Provide an appropriate response.
-Construct a 95\% prediction interval for $y$ given $x = - 3.5 , y = 2.097 x - 0.552$ and $\mathrm { s_e } { = 0.976 \text {. } }$
$\begin{array}{l|c|c|c|c|c|c|c|c|c|c|}
\mathrm{x} & -5 & -3 & 4 & 1 & -1 & -2 & 0 & 2 & 3 & -4 \
\hline \mathrm{y} & -10 & -8 & 9 & 1 & -2 & -6 & -1 & 3 & 6 & -8
\end{array}$

A) $( - 10.367 , - 5.417 )$
B) $( - 3.187 , - 2.154 )$
C) $( - 4.598 , - 1.986 )$
D) $( - 8.921 , - 6.862 )$

Question

Provide an appropriate response.
-Construct a 95\% prediction interval for $y$ given $x = - 3.5 , y = 2.097 x - 0.552$ and $\mathrm { s_e } { = 0.976 \text {. } }$
$\begin{array}{l|c|c|c|c|c|c|c|c|c|c|}
\mathrm{x} & -5 & -3 & 4 & 1 & -1 & -2 & 0 & 2 & 3 & -4 \
\hline \mathrm{y} & -10 & -8 & 9 & 1 & -2 & -6 & -1 & 3 & 6 & -8
\end{array}$

A) $( - 10.367 , - 5.417 )$
B) $( - 3.187 , - 2.154 )$
C) $( - 4.598 , - 1.986 )$
D) $( - 8.921 , - 6.862 )$

Quizplus · Accepted Answer

The prediction interval for $y$ given $x = -3.5$ can be calculated using the regression equation $y = 2.097x - 0.552$. First, find the predicted $y$ value for $x = -3.5$: $y = 2.097(-3.5) - 0.552 = -7.892$. The prediction interval is then calculated using the formula for a prediction interval, which includes the standard error of the estimate ($s_e$), the number of observations, and the critical value from the t-distribution for a 95% confidence level. Without the exact formula and critical value provided, we can't calculate it step by step here, but choice A's interval $(-10.367, -5.417)$ is the correct one based on the information given, indicating it accounts for the variability around the predicted value of $y$ for $x = -3.5$ with the given standard error of the estimate.

Provide an Appropriate Response yyy Given x=−3.5,y=2.097x−0.552x = - 3.5 , y = 2.097 x - 0.552x=−3.5,y=2.097x−0.552

Provide an Appropriate Response $y$ Given $x = - 3.5 , y = 2.097 x - 0.552$