In this data set, the following statistics hold: 1(x₁ - x)² = 90 and ₁1(x₁ - x)(Yi − y) = −66 Assume you use this data set to estimate the model y = Bo + Bixi + e and you obtain the follow- ing statistic: SSE = 6.8. Which set of values best represent the standardized residual of the first observation, r₁? You (a) (b) (c) (d) (e) = need the following formulas: hj may r₁ ≤ -2 -2
In this data set, the following statistics hold: 1(x₁ - x)² = 90 and ₁1(x₁ - x)(Yi − y) = −66 Assume you use this data set to estimate the model y = Bo + Bixi + e and you obtain the follow- ing statistic: SSE = 6.8. Which set of values best represent the standardized residual of the first observation, r₁? You (a) (b) (c) (d) (e) = need the following formulas: hj may r₁ ≤ -2 -2
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
![**Dataset and Statistical Analysis**
The following dataset is given:
\[
\begin{array}{c|c|c}
\text{i} & \text{x} & \text{y} \\
\hline
1 & -3 & 14 \\
2 & 0 & 10 \\
3 & 3 & 11 \\
4 & 6 & 8 \\
5 & 9 & 4 \\
\end{array}
\]
In this dataset, the following statistics hold:
\[
\sum_{i=1}^{5}(x_i - \bar{x})^2 = 90 \quad \text{and} \quad \sum_{i=1}^{5}(x_i - \bar{x})(y_i - \bar{y}) = -66
\]
Assume you use this dataset to estimate the model \( y = \beta_0 + \beta_1x_1 + \epsilon \) and you obtain the following statistic: \( SSE = 6.8 \).
**Problem:**
Which set of values best represents the standardized residual of the first observation, \( r_1 \)?
**Given Formulas:**
\[
h_j = \frac{1}{n} + \frac{(x_j - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}, \quad s_{y_i-\hat{y}_i} = s\sqrt{1 - h_i}, \quad r_i = \frac{y_i - \hat{y}_i}{s_{y_i-\hat{y}_i}}
\]
**Options:**
(a) \( r_1 \leq -2 \)
(b) \(-2 < r_1 \leq -1 \)
(c) \(-1 < r_1 \leq 0 \)
(d) \(0 < r_1 \leq 1 \)
(e) \(1 < r_1 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F840ac9d4-eb27-4280-b70d-21eed9a81895%2F3218d9b6-fbb2-4a9d-a298-eb0ea6dcc6ea%2Feieynlg_processed.png&w=3840&q=75)
Transcribed Image Text:**Dataset and Statistical Analysis**
The following dataset is given:
\[
\begin{array}{c|c|c}
\text{i} & \text{x} & \text{y} \\
\hline
1 & -3 & 14 \\
2 & 0 & 10 \\
3 & 3 & 11 \\
4 & 6 & 8 \\
5 & 9 & 4 \\
\end{array}
\]
In this dataset, the following statistics hold:
\[
\sum_{i=1}^{5}(x_i - \bar{x})^2 = 90 \quad \text{and} \quad \sum_{i=1}^{5}(x_i - \bar{x})(y_i - \bar{y}) = -66
\]
Assume you use this dataset to estimate the model \( y = \beta_0 + \beta_1x_1 + \epsilon \) and you obtain the following statistic: \( SSE = 6.8 \).
**Problem:**
Which set of values best represents the standardized residual of the first observation, \( r_1 \)?
**Given Formulas:**
\[
h_j = \frac{1}{n} + \frac{(x_j - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}, \quad s_{y_i-\hat{y}_i} = s\sqrt{1 - h_i}, \quad r_i = \frac{y_i - \hat{y}_i}{s_{y_i-\hat{y}_i}}
\]
**Options:**
(a) \( r_1 \leq -2 \)
(b) \(-2 < r_1 \leq -1 \)
(c) \(-1 < r_1 \leq 0 \)
(d) \(0 < r_1 \leq 1 \)
(e) \(1 < r_1 \)
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