Use the following linear regression equation to answer the questions. X- 1.2+ 3.6x - 7.6x + 2.5x4 (a) Which variable is the response variable? O 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 2 coefficient Xy coefficient
Use the following linear regression equation to answer the questions. X- 1.2+ 3.6x - 7.6x + 2.5x4 (a) Which variable is the response variable? O 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 2 coefficient Xy coefficient
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![**Linear Regression Analysis Exercise**
Use the following linear regression equation to answer the questions:
\[ x_1 = 1.2 + 3.6x_2 - 7.6x_3 + 2.5x_4 \]
(a) **Identify Variables**
1. Which variable is the response variable?
- ○ \( x_1 \)
- ○ \( x_4 \)
- ○ \( x_2 \)
- ○ \( x_3 \)
2. Which variables are the explanatory variables? (Select all that apply.)
- □ \( x_1 \)
- □ \( x_4 \)
- □ \( x_2 \)
- □ \( x_3 \)
(b) **Constant and Coefficients**
1. Which number is the constant term? List the coefficients with their corresponding explanatory variables.
- constant: [ ]
- \( x_2 \) coefficient: [ ]
- \( x_3 \) coefficient: [ ]
- \( x_4 \) coefficient: [ ]
(c) **Prediction Equation**
1. If \( x_2 = 8 \), \( x_3 = 6 \), and \( x_4 = 4 \), what is the predicted value for \( x_1 \)? (Use 1 decimal place.)
- [ ]
(d) **Understanding Coefficients**
1. Explain how each coefficient can be thought of as a "slope" under certain conditions.
- ○ If we look at all coefficients together, each one can be thought of as a "slope."
- ○ If we hold all explanatory variables as fixed constants, the intercept can be thought of as a "slope."
- ○ If we look at all coefficients together, the sum of them can be thought of as the overall "slope" of the regression line.
- ○ If we hold all other explanatory variables as fixed constants, then we can look at one coefficient as a "slope."
(e) **Changes in Variables**
1. 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 \( x_1 \)?
- [ ]
2. Suppose \( x_2 \) increased by 2 units. What would be the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5422827a-7860-4e7c-8a0f-f4498bf171e7%2Ffdf65817-7683-42a9-8a6a-2142cd895671%2F9lqp0c_processed.png&w=3840&q=75)
Transcribed Image Text:**Linear Regression Analysis Exercise**
Use the following linear regression equation to answer the questions:
\[ x_1 = 1.2 + 3.6x_2 - 7.6x_3 + 2.5x_4 \]
(a) **Identify Variables**
1. Which variable is the response variable?
- ○ \( x_1 \)
- ○ \( x_4 \)
- ○ \( x_2 \)
- ○ \( x_3 \)
2. Which variables are the explanatory variables? (Select all that apply.)
- □ \( x_1 \)
- □ \( x_4 \)
- □ \( x_2 \)
- □ \( x_3 \)
(b) **Constant and Coefficients**
1. Which number is the constant term? List the coefficients with their corresponding explanatory variables.
- constant: [ ]
- \( x_2 \) coefficient: [ ]
- \( x_3 \) coefficient: [ ]
- \( x_4 \) coefficient: [ ]
(c) **Prediction Equation**
1. If \( x_2 = 8 \), \( x_3 = 6 \), and \( x_4 = 4 \), what is the predicted value for \( x_1 \)? (Use 1 decimal place.)
- [ ]
(d) **Understanding Coefficients**
1. Explain how each coefficient can be thought of as a "slope" under certain conditions.
- ○ If we look at all coefficients together, each one can be thought of as a "slope."
- ○ If we hold all explanatory variables as fixed constants, the intercept can be thought of as a "slope."
- ○ If we look at all coefficients together, the sum of them can be thought of as the overall "slope" of the regression line.
- ○ If we hold all other explanatory variables as fixed constants, then we can look at one coefficient as a "slope."
(e) **Changes in Variables**
1. 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 \( x_1 \)?
- [ ]
2. Suppose \( x_2 \) increased by 2 units. What would be the
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Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case you require the unanswered parts also, kindly re-post that parts separately.
Given information:
a)
The response variable is x1.
Correct option: x1.
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