Consider the following regression model: y' = 0.396 + 0.106x Company Cars (in ten thousands) Revenue (in billions) A $7.0 3.9 aooou - B C D X 63.0 29.0 20.8 19.1 13.4 8.5 1) Find the explained, unexplained and total regression Sest = 2.1 2.8 1.4 1.5 y 2 2 y (y - y) (y y) (y - y) 2) Compute the standard error of the estimate. Σ( y − y')² n-2
Consider the following regression model: y' = 0.396 + 0.106x Company Cars (in ten thousands) Revenue (in billions) A $7.0 3.9 aooou - B C D X 63.0 29.0 20.8 19.1 13.4 8.5 1) Find the explained, unexplained and total regression Sest = 2.1 2.8 1.4 1.5 y 2 2 y (y - y) (y y) (y - y) 2) Compute the standard error of the estimate. Σ( y − y')² n-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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**Understanding Regression Analysis**
**Consider the following regression model:**
\[ y' = 0.396 + 0.106x \]
This model is used to predict a relationship between two variables: the independent variable \( x \) and the dependent variable \( y \).
**Data for Analysis:**
A table shows data for six companies, where \( x \) represents the number of cars (in ten thousands), and \( y \) represents the corresponding revenue (in billions).
| Company | Cars (in ten thousands) | Revenue (in billions) |
|---------|--------------------------|-----------------------|
| A | 63.0 | 7.0 |
| B | 29.0 | 3.9 |
| C | 20.8 | 2.1 |
| D | 19.1 | 2.8 |
| E | 13.4 | 1.4 |
| F | 8.5 | 1.5 |
---
**Tasks:**
1. Find the explained, unexplained, and total regression:
**Table Explanation:**
To complete the analysis, fill out the following table, where:
- \( x \) is the independent variable (cars),
- \( y \) is the observed dependent variable (revenue),
- \( y' \) is the predicted dependent variable from the regression equation,
- \( \overline{y} \) is the mean of the observed dependent variable,
- \( (y - \overline{y})^2 \) is the total sum of squares (measure of total variance),
- \( (y' - \overline{y})^2 \) is the regression sum of squares (measure of variance explained by the model),
- \( (y - y')^2 \) is the residual sum of squares (measure of variance not explained by the model).
| x | y | y' | (y - \(\overline{y}\))^2 | (y' - \(\overline{y}\))^2 | (y - y')^2 |
|------|-----|-------|-------------------------|--------------------------|--------------|
| | | | | | |
| | | | | | |
| | |](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8952a85a-85f1-4c32-8b45-c088a1def42e%2F67e42551-c0f9-44e9-be37-e5b1c752342e%2Fx0ypsr_processed.png&w=3840&q=75)
Transcribed Image Text:---
**Understanding Regression Analysis**
**Consider the following regression model:**
\[ y' = 0.396 + 0.106x \]
This model is used to predict a relationship between two variables: the independent variable \( x \) and the dependent variable \( y \).
**Data for Analysis:**
A table shows data for six companies, where \( x \) represents the number of cars (in ten thousands), and \( y \) represents the corresponding revenue (in billions).
| Company | Cars (in ten thousands) | Revenue (in billions) |
|---------|--------------------------|-----------------------|
| A | 63.0 | 7.0 |
| B | 29.0 | 3.9 |
| C | 20.8 | 2.1 |
| D | 19.1 | 2.8 |
| E | 13.4 | 1.4 |
| F | 8.5 | 1.5 |
---
**Tasks:**
1. Find the explained, unexplained, and total regression:
**Table Explanation:**
To complete the analysis, fill out the following table, where:
- \( x \) is the independent variable (cars),
- \( y \) is the observed dependent variable (revenue),
- \( y' \) is the predicted dependent variable from the regression equation,
- \( \overline{y} \) is the mean of the observed dependent variable,
- \( (y - \overline{y})^2 \) is the total sum of squares (measure of total variance),
- \( (y' - \overline{y})^2 \) is the regression sum of squares (measure of variance explained by the model),
- \( (y - y')^2 \) is the residual sum of squares (measure of variance not explained by the model).
| x | y | y' | (y - \(\overline{y}\))^2 | (y' - \(\overline{y}\))^2 | (y - y')^2 |
|------|-----|-------|-------------------------|--------------------------|--------------|
| | | | | | |
| | | | | | |
| | |
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