Many years ago I wondered if it was possible to estimate a person’s IQ from physical and demographic traits.  A member of the Prometheus society suggested I use a fascinating technique called multiple regression and I am indebted to him for introducing me to the math.  I suggested we try to co-write an article on the subject in the prestigious peer reviewed academic journal Intelligence which I have dreamed of publishing in since childhood (I’m now in my thirties)He thanked me for asking, but was not comfortable putting his name on something that was not well researched, and so for well over a decade, the concept stayed on the shelf.  However when I realized that others in the field were already using multiple regression to predict IQs from demographic variables, or simple regression to predict IQs from a biological variable, I decided it was time to publish our method, which combined both approaches.

Several commenters here have expressed an interest in Angela Merkel’s  IQ, including blogger AKarlin, and blogger Alcoholicwisdom so in part 1 of this series, I use a biodemographic approach to estimate her IQ from her three most extreme demographic and physical traits: Academic success, power, and physical coordination.

Expected IQ of an elite academic: 137

Merkel worked and studied at the Central Institute for Physical chemistry of the Academy of Sciences in Berlin-Adlershof from 1978 to 1990. After being awarded a doctorate (Dr. rer. nat.) for her thesis on quantum chemistry,[29] she worked as a researcher and published several papers.

According to Wikipedia, The German Academy of Sciences at Berlin (abbreviated AdW)  was the most important research institution of East Germany, and in the 1980s (near the time Merkel was there), had no more than 176 East German members.  Thus, the median ranked member of the AdW was roughly the 88th most academically accomplished person in East Germany.   Let’s say there were around 17.068 million East Germans when Merkel was at AdW, and 2/3rds were adults, and Merkel was the 88th most academically accomplished of these.  Thus, relative to East German adults, Merkel had a normalized Z score of +4.33 (one in 128,000 level).

Academic success seems to correlate between 0.5-0.6 with IQ.  In the United States, since by the late 1970s, IQ correlates 0.57 with IQ, and the correlation between IQ and grades appears to be 0.54.  In a recent post, I very crudely estimated the correlation between IQ and college attended to be 0.5, and that was probably an underestimate.  Overall, the correlation between IQ and academic accomplishments is probably 0.57 in the United States.  Assuming the correlation is similar in Germany, then Merkel’s academic Z score of +4.33 implies an IQ Z score of 0.57(+4.33) = +2.47 or roughly 137 (white norms).  Based on academic success alone, we can expect with 95% certainty that Merkel’s IQ is between 113 and 161.

Expected IQ of the most powerful person in Germany: 133

U.S. Presidents tend to have IQs only 40% as far above average as you’d expect if IQ and power were perfectly correlated, suggesting that the correlation between IQ and “power” is about +0.4.  Germany has about 81 million people and assuming about 2/3rds are adults, we’d expect the most powerful German to have a power Z score of +5.53 (one in 53 million), and thus have an IQ Z score only 40% as extreme (+2.21), equating to an expected IQ of 133 (95% confidence interval: 106-160)

Expected IQ of a klutz: 90

According to an in-depth profile of Merkel, she might be kinesthetically challenged:

Angela was physically clumsy—she later called herself ‘a little movement idiot.’ At the age of five, she could barely walk downhill without falling. ‘What a normal person knows automatically I had to first figure out mentally, followed by exhausting exercise,’ she has said.

According to technical studies by the U.S. Department of Labour, IQ and physical coordination correlate 0.35.  Scholar Arthur Jensen has put the figure at a potent 0.7, but that sounds impossible given the validity of the “dumb jock” and “clumsy nerd” stereotype.  We should expect physical coordination and intelligence to be correlated because they’re both functions of the brain, but since only intelligence is a function of the mind, the correlation should be modest.

However even small correlations can have big effects.  If Merkel is kinesthetically impaired, then by definition she’s at least 2 standard deviations below the mean in coordination.  Assuming a 0.35 correlation with intelligence, this would predict an IQ that is 2 SD(0.35) = 0.7 SD below the mean, or roughly 90 (95% confidence interval: 63 to 117)

Expected IQ of a hyper-educated, supremely powerful klutz: 135

Statistically, we’d expect Merkel to have an IQ of 137, 133, or 90, depending on whether we estimate her IQ from her education, power, or physical coordination respectively.  All of these predictions carry large margins of error, so it’s interesting to ask what happens when we combine them.

As the Promethean once told me, it’s not enough to know each variables correlation with IQ, we must also know each variables correlation with one another, and thus we get the following correlation matrix.

academic success power coordination iq
academic success 1.00 0.44 0.20 0.57
power 0.44 1.0 0.14 0.40
coordination 0.20 0.14 1.00 0.35
iq 0.57 0.40 0.35 1.00

Many of these correlates are very crudely estimated.  For example the correlation between academic success and power is derived by noticing that U.S. presidents are about 44% as academically successful (in Z score units) as they are powerful.  The correlation between academic success and coordination is derived from assuming the only link between these variables is their shared correlation with IQ.  Similarly for the correlation between power and coordination.  Such assumptions are admittedly speculative.

Nonetheless, the correlation matrix, speculative as it is, gives the following equation:

IQ Z score = 0.44(academic success Z score) + 0.17(power Z score) + 0.27(coordination Z score)

[Edit, June 7, 2016:  The regression coefficients in the formula above are smaller than each variable’s correlation with IQ.  This is because the intercorrelation between predictors means no two predictors are completely independent, so each predictor in the multiple regression formula must be adjusted for the predictive power already captured by the other two predictors]

Entering Merkel’s Z scores into the formula gives:

IQ Z score = 0.44(+4.33) + 0.17(+5.53) + 0.27(-2)

IQ Z score = 1.91 + 0.94 – 0.54

IQ Z score = 2.31

Now converting IQ Z score into IQ is simply a matter of multiplying by 15 and adding 100.

IQ = IQ Z score(15) + 100

IQ = 2.31(15) + 100

IQ = 135 (white norms)

We can say with 95% confidence that if given an updated German version of the WAIS, Merkel would score anywhere from 112 to 158 (white norms).

Considering we used three predictors, this is not as much precision as I would expect.  Part of the problem is that Merkel’s two most extreme traits (academic success and power) are moderately correlated, thus they do not add enough independent information.

Since the biodemographic prediction is uncertain, we search for psychometric data in part two.