**Regression Analysis: Understanding Coefficients**The following estimated regression equation was developed for a model involving two independent variables:\[\hat{y} = 40.7 + 8.63x_1 + 2.71x_2\]After $x_2$ was dropped from the model, the least squares method was used to obtain an estimated regression equation involving only $x_1$ as an independent variable:\[\hat{y} = 42.0 + 9.01x_1\]**(a) Interpretation of the Coefficient of $x_1$ in Both Models**In the two independent variable model, the coefficient of $x_1$ represents the expected change in $y$ corresponding to a change in $x_1$ when $x_2$ is held constant. In the single independent variable model, the coefficient of $x_1$ represents the expected change in $y$ corresponding to a change in $x_1$.**(b) Impact of Multicollinearity on the Coefficient of $x_1$**Could multicollinearity explain why the coefficient of $x_1$ differs in the two models? If so, how?When $x_1$ and $x_2$ are correlated, one would expect a change in $x_1$ to be linked with a change in $x_2$.

Given: The two independent variables are determined as below, In which the X2 gets dropped based on…

The following estimated regression equation was developed for a model involving two independent variables. ŷ = 40.7 + 8.63x, + 2.71x, After x, was dropped from the model, the least squares method was used to obtain an estimated regression equation involving only x, as an independent variable. ý = 42.0 + 9.01x, (a) Give an interpretation of the coefficient of x, in both models. In the two independent variable case, the coefficient of x, represents the expected change in y corresponding to a -Select--- v unit ---Select--- v in x, when x, is held constant. In the single independent variable case, the coefficient of x, represents the expected change in y corresponding to a --Select--- v unit increase in x,. (b) Could multicollinearity explain why the coefficient of x, differs in the two models? If so, how? |---Select--- v. If x, and x, are correlated, one would expect a change in x, to be --Select--- v a change in X,.

The following estimated regression equation was developed for a model involving two independent variables. ŷ = 40.7 + 8.63x, + 2.71x, After x, was dropped from the model, the least squares method was used to obtain an estimated regression equation involving only x, as an independent variable. ý = 42.0 + 9.01x, (a) Give an interpretation of the coefficient of x, in both models. In the two independent variable case, the coefficient of x, represents the expected change in y corresponding to a -Select--- v unit ---Select--- v in x, when x, is held constant. In the single independent variable case, the coefficient of x, represents the expected change in y corresponding to a --Select--- v unit increase in x,. (b) Could multicollinearity explain why the coefficient of x, differs in the two models? If so, how? |---Select--- v. If x, and x, are correlated, one would expect a change in x, to be --Select--- v a change in X,.

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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