5.1 Consider the multiple regression model y₁=xB₁+x₂ + xpB₂ +€₁ with the seven observations on y, XX. and x, given in Table 5.5. TABLE 5.5 Y₁ 4 1 -2 2 Data for Exercise 5.1 1 f. Find the sample correlation between g. Find the standar d. Find the least squares residuals ê, ê...... e. Find the variance estimate 6². X12 0 2 -2 1 -2 0 1 -2 2 * * -1 Use a hand calculator or spreadsheet to answer the following questions: a. Calculate the observations in terms of deviations from their means. That is, find x = -₂ XX-X. and y=y₁-3. b. Calculate Ex. Ex Ex. Ex and Ex c. Use the expressions in Appendix 5A to find least squares estimates b₁, by, and by. AC R
5.1 Consider the multiple regression model y₁=xB₁+x₂ + xpB₂ +€₁ with the seven observations on y, XX. and x, given in Table 5.5. TABLE 5.5 Y₁ 4 1 -2 2 Data for Exercise 5.1 1 f. Find the sample correlation between g. Find the standar d. Find the least squares residuals ê, ê...... e. Find the variance estimate 6². X12 0 2 -2 1 -2 0 1 -2 2 * * -1 Use a hand calculator or spreadsheet to answer the following questions: a. Calculate the observations in terms of deviations from their means. That is, find x = -₂ XX-X. and y=y₁-3. b. Calculate Ex. Ex Ex. Ex and Ex c. Use the expressions in Appendix 5A to find least squares estimates b₁, by, and by. AC R
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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Question
Please answer 5.1 d-f, thank you!
![**5.8 Exercises**
**5.8.1 Problems**
**5.1** Consider the multiple regression model
\(y_i = x_{i1}\beta_1 + x_{i2}\beta_2 + x_{i3}\beta_3 + \epsilon_i\)
with the seven observations on \(y_i\), \(x_{i1}\), \(x_{i2}\), and \(x_{i3}\) given in Table 5.5.
**TABLE 5.5: Data for Exercise 5.1**
\[
\begin{array}{cccc}
y_i & x_{i1} & x_{i2} & x_{i3} \\
\hline
1 & 1 & 0 & 1 \\
4 & 1 & 0 & 2 \\
1 & 1 & -1 & -2 \\
0 & 1 & 2 & 2 \\
-1 & 1 & 1 & 1 \\
2 & 1 & -2 & -2 \\
-2 & 1 & 0 & -1 \\
\end{array}
\]
Use a hand calculator or spreadsheet to answer the following questions:
a. Calculate the observations in terms of deviations from their means. That is, find \(x^*_{i1} = x_{i1} - \bar{x}_1\), \(x^*_{i2} = x_{i2} - \bar{x}_2\), and \(y^*_i = y_i - \bar{y}\).
b. Calculate \(\sum x^*_{i2} y^*_i\), \(\sum x^*_{i3} y^*_i\), \(\sum x^*_{i2} x^*_{i3}\), and \(\sum x^{*2}_{i2}\).
c. Use the expressions in Appendix 5A to find least squares estimates \(b_1\), \(b_2\), and \(b_3\).
d. Find the least-squares residuals \(\hat{\epsilon}_1, \hat{\epsilon}_2, \ldots, \hat{\epsilon}_7\).
e. Find the variance estimate \(\hat{\sigma}^2\).
f. Find the sample correlation between \(x_2\) and \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b1ec9e1-71c5-41a7-88e5-1ec0b0e62692%2Ff9034777-e49e-48bd-8557-ac8d949e6b7b%2F25jgzzu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**5.8 Exercises**
**5.8.1 Problems**
**5.1** Consider the multiple regression model
\(y_i = x_{i1}\beta_1 + x_{i2}\beta_2 + x_{i3}\beta_3 + \epsilon_i\)
with the seven observations on \(y_i\), \(x_{i1}\), \(x_{i2}\), and \(x_{i3}\) given in Table 5.5.
**TABLE 5.5: Data for Exercise 5.1**
\[
\begin{array}{cccc}
y_i & x_{i1} & x_{i2} & x_{i3} \\
\hline
1 & 1 & 0 & 1 \\
4 & 1 & 0 & 2 \\
1 & 1 & -1 & -2 \\
0 & 1 & 2 & 2 \\
-1 & 1 & 1 & 1 \\
2 & 1 & -2 & -2 \\
-2 & 1 & 0 & -1 \\
\end{array}
\]
Use a hand calculator or spreadsheet to answer the following questions:
a. Calculate the observations in terms of deviations from their means. That is, find \(x^*_{i1} = x_{i1} - \bar{x}_1\), \(x^*_{i2} = x_{i2} - \bar{x}_2\), and \(y^*_i = y_i - \bar{y}\).
b. Calculate \(\sum x^*_{i2} y^*_i\), \(\sum x^*_{i3} y^*_i\), \(\sum x^*_{i2} x^*_{i3}\), and \(\sum x^{*2}_{i2}\).
c. Use the expressions in Appendix 5A to find least squares estimates \(b_1\), \(b_2\), and \(b_3\).
d. Find the least-squares residuals \(\hat{\epsilon}_1, \hat{\epsilon}_2, \ldots, \hat{\epsilon}_7\).
e. Find the variance estimate \(\hat{\sigma}^2\).
f. Find the sample correlation between \(x_2\) and \(
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