You may need to use the appropriate appendix table or technology to answer this question. Given are five observations for two variables, x and y. (Round your answers to two decimal places.) \[ \begin{array}{ccc} x_i & y_i \\ \hline 3 & 50 \\ 12 & 45 \\ 6 & 55 \\ 20 & 5 \\ 15 & 15 \\ \end{array} \] (a) Estimate the standard deviation of $\hat{y}$ when \( x = 8 \). (b) Develop a 95% confidence interval for the expected value of y when \( x = 8 \). (c) Estimate the standard deviation of an individual value of y when \( x = 8 \). (d) Develop a 95% prediction interval for y when \( x = 8 \). The table provided lists pairs of \( x \) and \( y \) values which are: - \( (x_1, y_1) = (3, 50) \) - \( (x_2, y_2) = (12, 45) \) - \( (x_3, y_3) = (6, 55) \) - \( (x_4, y_4) = (20, 5) \) - \( (x_5, y_5) = (15, 15) \) Use these observations to answer the questions regarding standard deviation, confidence intervals, and prediction intervals for a given value of \( x \).
You may need to use the appropriate appendix table or technology to answer this question. Given are five observations for two variables, x and y. (Round your answers to two decimal places.) \[ \begin{array}{ccc} x_i & y_i \\ \hline 3 & 50 \\ 12 & 45 \\ 6 & 55 \\ 20 & 5 \\ 15 & 15 \\ \end{array} \] (a) Estimate the standard deviation of $\hat{y}$ when \( x = 8 \). (b) Develop a 95% confidence interval for the expected value of y when \( x = 8 \). (c) Estimate the standard deviation of an individual value of y when \( x = 8 \). (d) Develop a 95% prediction interval for y when \( x = 8 \). The table provided lists pairs of \( x \) and \( y \) values which are: - \( (x_1, y_1) = (3, 50) \) - \( (x_2, y_2) = (12, 45) \) - \( (x_3, y_3) = (6, 55) \) - \( (x_4, y_4) = (20, 5) \) - \( (x_5, y_5) = (15, 15) \) Use these observations to answer the questions regarding standard deviation, confidence intervals, and prediction intervals for a given value of \( x \).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![You may need to use the appropriate appendix table or technology to answer this question. Given are five observations for two variables, x and y. (Round your answers to two decimal places.)
\[
\begin{array}{ccc}
x_i & y_i \\
\hline
3 & 50 \\
12 & 45 \\
6 & 55 \\
20 & 5 \\
15 & 15 \\
\end{array}
\]
(a) Estimate the standard deviation of $\hat{y}$ when \( x = 8 \).
(b) Develop a 95% confidence interval for the expected value of y when \( x = 8 \).
(c) Estimate the standard deviation of an individual value of y when \( x = 8 \).
(d) Develop a 95% prediction interval for y when \( x = 8 \).
The table provided lists pairs of \( x \) and \( y \) values which are:
- \( (x_1, y_1) = (3, 50) \)
- \( (x_2, y_2) = (12, 45) \)
- \( (x_3, y_3) = (6, 55) \)
- \( (x_4, y_4) = (20, 5) \)
- \( (x_5, y_5) = (15, 15) \)
Use these observations to answer the questions regarding standard deviation, confidence intervals, and prediction intervals for a given value of \( x \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70237df8-dfb4-41d0-af11-e6f29414ce12%2F825e5f00-9798-46eb-b3eb-af9a4d6f1094%2Fdds9g2h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:You may need to use the appropriate appendix table or technology to answer this question. Given are five observations for two variables, x and y. (Round your answers to two decimal places.)
\[
\begin{array}{ccc}
x_i & y_i \\
\hline
3 & 50 \\
12 & 45 \\
6 & 55 \\
20 & 5 \\
15 & 15 \\
\end{array}
\]
(a) Estimate the standard deviation of $\hat{y}$ when \( x = 8 \).
(b) Develop a 95% confidence interval for the expected value of y when \( x = 8 \).
(c) Estimate the standard deviation of an individual value of y when \( x = 8 \).
(d) Develop a 95% prediction interval for y when \( x = 8 \).
The table provided lists pairs of \( x \) and \( y \) values which are:
- \( (x_1, y_1) = (3, 50) \)
- \( (x_2, y_2) = (12, 45) \)
- \( (x_3, y_3) = (6, 55) \)
- \( (x_4, y_4) = (20, 5) \)
- \( (x_5, y_5) = (15, 15) \)
Use these observations to answer the questions regarding standard deviation, confidence intervals, and prediction intervals for a given value of \( x \).
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