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**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
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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**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 -
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
Step 1

Given :

1st graph with least squares regression line equation,

y = 10.2×x+18

residual sum of squares = ∑iei2 = 1924

2nd graph with least squares regression line equation,

y = 10.32×x+1

residual sum of squares = ∑iei2 = 961 

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