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- W1307779 abstract "One of the most widely used tools in all of statistics is linear regression. This is often misnamed least squares regression, but a least squares estimation refers to a deterministic process, whereby the best straight line is fitted through a series of points. In statistical analysis, the interpretation is much different although the technical calculations remain the same. Normal theory linear regression carries the assumption that the response variable has a normal or Gaussian distribution:$$ f(y;mu ,{{sigma }^{2}}) = exp [{{(y - mu )}^{2}}/(2{{sigma }^{2}})]/sqrt {{2pi {{sigma }^{2}}}} $$(1.1)The mean of this distribution changes in some deterministic way with the values of the explanatory variable(s), e.g. $$ {{mu }_{i}} = {{beta }_{0}} + sumlimits_{j} {{{beta }_{j}}{{X}_{{ij}}}} $$(1.2)while the variance remains constant. Then, the regression equation specifies how the mean of the distribution changes for each value of the explanatory variable(s); individual observations will be dispersed about the mean with the given variance. This is illustrated in Figure 1.1." @default.
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- W1307779 date "1992-01-01" @default.
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- W1307779 title "Normal Theory Models and Some Extensions" @default.
- W1307779 doi "https://doi.org/10.1007/978-1-4612-2888-2_1" @default.
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