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${\mathbf{H}}_{\mathbf{0}}\mathbf{:}{\mathbf{尾}}_{\mathbf{1}}\mathbf{=}{\mathbf{尾}}_{\mathbf{2}}\mathbf{=}{\mathbf{尾}}_{\mathbf{3}}\mathbf{=}{\mathbf{尾}}_{\mathbf{4}}\mathbf{=}{\mathbf{尾}}_{\mathbf{5}}\mathbf{=}\mathbf{0}$

${\mathbf{H}}_{\mathbf{a}}\mathbf{:}$at least one of the parameters ${\mathbf{尾}}_{\mathbf{1}}$, ${\mathbf{尾}}_{\mathbf{2}}$, ${\mathbf{尾}}_{\mathbf{3}}$,${\mathbf{尾}}_{\mathbf{4}}$ and${\mathbf{尾}}_{\mathbf{5}}$ are non-zero.

Here, F test statistic =$\frac{\mathbf{SSE}}{\mathbf{n}\mathbf{-}\left(\mathbf{K}\mathbf{+}\mathbf{1}\right)}\mathbf{=}\frac{\mathbf{251}\mathbf{.}\mathbf{81}}{\mathbf{34}}\mathbf{=}\mathbf{7}\mathbf{.}\mathbf{406}$

${\mathbf{H}}_{\mathbf{0}}$is rejected if F 鈥� statistics < ${\mathbf{F}}_{\mathbf{0}\mathbf{.}\mathbf{05}\mathbf{,}\mathbf{34}\mathbf{,}\mathbf{34}}$. For $\mathbf{伪}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{05}$, since 7.406 > 1.843.

Not sufficient evidence to reject${\mathbf{H}}_{\mathbf{0}}$ at 95% confidence interval.

Therefore,${\mathbf{尾}}_{\mathbf{1}}\mathbf{=}{\mathbf{尾}}_{\mathbf{2}}\mathbf{=}{\mathbf{尾}}_{\mathbf{3}}\mathbf{=}{\mathbf{尾}}_{\mathbf{4}}\mathbf{=}{\mathbf{尾}}_{\mathbf{5}}\mathbf{=}\mathbf{0}$

$$\begin{gathered} {\mathbf{H}}_{\mathbf{0}}\mathbf{:}{\mathbf{尾}}_{\mathbf{4}}\mathbf{=}\mathbf{0}鈥� \\ {\mathbf{H}}_{\mathbf{a}}\mathbf{:}{\mathbf{尾}}_{\mathbf{4}}鈮�\mathbf{0} \end{gathered}$$

Here, t-test statistic$\mathbf{=}\frac{{\widehat{\mathbf{尾}}}_{\mathbf{4}}}{\mathbf{s}{\widehat{\mathbf{尾}}}_{\mathbf{4}}}\mathbf{=}\frac{\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{0043}}{\mathbf{0}\mathbf{.}\mathbf{0004}}\mathbf{=}\mathbf{-}\mathbf{10}\mathbf{.}\mathbf{75}$

Value of${\mathbf{t}}_{\mathbf{0}\mathbf{.}\mathbf{005}\mathbf{,}\mathbf{34}}$is 2.728

${\mathbf{H}}_{\mathbf{0}}$is rejected if t statistic > ${\mathbf{t}}_{\mathbf{0}\mathbf{.}\mathbf{005}\mathbf{,}\mathbf{34}}$. For $\mathbf{伪}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{01}$, since t <${\mathbf{t}}_{\mathbf{0}\mathbf{.}\mathbf{05}\mathbf{,}\mathbf{199}}$

Not sufficient evidence to reject${\mathbf{H}}_{\mathbf{0}}$ at a 95% confidence interval.

Thus,${\mathbf{尾}}_{\mathbf{4}}\mathbf{=}\mathbf{0}$

$$\begin{gathered} {\mathbf{H}}_{\mathbf{0}}\mathbf{:}{\mathbf{尾}}_{\mathbf{5}}\mathbf{=}\mathbf{0} \\ {\mathbf{H}}_{\mathbf{a}}\mathbf{:}{\mathbf{尾}}_{\mathbf{5}}鈮�\mathbf{0} \end{gathered}$$

Here, t-test statistic$\mathbf{=}\frac{{\widehat{\mathbf{尾}}}_{\mathbf{5}}}{\mathbf{s}{\widehat{\mathbf{尾}}}_{\mathbf{5}}}\mathbf{=}\frac{\mathbf{0}\mathbf{.}\mathbf{0020}}{\mathbf{0}\mathbf{.}\mathbf{0033}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{6060}$

Value of${\mathbf{t}}_{\mathbf{0}\mathbf{.}\mathbf{05}\mathbf{,}\mathbf{34}}$is 2.728

${\mathbf{H}}_{\mathbf{0}}$is rejected if t statistic > ${\mathbf{t}}_{\mathbf{0}\mathbf{.}\mathbf{005}\mathbf{,}\mathbf{34}}$. For $\mathbf{伪}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{01}$, since t <${\mathbf{t}}_{\mathbf{0}\mathbf{.}\mathbf{005}\mathbf{,}\mathbf{34}}$

Not sufficient evidence to reject at a 95% confidence interval.

So, ${\mathbf{尾}}_{\mathbf{5}}\mathbf{=}\mathbf{0}$.

Since, the value of${\mathbf{尾}}_{\mathbf{4}}\mathbf{=}\mathbf{0}$and${\mathbf{尾}}_{\mathbf{5}}\mathbf{=}\mathbf{0}$at 99% confidence level, this means that the parabola does not have a curvature and it essentially is a straight line.

Here, a straight line can be drawn relating y toholding${\mathbf{x}}_{\mathbf{2}}$constant or the other way round.