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What is a Generalized Linear Model? A traditional linear model is of the form
where Yi is the response variable for the ith observation, xi is a column vector of explanatory variables for the ith response. Note that the p-dimensional vector xi is usually considered to be ?xed, or nonrandom. The p-dimensional vector β of unknown coe?cients is to be estimated on the basis of n observations. The errors i are assumed to be independent normally distributed zero-mean random variables with a constant variance. Hence, holds, that is, the expected value of the output random variable is a linear transformation of the input. All these assumptions are limitations and may not hold in some cases. In particular:
These limitations are dealt with in the setting of the generalized linear model (GLM) or their generalization, the generalized additive model (GAM). GLM have been introduced in Statistics by Nelder and Wedderburn (1972).
Johnson-Neyman technique: The technique which can be used in the situations where analysis of the covariance is not valid because of the heterogeneity of slopes. With this method
Prior distributions : The probability distributions which summarize the information about a random variable or parameter known or supposed at a given time instant, prior to attaini
A law supposedly applicable to voting behaviour which has a history of several decades. It may be stated thus: Consider a two-party system and suppose that the representatives of t
Mardia's multivariate normality test is a test that a set of the multivariate data arise from the multivariate normal distribution against departures due to the kurtosis. The test
The term used when the aggregated data (for instance, aggregated over different areas) are analysed and the results supposed to apply to the relationships at the individual level.
Influence statistics: The range of statistics designed to assess the effect or the in?uence of an observation in determining results of the regression analysis. The general approa
Johnson''s Job Sequencing for n jobs and 2 machines
How large would the sample need to be if we are to pick a 95% confidence level sample: (i) From a population of 70; (ii) From a population of 450; (iii) From a population of 1000;
An investor with a stock portfolio sued his broker, claiming that a lack of diversification in his portfolio had led to poor performance. The data, shown below, are the rates of re
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