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For ${\mathbf{尾}}_{\mathbf{1}}$:

${\mathbf{H}}_{\mathbf{0}}\mathbf{:}{\mathbf{尾}}_{\mathbf{1}}\mathbf{=}\mathbf{0}$, whereas, ${\mathbf{H}}_{\mathbf{a}}\mathbf{:}{\mathbf{尾}}_{\mathbf{1}}鈮�\mathbf{0}$

Here, the test statistic $\mathbf{=}\frac{{\widehat{\mathbf{尾}}}_{\mathbf{1}}}{{\mathbf{蝉尾}}_{\mathbf{1}}}$

Test statistic $$\begin{gathered} \mathbf{=}\frac{\mathbf{0}\mathbf{.}\mathbf{03}}{\mathbf{0}\mathbf{.}\mathbf{006}} \\ \mathbf{=}\mathbf{5} \end{gathered}$$

For $\mathbf{伪}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{05}$the critical value of ${\mathbf{t}}_{\mathbf{0}\mathbf{.}\mathbf{05}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{699}$using the formulae table

${\mathbf{H}}_{\mathbf{0}}$is rejected if$\left|\mathbf{t}\right|\mathbf{>}{\mathbf{t}}_{\mathbf{0}\mathbf{.}\mathbf{05}}$. Since 5 > 1.699,

Reject the null hypothesis at a 95% significance level

Therefore, the value of ${\mathbf{尾}}_{\mathbf{1}}鈮�\mathbf{0}$

For ${\mathbf{尾}}_{\mathbf{2}}$:

${\mathbf{H}}_{\mathbf{0}}\mathbf{:}{\mathbf{尾}}_{\mathbf{2}}\mathbf{=}\mathbf{0}$whereas${\mathbf{H}}_{\mathbf{a}}\mathbf{:}{\mathbf{尾}}_{\mathbf{2}}鈮�\mathbf{0}$

Here, the test statistic $\mathbf{=}\frac{{\widehat{\mathbf{尾}}}_{\mathbf{2}}}{{\mathbf{蝉尾}}_{\mathbf{2}}}$

$$\begin{gathered} Teststatistic\mathbf{=}\frac{\mathbf{0}\mathbf{.}\mathbf{60}}{\mathbf{0}\mathbf{.}\mathbf{120}} \\ \mathbf{=}\mathbf{5} \end{gathered}$$

For $\mathbf{伪}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{05}$, the critical value of ${\mathbf{t}}_{\mathbf{0}\mathbf{.}\mathbf{05}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{699}$using the formulae table

${\mathbf{H}}_{\mathbf{0}}$is rejected if $\left|\mathbf{t}\right|\mathbf{>}{\mathbf{t}}_{\mathbf{0}\mathbf{.}\mathbf{05}}$. Since 5 > 1.699,

Reject the null hypothesis at a 95% significant level

Thus, the value of ${\mathbf{尾}}_{\mathbf{2}}鈮�\mathbf{0}$

For${\mathbf{尾}}_{\mathbf{3}}$:

${\mathbf{H}}_{\mathbf{0}}\mathbf{:}{\mathbf{尾}}_{\mathbf{3}}\mathbf{=}\mathbf{0}$, whereas, ${\mathbf{H}}_{\mathbf{a}}\mathbf{:}{\mathbf{尾}}_{\mathbf{3}}鈮�\mathbf{0}$

Here, the test statistic $\mathbf{=}\frac{{\widehat{\mathbf{尾}}}_{\mathbf{3}}}{{\mathbf{蝉尾}}_{\mathbf{3}}}$

Test statistic $$\begin{gathered} \mathbf{=}\frac{\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{004}}{\mathbf{0}\mathbf{.}\mathbf{001}} \\ \mathbf{=}\mathbf{-}\mathbf{4} \end{gathered}$$

For $\mathbf{伪}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{05}$, the critical value of ${\mathbf{t}}_{\mathbf{0}\mathbf{.}\mathbf{05}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{699}$using the formulae table

${\mathbf{H}}_{\mathbf{0}}$is rejected if $\left|\mathbf{t}\right|\mathbf{>}{\mathbf{t}}_{\mathbf{0}\mathbf{.}\mathbf{05}}$. Since, -4 < 1.699,

Do not reject the null hypothesis at a 95% significance level.

Hence, the value of${\mathbf{尾}}_{\mathbf{3}}\mathbf{=}\mathbf{0}$

For ${\mathbf{尾}}_{\mathbf{4}}$:

${\mathbf{H}}_{\mathbf{0}}\mathbf{:}{\mathbf{尾}}_{\mathbf{4}}\mathbf{=}\mathbf{0}$, whereas, ${\mathbf{H}}_{\mathbf{a}}\mathbf{:}{\mathbf{尾}}_{\mathbf{4}}鈮�\mathbf{0}$

Here, the test statistic $\mathbf{=}\frac{{\widehat{\mathbf{尾}}}_{\mathbf{4}}}{{\mathbf{蝉尾}}_{\mathbf{4}}}$

Test statistic$$\begin{gathered} \mathbf{=}\frac{\mathbf{0}\mathbf{.}\mathbf{0015}}{\mathbf{0}\mathbf{.}\mathbf{0005}} \\ \mathbf{=}\mathbf{3} \end{gathered}$$

For $\mathbf{伪}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{05}$, the critical value of ${\mathbf{t}}_{\mathbf{0}\mathbf{.}\mathbf{05}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{699}$using the formulae table

$H_0$is rejected if $\left|\mathbf{t}\right|\mathbf{>}{\mathbf{t}}_{\mathbf{0}\mathbf{.}\mathbf{05}}$. Since 3 > 1.699,

Reject the null hypothesis at a 95% significance level

Wherefore, the value of${\mathbf{尾}}_{\mathbf{4}}鈮�\mathbf{0}$

Antilogarithm formulae to be used to explain the percentage change in y for every 1-unit increase in the x-value is ${\mathbf{e}}^{\mathbf{尾迟}}\mathbf{-}\mathbf{1}$

For ${\mathbf{x}}_{\mathbf{1}}\mathbf{,}{\mathbf{尾}}_{\mathbf{1}}$ will have the effect of $\mathbf{(}{\mathbf{e}}^{\mathbf{0}\mathbf{.}\mathbf{03}}\mathbf{-}\mathbf{1}\mathbf{)}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{03045}$

This means that for every 1- unit change in $X_1$, y changes by 0.0345 units.

For ${\mathbf{x}}_{\mathbf{2}}\mathbf{,}{\mathbf{尾}}_{\mathbf{2}}$will have the effect of $\mathbf{(}{\mathbf{e}}^{\mathbf{0}\mathbf{.}\mathbf{60}}\mathbf{-}\mathbf{1}\mathbf{)}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{8221}$

According to, the values of ${\mathbf{R}}^{\mathbf{2}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{85}$and the value of s = 0.30

Value of $R^2$ greater than 0.70 denoted that the model is available to explain the variations in the data. The value of s is 0.30 which indicates that there is less variability between the data points and that the data is not very spread.

The lower value of s and high value of makes the model a good fit for the data.