91影视

The independent variables were categorized as Demographic (4 variables), Diagnostic (7 variables), Treatment (4 variables), and Community (6 variables).

Here, the demographic variables are from${\mathbf{x}}_{\mathbf{1}}\mathbf{-}{\mathbf{x}}_{\mathbf{4}}$, the diagnostic variables beinglocalid="1662025858306" ${\mathbf{x}}_{\mathbf{12}}\mathbf{-}{\mathbf{x}}_5$, treatment variables being${\mathbf{x}}_{\mathbf{13}}\mathbf{-}{\mathbf{x}}_{\mathbf{17}}$, and community variables being${\mathbf{x}}_{\mathbf{18}}\mathbf{-}{\mathbf{x}}_{\mathbf{21}}$.

The equation for E(Y) for the complete model would be 鈥�

$$\begin{gathered} \mathbf{E}\left(\mathbf{y}\right)\mathbf{=}{\mathbf{尾}}_{\mathbf{0}}\mathbf{+}{\mathbf{尾}}_{\mathbf{1}}{\mathbf{x}}_{\mathbf{1}}\mathbf{+}{\mathbf{尾}}_{\mathbf{2}}{\mathbf{x}}_{\mathbf{2}}\mathbf{+}{\mathbf{尾}}_{\mathbf{3}}{\mathbf{x}}_{\mathbf{3}}\mathbf{+}{\mathbf{尾}}_{\mathbf{4}}{\mathbf{x}}_{\mathbf{4}}\mathbf{+}{\mathbf{尾}}_{\mathbf{5}}{\mathbf{x}}_{\mathbf{5}}\mathbf{+}{\mathbf{尾}}_{\mathbf{6}}{\mathbf{x}}_{\mathbf{6}}\mathbf{+}{\mathbf{尾}}_{\mathbf{7}}{\mathbf{x}}_{\mathbf{7}} \\ \mathbf{+}{\mathbf{尾}}_{\mathbf{8}}{\mathbf{x}}_{\mathbf{8}}\mathbf{+}{\mathbf{尾}}_{\mathbf{9}}{\mathbf{x}}_{\mathbf{9}}\mathbf{+}{\mathbf{尾}}_{\mathbf{10}}{\mathbf{x}}_{\mathbf{10}}\mathbf{+}{\mathbf{尾}}_{\mathbf{11}}{\mathbf{x}}_{\mathbf{11}}\mathbf{+}{\mathbf{尾}}_{\mathbf{12}}{\mathbf{x}}_{\mathbf{12}}\mathbf{+}{\mathbf{尾}}_{\mathbf{13}}{\mathbf{x}}_{\mathbf{13}}\mathbf{+}{\mathbf{尾}}_{\mathbf{14}}{\mathbf{x}}_{\mathbf{14}}\mathbf{+}{\mathbf{尾}}_{\mathbf{15}}{\mathbf{x}}_{\mathbf{15}} \\ \mathbf{+}{\mathbf{尾}}_{\mathbf{16}}{\mathbf{x}}_{\mathbf{16}}\mathbf{+}{\mathbf{尾}}_{\mathbf{17}}{\mathbf{x}}_{\mathbf{17}}\mathbf{+}{\mathbf{尾}}_{\mathbf{18}}{\mathbf{x}}_{\mathbf{18}}\mathbf{+}{\mathbf{尾}}_{\mathbf{19}}{\mathbf{x}}_{\mathbf{19}}\mathbf{+}{\mathbf{尾}}_{\mathbf{20}}{\mathbf{x}}_{\mathbf{20}}\mathbf{+}{\mathbf{尾}}_{\mathbf{21}}{\mathbf{x}}_{\mathbf{21}} \end{gathered}$$

b.

The null hypothesis for testing whether the 7 Diagnostic variables contribute information for the prediction of y can be written as

${\mathbf{H}}_{\mathbf{0}}\mathbf{:}{\mathbf{尾}}_{\mathbf{5}}\mathbf{=}{\mathbf{尾}}_{\mathbf{6}}\mathbf{=}{\mathbf{尾}}_{\mathbf{7}}\mathbf{=}{\mathbf{尾}}_{\mathbf{8}}\mathbf{=}{\mathbf{尾}}_{\mathbf{9}}\mathbf{=}{\mathbf{尾}}_{\mathbf{10}}\mathbf{=}{\mathbf{尾}}_{\mathbf{11}}\mathbf{=}{\mathbf{尾}}_{\mathbf{12}}\mathbf{=}\mathbf{0}$

Equation of the reduced model can be written as

$\mathbf{E}\mathbf{\left(}\mathbf{y}\mathbf{\right)}\mathbf{=}{\mathbf{尾}}_{\mathbf{0}}\mathbf{+}{\mathbf{尾}}_{\mathbf{1}}{\mathbf{x}}_{\mathbf{1}}\mathbf{+}{\mathbf{尾}}_{\mathbf{2}}{\mathbf{x}}_{\mathbf{2}}\mathbf{+}{\mathbf{尾}}_{\mathbf{3}}{\mathbf{x}}_{\mathbf{3}}\mathbf{+}{\mathbf{尾}}_{\mathbf{4}}{\mathbf{x}}_{\mathbf{4}}\mathbf{+}{\mathbf{尾}}_{\mathbf{5}}{\mathbf{x}}_{\mathbf{5}}\mathbf{+}{\mathbf{尾}}_{\mathbf{6}}{\mathbf{x}}_{\mathbf{6}}\mathbf{+}{\mathbf{尾}}_{\mathbf{7}}{\mathbf{x}}_{\mathbf{7}}$

The null hypothesis is rejected when $\mathbf{F}\mathbf{-}\mathbf{statistic}\mathbf{>}\mathbf{F}$values or when p-value for the test is less than 0.05. given here is that p-value for the test conducted is less than 0.0001 which is less than 0.05 indicating that${\mathbf{H}}_{\mathbf{0}}$ is rejected. This means that the 7 diagnostic variables contribute information for the prediction of y.