## Sunday, October 6, 2013

### Heteroscedasticity

Useless Definition of the quarter: heteroscedasticity, a form of heteroscedastic:

heteroscedastic [ˌhɛtərəʊskɪˈdæstɪk]
1. (Mathematics & Measurements / Statistics) (of several distributions) having different variances
2. (Mathematics & Measurements / Statistics) (of a bivariate or multivariate distribution) not having any variable whose variance is the same for all values of the other or others
3. (Mathematics & Measurements / Statistics) (of a random variable) having different variances for different values of the others in a multivariate distribution Compare homoscedastic
[from hetero- + scedastic, from Greek skedasis a scattering, dispersal]
heteroscedasticity  [ˌhɛtərəʊskɪdæsˈtɪsɪtɪ] n

Examples, from www.wikipedia.org:

Heteroscedasticity often occurs when there is a large difference among the sizes of the observations.
• A classic example of heteroscedasticity is that of income versus expenditure on meals. As one's income increases, the variability of food consumption will increase. A poorer person will spend a rather constant amount by always eating inexpensive food; a wealthier person may occasionally buy inexpensive food and at other times eat expensive meals. Those with higher incomes display a greater variability of food consumption.

• Imagine you are watching a rocket take off nearby and measuring the distance it has traveled once each second. In the first couple of seconds your measurements may be accurate to the nearest centimeter, say. However, 5 minutes later as the rocket recedes into space, the accuracy of your measurements may only be good to 100 m, because of the increased distance, atmospheric distortion and a variety of other factors. The data you collect would exhibit heteroscedasticity.