Use the properties of the least-squares estimators given

Chapter 11, Problem 27E

(choose chapter or problem)

Use the properties of the least-squares estimators given in Section 11.4 to complete the following.

a Show that under the null hypothesis $H_{0}: \beta_{1}=\beta_{1} 0$

$T=\frac{\widehat{B}_{i}-\beta_{i} 0}{S_{1} \sqrt{c_{i i}}}$

possesses a t distribution with n − 2 df, where i = 1, 2.

b Derive the confidence intervals for $\beta_{1}$ given in this section.

Equation transcription:

${H}_{0}:{\beta{}}_{1}={\beta{}}_{1}0$

$T=\frac{\widehat{{B}_{i}}-{\beta{}}_{i}0}{S\sqrt{{c}_{ii}}}$

${\beta{}}_{1}$

Text transcription:

H_{0}: \beta{1}=\beta{1} 0

T=frac{\widehat{B}{i}-\beta{i} 0}{S{1} \sqrt{c{i i}}}

beta{1}

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