Uploaded December 2012 | Updated September 2026, 2 hours ago
An investigation of the normality, constant variance, and linearity assumptions of the simple linear regression model through residual plots.
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 investigation of the normality, constant variance, and linearity assumptions of the simple linear regression model through residual plots.
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.

![Introduction to the Continuous Uniform Distribution
A brief introduction to the (continuous) uniform distribution. I discuss its pdf, median, mean, and variance. I also work through an example of finding a probability and a percentile. I dont do any integration in this video.
For those using R, here is the R code to find the probabilities for the examples in this video:
P(X greater than 230) where X is U(200,250):
1-punif(230,200,250)
[1] 0.4
(punif yields the area to the *left*, and here we need the area to the *right*)
20th percentile of a U(200,250) distribution:
qunif(.2,200,250)
[1] 210 Introduction to the Continuous Uniform Distribution](https://i.ytimg.com/vi/izE1dXrH5JA/mqdefault.jpg)
![An Introduction to the Poisson Distribution
An introduction to the Poisson distribution. I discuss the conditions required for a random variable to have a Poisson distribution. work through a simple calculation example, and briefly discuss the relationship between the binomial distribution and the Poisson distributions.
Plutonium-239 example (an average of 2.3 radioactive decays per second).
Finding the probability of exactly 3 radioactive decays in a 2 second period:
dpois(3,2*2.3)
[1] 0.1630676
Finding the probability of no more than 3 radioactive decays in a 2 second period:
dpois(0,2*2.3)+dpois(1,2*2.3)+dpois(2,2*2.3)+dpois(3,2*2.3)
[1] 0.3257063
or
ppois(3,2*2.3)
[1] 0.3257063 An Introduction to the Poisson Distribution](https://i.ytimg.com/vi/jmqZG6roVqU/mqdefault.jpg)







