Question

Part 1:

Suppose that you have run a regression model to estimate the equation using 1,000 observations and have obtained the following results.

Standard errors are in parentheses.

State whether or not you reject the null hypothesis that , and provide any statistics that lead you to this conclusion.

Part 2:

Use the same regression results as in the previous question.

State whether or not you reject the null hypothesis that , and provide any statistics that lead you to this conclusion.

Answer 1

$Part~1:\\ Null~hypothesis,~H_0:\alpha=0~vs.~Alternative~hypothesis,~H_1:\alpha\neq 0\\ Value~of~t~statistic=0.10/0.02=5\\ p-value=2P(t>5|t\sim t_{998})=0.0000007<0.05\\ Hence~we~reject~H_0~and~conclude~that~intercept~term~\alpha~is~significantly\\ different~from~zero.\\ Part~2:\\ Null~hypothesis,~H_0:\beta=1~vs.~Alternative~hypothesis,~H_1:\beta\neq 1\\ Value~of~t~statistic=(0.90-1)/0.07=-1.4286\\ p-value=2P(t>1.4286|t\sim t_{998})=0.1534>0.05\\ Hence~we~fail~to~reject~H_0~and~conclude~that~slope~\beta~is~insignificantly\\ different~from~1.\\$