mother and birth weight of the baby?

Looking at the scatter plot, there seems to be little relationship between age of the mother and birth weight of the baby. Most babies are in a narrow range of weights regardless of how old the mother is.

Looking at the percentile plot, there again seems to be little relationship apparent. All three percentiles have a similar slope. That slope is almost a straight line across - maybe there is a chance that older mothers have heavier babies, but it's very small. This is evident from the very small values of Pearson's and Spearman's correlations.