MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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.
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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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