Consider the following model:

$=0+11+++$

$,$ Model $(1)$

known as the Classical Linear Regression Model $($CLRM$).$

i$.$ How do you test for the significance of the coefficient of the regressor $1$ in Model $(1)?$

Write the null and alternative hypotheses, the test statistic, and explain the decision rule

to reject the null hypothesis.

$[8$ marks$]$

ii$.$ Explain the logic behind the $$

$$

$.$ What happens to the $$

$$

in case one extra variable is

added to Model $(1)$ above? Discuss brief