Use the following linear regression equation to answer the questions. X - 1.2 + 3.6x - 7.6xy + 2.5x4 (a) Which variable is the response variable? O KA O x2 Oxy Which variables are the explanatory variables? (Select all that apply.) (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant 12 X2 coefficient 3.6 Xy coefficient 7.6 X4 coefficient 2.5 (c) If x - 8, x - 6, and x4 - 4, what is the predicted value for x? (Use 1 decimal place.) 5.6 (d) Explain how each coefficient can be thought of as a "slope" under certain conditions. O If we look at all coefficients together, each one can be thought of as a "slope."
Use the following linear regression equation to answer the questions. X - 1.2 + 3.6x - 7.6xy + 2.5x4 (a) Which variable is the response variable? O KA O x2 Oxy Which variables are the explanatory variables? (Select all that apply.) (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant 12 X2 coefficient 3.6 Xy coefficient 7.6 X4 coefficient 2.5 (c) If x - 8, x - 6, and x4 - 4, what is the predicted value for x? (Use 1 decimal place.) 5.6 (d) Explain how each coefficient can be thought of as a "slope" under certain conditions. O If we look at all coefficients together, each one can be thought of as a "slope."
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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![**Linear Regression Equation Analysis**
Use the following linear regression equation to answer the questions:
\[
x_1 = 1.2 + 3.6x_2 - 7.6x_3 + 2.5x_4
\]
(a) **Which variable is the response variable?**
- \( x_1 \) [Selected]
- \( x_4 \)
- \( x_2 \)
- \( x_3 \)
**Explanatory Variables:**
- \( x_2 \) [Selected]
- \( x_3 \) [Selected]
- \( x_4 \) [Selected]
**Constant Term:**
(b) Which number is the constant term?
List the coefficients with their corresponding explanatory variables.
- **Constant:** 1.2 [Selected]
- \( x_2 \) coefficient: 3.6 [Selected]
- \( x_3 \) coefficient: 7.6 [Selected]
- \( x_4 \) coefficient: 2.5 [Selected]
(c) If \( x_2 = 8 \), \( x_3 = 6 \), and \( x_4 = 4 \), what is the predicted value for \( x_1 \)? (Use 1 decimal place.)
- **Answer:** 5.8
(d) **Explanation of Coefficients as Slopes:**
- **Condition:** If we hold all other explanatory variables as fixed constants, then we can look at one coefficient as a "slope." [Correct]
**Scenarios:**
- Suppose \( x_3 \) and \( x_4 \) were held at fixed but arbitrary values, and \( x_2 \) increased by 1 unit. What would be the corresponding change in \( x_1 \)?
- **Answer:** 3.6
- Suppose \( x_2 \) increased by 2 units. What would be the expected change in \( x_1 \)?
- **Answer:** 7.2
- Suppose \( x_2 \) decreased by 4 units. What would be the expected change in \( x_1 \)?
- **Answer:** 14.4
**Graph/Diagram Explanation:**
There is a boxed section which highlights the correct explanation of how coefficients can be thought of as slopes under certain conditions. The correct statement is underlined.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5422827a-7860-4e7c-8a0f-f4498bf171e7%2F19c09093-00eb-495a-90cd-710dbf2bb719%2Ft1ih2ih_processed.png&w=3840&q=75)
Transcribed Image Text:**Linear Regression Equation Analysis**
Use the following linear regression equation to answer the questions:
\[
x_1 = 1.2 + 3.6x_2 - 7.6x_3 + 2.5x_4
\]
(a) **Which variable is the response variable?**
- \( x_1 \) [Selected]
- \( x_4 \)
- \( x_2 \)
- \( x_3 \)
**Explanatory Variables:**
- \( x_2 \) [Selected]
- \( x_3 \) [Selected]
- \( x_4 \) [Selected]
**Constant Term:**
(b) Which number is the constant term?
List the coefficients with their corresponding explanatory variables.
- **Constant:** 1.2 [Selected]
- \( x_2 \) coefficient: 3.6 [Selected]
- \( x_3 \) coefficient: 7.6 [Selected]
- \( x_4 \) coefficient: 2.5 [Selected]
(c) If \( x_2 = 8 \), \( x_3 = 6 \), and \( x_4 = 4 \), what is the predicted value for \( x_1 \)? (Use 1 decimal place.)
- **Answer:** 5.8
(d) **Explanation of Coefficients as Slopes:**
- **Condition:** If we hold all other explanatory variables as fixed constants, then we can look at one coefficient as a "slope." [Correct]
**Scenarios:**
- Suppose \( x_3 \) and \( x_4 \) were held at fixed but arbitrary values, and \( x_2 \) increased by 1 unit. What would be the corresponding change in \( x_1 \)?
- **Answer:** 3.6
- Suppose \( x_2 \) increased by 2 units. What would be the expected change in \( x_1 \)?
- **Answer:** 7.2
- Suppose \( x_2 \) decreased by 4 units. What would be the expected change in \( x_1 \)?
- **Answer:** 14.4
**Graph/Diagram Explanation:**
There is a boxed section which highlights the correct explanation of how coefficients can be thought of as slopes under certain conditions. The correct statement is underlined.
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