General linear model: Difference between revisions

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m The indexing for the regression coefficients here uses the variable k, but the description uses the variable j. I changed the description to k so that it matches the example equation
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for each observation ''i'' = 1, ... , ''n''.
 
In the formula above we consider ''n'' observations of one dependent variable and ''p'' independent variables. Thus, ''Y''<sub>''i''</sub> is the ''i''<sup>th</sup> observation of the dependent variable, ''X''<sub>''ik''</sub> is ''k''<sup>th</sup> observation of the ''k''<sup>th</sup> independent variable, ''jk'' = 1, 2, ..., ''p''. The values ''ββk''<sub>''j''</sub> represent parameters to be estimated, and ''ε''<sub>''i''</sub> is the ''i''<sup>th</sup> 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: