The summary statistics for a certain set of points are: $n = 19 , s _ { \mathrm { e } } = 3.899$
$\sum ( x - \bar { x } ) ^ { 2 } = 14.425 , \text { and } b _ { 1 } = 1.672$
Assume the conditions of the linear model hold A 99% confidence interval for $\beta _ { 1 }$ will be constructed.
Construct the 99% confidence interval.
A) $- 0.9632

Question

The summary statistics for a certain set of points are: $n = 19 , s _ { \mathrm { e } } = 3.899$
$\sum ( x - \bar { x } ) ^ { 2 } = 14.425 , \text { and } b _ { 1 } = 1.672$
Assume the conditions of the linear model hold A 99%  confidence interval for $\beta _ { 1 }$ will be constructed.
Construct the  99%  confidence interval.
A) $- 0.9632 < \beta _ { 1 } < 4.3072$
B) $- 1.2825 < \beta _ { 1 } < 4.6265$
C) $- 0.9478 < \beta _ { 1 } < 4.6265$
D) $- 1.3030 < \beta _ { 1 } < 4.6470$

Quizplus · Accepted Answer

The confidence interval for $\beta_1$ is calculated using the formula: $b_1 \pm t^* \cdot \frac{s_e}{\sqrt{\sum (x - \bar{x})^2}}$. For 18 degrees of freedom (n-1) and a 99% confidence level, the critical value $t^*$ is approximately 2.878. Plugging in the values, the interval is approximately $-1.3030 < \beta_1 < 4.6470$.

The Summary Statistics for a Certain Set of Points Are n=19,se=3.899n = 19 , s _ { \mathrm { e } } = 3.899n=19,se​=3.899

The Summary Statistics for a Certain Set of Points Are $n = 19 , s _ { \mathrm { e } } = 3.899$