You are given the following information abouty andx. Dependent Variable (y) Independent Variable (x) 6 4 8 6 10 12 The least squares estimate of the intercept or bo equals
You are given the following information abouty andx. Dependent Variable (y) Independent Variable (x) 6 4 8 6 10 12 The least squares estimate of the intercept or bo equals
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![**Title: Understanding Least Squares Regression**
**Introduction:**
In the study of statistical modeling, understanding the relationship between variables is essential. This guide explores the concept of least squares regression, focusing on estimating the intercept of a linear model.
**Dataset:**
You are given the following information about the variables \( y \) and \( x \):
- **Dependent Variable (\( y \)):** Data not provided in the text.
- **Independent Variable (\( x \)):** 6, 4, 8, 6, 10, 2, 12, 4
**Objective:**
Determine the least squares estimate of the intercept, denoted as \( b_0 \).
**Options:**
- **A:** \(-12\)
- **B:** \(12\)
- **C:** \(5\)
- **D:** \(-5\)
**Explanation:**
In linear regression, the equation of the line is given by:
\[ y = b_0 + b_1x \]
where:
- \( b_0 \) is the intercept,
- \( b_1 \) is the slope.
The least squares method aims to minimize the sum of the squared differences between the observed and predicted values.
**Conclusion:**
With the data provided, the task is to identify the correct intercept from the given options using least squares estimation techniques.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84a4babe-df88-4dc0-9444-4ec24957d88f%2F67ad23c7-31c7-4954-bc42-70fb73ff9782%2Fvv7u3me_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Least Squares Regression**
**Introduction:**
In the study of statistical modeling, understanding the relationship between variables is essential. This guide explores the concept of least squares regression, focusing on estimating the intercept of a linear model.
**Dataset:**
You are given the following information about the variables \( y \) and \( x \):
- **Dependent Variable (\( y \)):** Data not provided in the text.
- **Independent Variable (\( x \)):** 6, 4, 8, 6, 10, 2, 12, 4
**Objective:**
Determine the least squares estimate of the intercept, denoted as \( b_0 \).
**Options:**
- **A:** \(-12\)
- **B:** \(12\)
- **C:** \(5\)
- **D:** \(-5\)
**Explanation:**
In linear regression, the equation of the line is given by:
\[ y = b_0 + b_1x \]
where:
- \( b_0 \) is the intercept,
- \( b_1 \) is the slope.
The least squares method aims to minimize the sum of the squared differences between the observed and predicted values.
**Conclusion:**
With the data provided, the task is to identify the correct intercept from the given options using least squares estimation techniques.
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