Question

Given a simple regression analysis, suppose that we have obtained a fitted regression model $$ \hat{y}_i=8+10 x_i $$ and also $$ s_e=11.23 \quad \bar{x}=8 \quad n=44 \sum_{i=1}^n\left(x_i-\bar{x}\right)^2=800 $$ Find the $95 \%$ confidence interval and $95 \%$ prediction interval for the point where $x=17$.

   Given a simple regression analysis, suppose that we have obtained a fitted regression model
$$
\hat{y}_i=8+10 x_i
$$
and also
$$
s_e=11.23 \quad \bar{x}=8 \quad n=44 \sum_{i=1}^n\left(x_i-\bar{x}\right)^2=800
$$
Find the $95 \%$ confidence interval and $95 \%$ prediction interval for the point where $x=17$.

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Statistics for Business and Economics: Global Edition

Statistics for Business and Economics: Global Edition

Newbold P., Carlson… 8th Edition

Chapter 11, Problem 42

Instant Answer

Step 1

Given the regression equation $\hat{y}_i = 8 + 10x_i$, substitute $x_i = 17$: $$ \hat{y}_{x=17} = 8 + 10(17) = 8 + 170 = 178. $$ Show more…

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Given a simple regression analysis, suppose that we have obtained a fitted regression model $$ \hat{y}_i=8+10 x_i $$ and also $$ s_e=11.23 \quad \bar{x}=8 \quad n=44 \sum_{i=1}^n\left(x_i-\bar{x}\right)^2=800 $$ Find the $95 \%$ confidence interval and $95 \%$ prediction interval for the point where $x=17$.

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