In the least-squares line y -5+ 3x, what is the marginal change in y for each unit change in x?
In the least-squares line y -5+ 3x, what is the marginal change in y for each unit change in x?
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 1: [-/1 Points]**
**DETAILS**
**BBUNDERSTAT11 9.2.002.**
In the least-squares line \( \hat{y} = 5 + 3x \), what is the marginal change in \( \hat{y} \) for each unit change in \( x \)?
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**Explanation:**
The question relates to understanding linear regression, specifically the interpretation of the slope in the least-squares regression equation. The equation given is \( \hat{y} = 5 + 3x \), where:
- \( \hat{y} \) is the predicted value of the dependent variable.
- \( 5 \) is the y-intercept, indicating the value of \( \hat{y} \) when \( x = 0 \).
- \( 3 \) is the slope of the line, representing the marginal change in \( \hat{y} \) for each unit change in \( x \). This means for every one unit increase in \( x \), \( \hat{y} \) increases by 3 units.
There are no graphs or diagrams in this image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5422827a-7860-4e7c-8a0f-f4498bf171e7%2F5c3f4e8f-d27f-4568-b784-2c2d4998180f%2Fzis5th_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 1: [-/1 Points]**
**DETAILS**
**BBUNDERSTAT11 9.2.002.**
In the least-squares line \( \hat{y} = 5 + 3x \), what is the marginal change in \( \hat{y} \) for each unit change in \( x \)?
[Submit Answer]
**Explanation:**
The question relates to understanding linear regression, specifically the interpretation of the slope in the least-squares regression equation. The equation given is \( \hat{y} = 5 + 3x \), where:
- \( \hat{y} \) is the predicted value of the dependent variable.
- \( 5 \) is the y-intercept, indicating the value of \( \hat{y} \) when \( x = 0 \).
- \( 3 \) is the slope of the line, representing the marginal change in \( \hat{y} \) for each unit change in \( x \). This means for every one unit increase in \( x \), \( \hat{y} \) increases by 3 units.
There are no graphs or diagrams in this image.
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