Construct Confidence Intervals for a Mean Response
-Construct a $95 \%$ confidence interval about the mean value of $y$, given $x = - 3.5 , \hat { y } = 2.097 x - 0.552$ and $s _ { e } = 0.976$.
$\begin{array}{l|c|c|c|c|c|c|c|c|c|c|}
\mathrm{x} & -5 & -3 & 4 & 1 & -1 & -2 & 0 & 2 & 3 & -4 \
\hline \mathrm{y} & -10 & -8 & 9 & 1 & -2 & -6 & -1 & 3 & 6 & -8
\end{array}$

A) $( - 8.921 , - 6.862 )$
B) $( - 10.367 , - 5.417 )$
C) $( - 4.598 , - 1.986 )$
D) $( - 12.142 , - 6.475 )$

Question

Construct Confidence Intervals for a Mean Response
-Construct a $95 \%$ confidence interval about the mean value of $y$, given $x = - 3.5 , \hat { y } = 2.097 x - 0.552$ and $s _ { e } = 0.976$.
$\begin{array}{l|c|c|c|c|c|c|c|c|c|c|}
\mathrm{x} & -5 & -3 & 4 & 1 & -1 & -2 & 0 & 2 & 3 & -4 \
\hline \mathrm{y} & -10 & -8 & 9 & 1 & -2 & -6 & -1 & 3 & 6 & -8
\end{array}$

A) $( - 8.921 , - 6.862 )$
B) $( - 10.367 , - 5.417 )$
C) $( - 4.598 , - 1.986 )$
D) $( - 12.142 , - 6.475 )$

Quizplus · Accepted Answer

To construct a 95% confidence interval for the mean value of $y$ given $x = -3.5$, we first calculate the predicted value of $y$ ($\hat{y}$) using the given regression equation $\hat{y} = 2.097x - 0.552$. Substituting $x = -3.5$ into the equation gives $\hat{y} = 2.097(-3.5) - 0.552 = -7.8915$. The confidence interval is then calculated using the formula for a confidence interval around a predicted value, which includes the standard error of the estimate ($s_e$). However, without the exact formula or additional details like the number of observations or the critical value from the t-distribution, we can't calculate the exact bounds here. The choice that closely matches the calculated mean value of $y$ when $x = -3.5$ is option A, assuming typical procedures for calculating confidence intervals around a regression prediction.

Construct Confidence Intervals for a Mean Response -Construct A 95%95 \%95%

Construct Confidence Intervals for a Mean Response
-Construct A $95 \%$