Question: Suppose that you fit the model with 5 independent variables \[Y={{\beta }_{0}}+{{\beta }_{1}}{{x}_{1}}+{{\beta }_{2}}{{x}_{2}}+{{\beta }_{3}}{{x}_{3}}+{{\beta }_{4}}{{x}_{4}}+{{\beta }_{5}}{{x}_{5}}+\varepsilon \] to n = 30 data points, and you obtain SSE = 0.46 and R-Square = 0.87.

Is the model of any use in predicting y? Using ? = 0.05, test the null hypothesis:

\[{{H}_{0}}:{{\beta }_{1}}={{\beta }_{2}}={{\beta }_{3}}={{\beta }_{4}}={{\beta }_{5}}=0\]

against the alternative hypothesis

\[{{H}_{1}}:\text{At}\,\,\text{least}\,\,\text{one}\,\,\text{of}\,\,\text{the}\,\,\text{parameters}\,\,{{\beta }_{1}},\,\,{{\beta }_{2}},\,\,{{\beta }_{3}},\,\,{{\beta }_{4}},\,\,{{\beta }_{5}}\,\,\,\text{is}\,\,\text{not}\,\,\text{zero}\]