Uploaded December 2012 | Updated September 2026, 2 hours ago
An introduction to the least squares regression line in simple linear regression.
The pain-empathy data is estimated from a figure given in:
Singer et al. (2004). Empathy for pain involves the affective but not sensory components of pain. Science, 303:1157--1162.
The Janka hardness-density data is found in:
Hand, D.J., Daly, F. , Lunn, A.D., McConway, K., and Ostrowski, E., editors (1994). The Handbook of Small Data Sets. Chapman & Hall, London.
Original source: Williams, E.J. (1959). Regression Analysis. John Wiley & Sons, New York. Page 43, Table 3.7.
An introduction to the least squares regression line in simple linear regression.
The pain-empathy data is estimated from a figure given in:
Singer et al. (2004). Empathy for pain involves the affective but not sensory components of pain. Science, 303:1157--1162.
The Janka hardness-density data is found in:
Hand, D.J., Daly, F. , Lunn, A.D., McConway, K., and Ostrowski, E., editors (1994). The Handbook of Small Data Sets. Chapman & Hall, London.
Original source: Williams, E.J. (1959). Regression Analysis. John Wiley & Sons, New York. Page 43, Table 3.7.





![The Relationship Between the Binomial and Poisson Distributions
A look at the relationship between the binomial and Poisson distributions (roughly, that the Poisson distribution approximates the binomial for large n and small p). I work through some calculations in an example, showing that the approximate probability from the Poisson can be quite close to the exact probability from the binomial distribution.
(The example used involves albinism. Albinism affects all races, but the rates of albinism vary a little around the world. In Europe and North America, roughly 1 in 20,000 people have some form of albinism).
For those using R, here is the R code to find the probabilities for the example in this video:
Finding the probability of getting exactly 2 with albinism in a random sample of 1000 Europeans.
Binomial (exact):
dbinom(2,1000,1/20000)
[1] 0.001187965
Poisson (approximate):
dpois(2,1000*1/20000)
[1] 0.001189037 The Relationship Between the Binomial and Poisson Distributions](https://i.ytimg.com/vi/eexQyHj6hEA/mqdefault.jpg)




