TABLE 2.4 X y 1 6 Exercise 2.3 Data 2 4 3 11 4 9 5 13 e. Find their sum, Σê, and their sum of squared values, f. Calculate Exê. 6 17 a. Using a ruler, draw a line that fits through the data. Measure the slope and intercept of the line you have drawn. b. Use formulas (2.7) and (2.8) to compute, using only a hand calculator, the least squares estimates of the slope and the intercept. Plot this line on your graph. c. Obtain the sample means y = Ey/N and x = x/N. Obtain the predicted value of y for x = x and plot it on your graph. What do you observe about this predicted value? d. Using the least squares estimates from (b), compute the least squares residuals ê;.
TABLE 2.4 X y 1 6 Exercise 2.3 Data 2 4 3 11 4 9 5 13 e. Find their sum, Σê, and their sum of squared values, f. Calculate Exê. 6 17 a. Using a ruler, draw a line that fits through the data. Measure the slope and intercept of the line you have drawn. b. Use formulas (2.7) and (2.8) to compute, using only a hand calculator, the least squares estimates of the slope and the intercept. Plot this line on your graph. c. Obtain the sample means y = Ey/N and x = x/N. Obtain the predicted value of y for x = x and plot it on your graph. What do you observe about this predicted value? d. Using the least squares estimates from (b), compute the least squares residuals ê;.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Please solve 2.3 in its entirety, thanks!
![**Educational Website Transcription:**
**Exercise 2.3**
1. **Using a ruler, draw a line that fits through the data you have drawn.**
2. **Use formulas (7) and (8) to compute, using only a hand calculator, the least squares estimates of the slope and intercept. Plot this line on your graph.**
3. **Using the least squares estimates from part (b), find their sum, and their sum of squared values, \( \Sigma \hat{y_i}^2 \).**
4. **What is the predicted value of y, for \( x = \bar{x} \)? Calculate the least squares residuals \( \hat{e_i} \).**
**24. Given the simple linear regression model \( y_i = \beta_1 + \beta_2 x_i + e_i \), suppose, however, that we knew, algebraically, that \( \beta_2 = 0 \);**
a. **What does the linear regression model look like graphically if \( \beta_2 = 0 \)?**
b. **If \( \beta_2 \) = 0, in the least squares sum of squares function, we aim to minimize:**
c. **Using the data in Table 2.4 from Exercise 2.3, plot the value, \( y_i \), that minimizes \( \sum(y_i - \beta_1)^2 \). Use this to compute \( \Sigma y_i \).**
**Table 2.4: Exercise 2.3 Data**
\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
1 & 6 \\
2 & 4 \\
3 & 11 \\
4 & 9 \\
5 & 13 \\
6 & 17 \\
\hline
\end{array}
\]
**2.3 Graph the following observations of x and y on graph paper.**
This section provides the dataset for a simple linear regression analysis and guides through plotting the data and calculating the regression line.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b1ec9e1-71c5-41a7-88e5-1ec0b0e62692%2F9b0044a3-1d9e-42ef-83fa-947ee24c7ab9%2Fhqapdi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Website Transcription:**
**Exercise 2.3**
1. **Using a ruler, draw a line that fits through the data you have drawn.**
2. **Use formulas (7) and (8) to compute, using only a hand calculator, the least squares estimates of the slope and intercept. Plot this line on your graph.**
3. **Using the least squares estimates from part (b), find their sum, and their sum of squared values, \( \Sigma \hat{y_i}^2 \).**
4. **What is the predicted value of y, for \( x = \bar{x} \)? Calculate the least squares residuals \( \hat{e_i} \).**
**24. Given the simple linear regression model \( y_i = \beta_1 + \beta_2 x_i + e_i \), suppose, however, that we knew, algebraically, that \( \beta_2 = 0 \);**
a. **What does the linear regression model look like graphically if \( \beta_2 = 0 \)?**
b. **If \( \beta_2 \) = 0, in the least squares sum of squares function, we aim to minimize:**
c. **Using the data in Table 2.4 from Exercise 2.3, plot the value, \( y_i \), that minimizes \( \sum(y_i - \beta_1)^2 \). Use this to compute \( \Sigma y_i \).**
**Table 2.4: Exercise 2.3 Data**
\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
1 & 6 \\
2 & 4 \\
3 & 11 \\
4 & 9 \\
5 & 13 \\
6 & 17 \\
\hline
\end{array}
\]
**2.3 Graph the following observations of x and y on graph paper.**
This section provides the dataset for a simple linear regression analysis and guides through plotting the data and calculating the regression line.
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