Part 1: Analysis with Galton’s original data set

Galton’s work on children and parents’ height was published in: Galton, F. (1886): “Regression

towards mediocrity in hereditary stature”, Journal of the Anthropological Institute, 15: 246-63. In

this first part of the project you are asked to reconstruct the original data from this original article

and replicate his analysis.

• Question 1. Find Galton’s original article (on jstor.org or LEARN). On Table I of his article,

the data used are summarized. You need to create a STATA data set that contains the 928

observations that Galton collected. It is recommended that you first type the data in an excel

file and then have STATA read that file. Some versions of the Galton data set are available

online. You are advised NOT to use them. It is part of this project that you show that you

understand how to make a data set from such a table. There are important conceptual issues

that you will miss if you borrow the data from somewhere else.

For those observations reported in Table I of Galton’s article as “below” or “above” the minimum and maximum height values, you need to assume some particular values. Please state

these explicitly in a table and provide a justification with one sentence. Define “tall parents”

and “short parents” according to your data. Then divide your sample into these two groups

and report relevant statistics for the adult children and for parents in each group. Report this

information in a table and comment it.

• Question 2. Galton was the first to describe and explain the phenomenon of “regression towards the mean”. Being concerned about the height of the English aristocracy, he interpreted

his results as “regression to mediocrity” (hence the name “regression”).

Regress the height of adult children against the height of parents. Report your results in a table

and interpret the estimated coecients. What can you say about the relationship between the

height of parents and their children? Are children of tall (short) parents as tall (short) as

their parents?

• Question 3. Taking your regression results from question 2, and using your definition of

“tall parents” and “short parents” from question 1:

Calculate the predicted adult children’s height whose parents are “tall” after 1, 2, 3, …, Z

generations. And similarly, for adult children of “short” parents. Report your results in a

table. Is there convergence in heights? If so, how many generations does it take? Is Galton’s

prediction correct?

• Question 4. Using the same data set,

Regress the height of parents against the height of adult children. Report your results in a

table. Is this regression equivalent to that in question 2? Are the estimated parameters the

same? Why or why not?

EofE Groups project, page 3 of 4

Template Answer Sheet

GROUP PROJECT, ESSENTIALS OF ECONOMETRICS

Group number: XX

Group members (student numbers only): s123, s345, etc.

Declaration:

Group XX, composed by students s123, s345, etc., confirms that the data collection has been conducted under the ethical guidelines of the School of Economics (www.ed.ac.uk/economics/research/ethics).

The data collection has only involved individuals 18 years old and over. The information collected

is not sensitive in any way that can harm the well-being and dignity of the subjects interviewed.

To maintain confidentiality, no names or any contact details have been collected. All interviewed

subjects have been told that this is part of the EofE course project.

Recall: each question has to be answered in one page maximum, font 12, double spaced.

• Question 1.1. Table 1.1.a. summarizes the height values assumed for cases below/above the

minimum/maximum height. We have assumed these values because ….

Table 1.1.a. Heights below/above the minimum/maximum height

assumed height

Adult children

Heights below the minimum xyz

Heights above the maximum xyz

Mid-parents

Heights below the minimum xyz

Heights above the maximum xyz

Reference: Table I in Galton (1886).

Table 1.1.b reports the mean and standard deviation for adult children and parents.

Table 1.1.b. Summary Statistics

Mean Standard Deviation Number obs.

Adult Children xyz xyz xyz

Mid parents xyz xyz xyz

Source: Galton’s data with authors assumptions.

• Question 1.2. We have defined tall and short as… (i) Table 1.2. reports …. (ii) The

assumption of having 928 parents rather than 205…

• Question 1.3. Table 1.3 reports…

• Question 1.4. Table 1.4 reports…

• Question 1.5. Table 1.5 reports…

EofE Groups project, page 5 of 7

• Question 2.1. Description of own data set: population of interest, data collection process,

survey … Table 2.1 reports ….

• Question 2.2. Table 2.2. reports… Figure 2.2. shows…

• Question 2.3. Table 2.3. reports…

• Question 2.4. Table 2.4. reports…

• Question 2.5. Another literature in Economics that has analysed regression towards the

mean is….

EofE Groups project, page 6 of 7

Template Appendix: log file resulting running from

EEproject.do

clear

capture log close

set more 1

log using project.log, replace

/*question 1.1*/

use namedatagalton.dta

. sum X

Variable | Obs Mean Std. Dev. Min Max

X | n xyz ….

/*question 1.2*/

etc..

log close

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