General linear model: Difference between revisions

Revision as of 19:45, 29 October 2018

Revision as of 23:26, 29 October 2018

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for each observation ''i'' = 1, ... , ''n''.

In the formula above we consider ''n'' observations of one independentdependent variable and ''p'' dependentindependent variables. Thus, ''Y''_''i'' is the ''i''^th observation of the dependent variable, ''X''_''ij'' is ''i''^th observation of the ''j''^th independent variable, ''j'' = 1, 2, ..., ''p''. The values ''β''_''j'' represent parameters to be estimated, and ''ε''_''i'' is the ''i''^th independent identically distributed normal error.

In the more general multivariate linear regression, there is one equation of the above form for each of ''m'' > 1 dependent variables that share the same set of explanatory variables and hence are estimated simultaneously with each other: