**Title: Analyzing Least Squares Regression Lines** **Question:** Which of the following two graphs CANNOT be the least squares regression line through the given points? Please explain your reasoning. **Table and Graph Analysis:** 1. **Table Analysis:** **First Table: Using Line through Points 2 and 3** - Columns: \( x \) (obs), \( y \) (obs), \( y \) (pred), \( e \), \( e^2 \) - Row Data: - \( x = 5 \), \( y \) (obs) = 37, \( y \) (pred) = 69, \( e \) = -32, \( e^2 \) = 1024 - \( x = 10 \), \( y \) (obs) = 120, \( y \) (pred) = 120, \( e \) = 0, \( e^2 \) = 0 - \( x = 15 \), \( y \) (obs) = 171, \( y \) (pred) = 171, \( e \) = 0, \( e^2 \) = 0 - \( x = 20 \), \( y \) (obs) = 192, \( y \) (pred) = 222, \( e \) = -30, \( e^2 \) = 900 - Total Σ\( e^2 = 1924 \) **Second Table:** - Columns: \( x \) (obs), \( y \) (obs), \( y \) (pred), \( y \) (obs) - \( y \) (pred), \( (y \) (obs) - \( y \) (pred))^2 - Row Data: - \( x = 5 \), \( y \) (obs) = 37, \( y \) (pred) = 37, \( e \) = -15.6, \( e^2 \) = 243.4 - \( x = 10 \), \( y \) (obs) = 120, \( y \) (pred) = 134.2, \( e \) = 15.8, \( e^2 \) = 249.6 -
**Title: Analyzing Least Squares Regression Lines** **Question:** Which of the following two graphs CANNOT be the least squares regression line through the given points? Please explain your reasoning. **Table and Graph Analysis:** 1. **Table Analysis:** **First Table: Using Line through Points 2 and 3** - Columns: \( x \) (obs), \( y \) (obs), \( y \) (pred), \( e \), \( e^2 \) - Row Data: - \( x = 5 \), \( y \) (obs) = 37, \( y \) (pred) = 69, \( e \) = -32, \( e^2 \) = 1024 - \( x = 10 \), \( y \) (obs) = 120, \( y \) (pred) = 120, \( e \) = 0, \( e^2 \) = 0 - \( x = 15 \), \( y \) (obs) = 171, \( y \) (pred) = 171, \( e \) = 0, \( e^2 \) = 0 - \( x = 20 \), \( y \) (obs) = 192, \( y \) (pred) = 222, \( e \) = -30, \( e^2 \) = 900 - Total Σ\( e^2 = 1924 \) **Second Table:** - Columns: \( x \) (obs), \( y \) (obs), \( y \) (pred), \( y \) (obs) - \( y \) (pred), \( (y \) (obs) - \( y \) (pred))^2 - Row Data: - \( x = 5 \), \( y \) (obs) = 37, \( y \) (pred) = 37, \( e \) = -15.6, \( e^2 \) = 243.4 - \( x = 10 \), \( y \) (obs) = 120, \( y \) (pred) = 134.2, \( e \) = 15.8, \( e^2 \) = 249.6 -
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Related questions
Question
![**Title: Analyzing Least Squares Regression Lines**
**Question:**
Which of the following two graphs CANNOT be the least squares regression line through the given points? Please explain your reasoning.
**Table and Graph Analysis:**
1. **Table Analysis:**
**First Table: Using Line through Points 2 and 3**
- Columns: \( x \) (obs), \( y \) (obs), \( y \) (pred), \( e \), \( e^2 \)
- Row Data:
- \( x = 5 \), \( y \) (obs) = 37, \( y \) (pred) = 69, \( e \) = -32, \( e^2 \) = 1024
- \( x = 10 \), \( y \) (obs) = 120, \( y \) (pred) = 120, \( e \) = 0, \( e^2 \) = 0
- \( x = 15 \), \( y \) (obs) = 171, \( y \) (pred) = 171, \( e \) = 0, \( e^2 \) = 0
- \( x = 20 \), \( y \) (obs) = 192, \( y \) (pred) = 222, \( e \) = -30, \( e^2 \) = 900
- Total Σ\( e^2 = 1924 \)
**Second Table:**
- Columns: \( x \) (obs), \( y \) (obs), \( y \) (pred), \( y \) (obs) - \( y \) (pred), \( (y \) (obs) - \( y \) (pred))^2
- Row Data:
- \( x = 5 \), \( y \) (obs) = 37, \( y \) (pred) = 37, \( e \) = -15.6, \( e^2 \) = 243.4
- \( x = 10 \), \( y \) (obs) = 120, \( y \) (pred) = 134.2, \( e \) = 15.8, \( e^2 \) = 249.6
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa12589fb-477e-4a42-9225-2d1cc3fb7157%2F7d5f3e53-2c39-441c-a76a-3c6ed024f0e1%2Fr3cgavm.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Analyzing Least Squares Regression Lines**
**Question:**
Which of the following two graphs CANNOT be the least squares regression line through the given points? Please explain your reasoning.
**Table and Graph Analysis:**
1. **Table Analysis:**
**First Table: Using Line through Points 2 and 3**
- Columns: \( x \) (obs), \( y \) (obs), \( y \) (pred), \( e \), \( e^2 \)
- Row Data:
- \( x = 5 \), \( y \) (obs) = 37, \( y \) (pred) = 69, \( e \) = -32, \( e^2 \) = 1024
- \( x = 10 \), \( y \) (obs) = 120, \( y \) (pred) = 120, \( e \) = 0, \( e^2 \) = 0
- \( x = 15 \), \( y \) (obs) = 171, \( y \) (pred) = 171, \( e \) = 0, \( e^2 \) = 0
- \( x = 20 \), \( y \) (obs) = 192, \( y \) (pred) = 222, \( e \) = -30, \( e^2 \) = 900
- Total Σ\( e^2 = 1924 \)
**Second Table:**
- Columns: \( x \) (obs), \( y \) (obs), \( y \) (pred), \( y \) (obs) - \( y \) (pred), \( (y \) (obs) - \( y \) (pred))^2
- Row Data:
- \( x = 5 \), \( y \) (obs) = 37, \( y \) (pred) = 37, \( e \) = -15.6, \( e^2 \) = 243.4
- \( x = 10 \), \( y \) (obs) = 120, \( y \) (pred) = 134.2, \( e \) = 15.8, \( e^2 \) = 249.6
-
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
Given :
1st graph with least squares regression line equation,
residual sum of squares = = 1924
2nd graph with least squares regression line equation,
residual sum of squares = = 961
Step by step
Solved in 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
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