The equation of the regression line for the paired data below is $\hat{\mathrm { y }} = 3 \mathrm { x }$ and the standard error of estimate is se $=$ 2.2361. Find the $90 \%$ prediction interval of $y$ for $x = 3$.
$\begin{array}{r|rrrr}
x & 2 & 4 & 5 & 6 \
\hline y & 7 & 11 & 13 & 20
\end{array}$
A) $1.2

Question

The equation of the regression line for the paired data below is $\hat{\mathrm { y }} = 3 \mathrm { x }$ and the standard error of estimate is se $=$ 2.2361. Find the $90 \%$ prediction interval of $y$ for $x = 3$.
$\begin{array}{r|rrrr}
x & 2 & 4 & 5 & 6 \
\hline y & 7 & 11 & 13 & 20
\end{array}$
A) $1.2 < y < 16.8$
B) $6.8 < y < 11.2$
C) $4.5 < y < 13.5$
D) $7.1 < y < 10.9$

Quizplus · Accepted Answer

The 90% prediction interval for y for x = 3 is:$\hat{\mathrm { y }} \pm t_{\alpha/2, n-2} \times se$where $\hat{\mathrm { y }}$ is the predicted value of y for x = 3, $t_{\alpha/2, n-2}$ is the critical value of the t-distribution with n-2 degrees of freedom and a significance level of $\alpha/2$, and se is the standard error of estimate.For a 90% prediction interval, $\alpha/2$ = 0.05 and $n-2$ = 2. The critical value of the t-distribution with 2 degrees of freedom and a significance level of 0.05 is 2.920.Therefore, the 90% prediction interval for y for x = 3 is:$3 \pm 2.920 \times 2.2361$$= 1.2 < y < 16.8$

The Equation of the Regression Line for the Paired Data y^=3x\hat{\mathrm { y }} = 3 \mathrm { x }y^​=3x

The Equation of the Regression Line for the Paired Data $\hat{\mathrm { y }} = 3 \mathrm { x }$