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For this problem, use the multiple regression equation below to complete parts (a) and (b). Y₁ = 10 + 5X₁₁ +3X2i a. Interpret the meaning of the slopes. O A. If X₁ increases one unit, Y increases 5 units. If X₂ increases one unit, Y increases 3 units. O B. If X₂ is constant, when X₁ increases one unit, Y increases 5 units. If X₁ is constant, when X₂ increases one unit, Y increases 3 units. O C. If X₂ is constant, when X₁ increases one unit, Y increases 3 units. If X₁ is constant, when X₂ increases one unit, Y increases 5 units. O D. If X₁ increases one unit, Y increases 3 units. If X₂ increases one unit, Y increases 5 units. b. Interpret the meaning of the Y-intercept. O A. The Y-intercept 10 is the estimate of the mean value of Y if X₁ and X₂ are both 0. O B. The Y-intercept 10 is the estimate of the mean value of Y if X₁ is 0. The Vintoroont 5 in the netimoto of the moon value of Vif V is 0

For this problem, use the multiple regression equation below to complete parts (a) and (b). Y₁ = 10 + 5X₁₁ +3X2i a. Interpret the meaning of the slopes. O A. If X₁ increases one unit, Y increases 5 units. If X₂ increases one unit, Y increases 3 units. O B. If X₂ is constant, when X₁ increases one unit, Y increases 5 units. If X₁ is constant, when X₂ increases one unit, Y increases 3 units. O C. If X₂ is constant, when X₁ increases one unit, Y increases 3 units. If X₁ is constant, when X₂ increases one unit, Y increases 5 units. O D. If X₁ increases one unit, Y increases 3 units. If X₂ increases one unit, Y increases 5 units. b. Interpret the meaning of the Y-intercept. O A. The Y-intercept 10 is the estimate of the mean value of Y if X₁ and X₂ are both 0. O B. The Y-intercept 10 is the estimate of the mean value of Y if X₁ is 0. The Vintoroont 5 in the netimoto of the moon value of Vif V is 0

MATLAB: An Introduction with Applications
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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### Transcription for Educational Website **Question b: Interpret the Meaning of the Y-intercept** - **Option A:** "The Y-intercept 10 is the estimate of the mean value of Y if \( X_1 \) and \( X_2 \) are both 0." - **Option B:** "The Y-intercept 10 is the estimate of the mean value of Y if \( X_1 \) is 0." - **Option C:** "The Y-intercept 5 is the estimate of the mean value of Y if \( X_1 \) is 0." - **Option D:** "The Y-intercept 5 is the estimate of the mean value of Y if \( X_1 \) and \( X_2 \) are both 0." **Explanation:** In this question, students are asked to interpret the Y-intercept in a regression equation. The Y-intercept is where the fitted line crosses the Y-axis, representing the expected value of the dependent variable (Y) when all independent variables (in this case, \( X_1 \) and \( X_2 \)) are equal to zero. The correct interpretation depends on the values provided for the Y-intercept and the given conditions for \( X_1 \) and \( X_2 \).
Transcribed Image Text:### Transcription for Educational Website **Question b: Interpret the Meaning of the Y-intercept** - **Option A:** "The Y-intercept 10 is the estimate of the mean value of Y if \( X_1 \) and \( X_2 \) are both 0." - **Option B:** "The Y-intercept 10 is the estimate of the mean value of Y if \( X_1 \) is 0." - **Option C:** "The Y-intercept 5 is the estimate of the mean value of Y if \( X_1 \) is 0." - **Option D:** "The Y-intercept 5 is the estimate of the mean value of Y if \( X_1 \) and \( X_2 \) are both 0." **Explanation:** In this question, students are asked to interpret the Y-intercept in a regression equation. The Y-intercept is where the fitted line crosses the Y-axis, representing the expected value of the dependent variable (Y) when all independent variables (in this case, \( X_1 \) and \( X_2 \)) are equal to zero. The correct interpretation depends on the values provided for the Y-intercept and the given conditions for \( X_1 \) and \( X_2 \).
For this problem, use the multiple regression equation below to complete parts (a) and (b). \[ \hat{Y}_i = 10 + 5X_{1i} + 3X_{2i} \] **a. Interpret the meaning of the slopes.** - **A.** If \(X_1\) increases one unit, \(Y\) increases 5 units. If \(X_2\) increases one unit, \(Y\) increases 3 units. - **B.** If \(X_2\) is constant, when \(X_1\) increases one unit, \(Y\) increases 5 units. If \(X_1\) is constant, when \(X_2\) increases one unit, \(Y\) increases 3 units. - **C.** If \(X_2\) is constant, when \(X_1\) increases one unit, \(Y\) increases 3 units. If \(X_1\) is constant, when \(X_2\) increases one unit, \(Y\) increases 5 units. - **D.** If \(X_1\) increases one unit, \(Y\) increases 3 units. If \(X_2\) increases one unit, \(Y\) increases 5 units. **b. Interpret the meaning of the Y-intercept.** - **A.** The Y-intercept 10 is the estimate of the mean value of \(Y\) if \(X_1\) and \(X_2\) are both 0. - **B.** The Y-intercept 10 is the estimate of the mean value of \(Y\) if \(X_1\) is 0. - **C.** The Y-intercept 5 is the estimate of the mean value of \(Y\) if \(X_2\) is 0.
Transcribed Image Text:For this problem, use the multiple regression equation below to complete parts (a) and (b). \[ \hat{Y}_i = 10 + 5X_{1i} + 3X_{2i} \] **a. Interpret the meaning of the slopes.** - **A.** If \(X_1\) increases one unit, \(Y\) increases 5 units. If \(X_2\) increases one unit, \(Y\) increases 3 units. - **B.** If \(X_2\) is constant, when \(X_1\) increases one unit, \(Y\) increases 5 units. If \(X_1\) is constant, when \(X_2\) increases one unit, \(Y\) increases 3 units. - **C.** If \(X_2\) is constant, when \(X_1\) increases one unit, \(Y\) increases 3 units. If \(X_1\) is constant, when \(X_2\) increases one unit, \(Y\) increases 5 units. - **D.** If \(X_1\) increases one unit, \(Y\) increases 3 units. If \(X_2\) increases one unit, \(Y\) increases 5 units. **b. Interpret the meaning of the Y-intercept.** - **A.** The Y-intercept 10 is the estimate of the mean value of \(Y\) if \(X_1\) and \(X_2\) are both 0. - **B.** The Y-intercept 10 is the estimate of the mean value of \(Y\) if \(X_1\) is 0. - **C.** The Y-intercept 5 is the estimate of the mean value of \(Y\) if \(X_2\) is 0.
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Given regression line 

Yi^=10+5X1+3X2 

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