Question

Round your answers to two decimal places. 

a. Using the following equation:

\(S_{\hat{y}},=s \sqrt{\frac{1}{n}+\frac{\left(x^{*}-\bar{x}\right)^{2}}{\sum\left(x_{i}-\bar{x}\right)^{2}}}\) Estimate the standard deviation of \(\hat{y}^{*}\) when \(x=3 .\)

b. Using the following expression:

\(\hat{y} * \pm t_{\alpha / 2} s_{\hat{y}}\)

Develop a \(95 \%\) confidence interval for the expected value of \(y\) when \(x=3\). to

c. Using the following equation:

$$ s_{\text {pred }}=s \sqrt{1+\frac{1}{n}+\frac{\left(x^{*}-\bar{x}\right)^{2}}{\sum\left(x_{i}-\bar{x}\right)^{2}}} $$

Estimate the standard deviation of an individual value of \(y\) when \(x=3\).

d. Using the following expression:

\(\hat{y}^{*} \pm t_{\alpha / 2} s_{\text {pred }}\)

Develop a \(95 \%\) prediction interval for \(y\) when \(x=3\).

to

Answer 1

a)

std error of confidence interval =

s*√(1/n+(x0-x̅)2/Sxx)=

0.8287~ 0.83

b)

for 95 % confidence and 3degree of freedom critical t=						3.1820
95% confidence interval =xo -/+ t*standard error=					(5.96,11.24)

c)

std error of prediction interval=s*√(1+1/n+(x0-x̅)2/Sxx)=

2.0298~ 2.03

d)

for 95 % confidence and -2degree of freedom critical t=						3.1820
95% prediction interval =xo -/+ t*standard error=					(2.14,15.06)