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Regression Models and Variable Descriptions The original model is shown below. y = 0.61 -0.051x1 -0.005x2 (0.017) (0.041) R² = 0.163 y = growth rate in real gross domestic product X₁ = real income per capita X2 = average tax rate, as a proportion of gross national product The numbers below the coefficients are the coefficient standard errors. After removing x₁ from the original model above, the resulting fitted model is shown below. y = 0.055 -0.078x2 (0.35) R² = 0.072

Regression Models and Variable Descriptions The original model is shown below. y = 0.61 -0.051x1 -0.005x2 (0.017) (0.041) R² = 0.163 y = growth rate in real gross domestic product X₁ = real income per capita X2 = average tax rate, as a proportion of gross national product The numbers below the coefficients are the coefficient standard errors. After removing x₁ from the original model above, the resulting fitted model is shown below. y = 0.055 -0.078x2 (0.35) R² = 0.072

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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Regression Models and Variable Descriptions The original model is shown below. y = 0.61 -0.051×1 -0.005x2 (0.017) (0.041) R² = = 0.163 y = growth rate in real gross domestic product X₁ = real income per capita X2 = average tax rate, as a proportion of gross national product The numbers below the coefficients are the coefficient standard errors. After removing x₁ from the original model above, the resulting fitted model is shown below. y = 0.055 -0.078x2 (0.35) R² = = 0.072
Transcribed Image Text:Regression Models and Variable Descriptions The original model is shown below. y = 0.61 -0.051×1 -0.005x2 (0.017) (0.041) R² = = 0.163 y = growth rate in real gross domestic product X₁ = real income per capita X2 = average tax rate, as a proportion of gross national product The numbers below the coefficients are the coefficient standard errors. After removing x₁ from the original model above, the resulting fitted model is shown below. y = 0.055 -0.078x2 (0.35) R² = = 0.072
Based on the data from 63 countries, a model was estimated by least squares. After the independent variable x₁ was dropped from the model, the regression of growth rate in real gross domestic product on x2 was estimated and the new fitted model was found. i Click the icon to see the regression models and variable descriptions. Comment on the change in the coefficient of x2 as x₁ is removed from the model. Choose the correct answer below. A. The change in the coefficient of x2 indicates neither a presence nor a lack of multicollinearity in the original model. Changes in the estimates of the coefficients could be the result of many factors and there is not enough information given to say that this change resulted from multicollinearity. B. The large change in the coefficient of x2 as x₁ is removed from the model is an indicator of the likely presence of multicollinearity in the original model. When there is multicollinearity in a model, the coefficients of the collinear variables often change drastically from their true values and can even change signs. C. The large change in the coefficient of x2 as x₁ is removed from the model is an indicator that there is no multicollinearity in the original model. Whenever an independent variable is removed from a regression equation, the coefficients of the remaining variables often change drastically.
Transcribed Image Text:Based on the data from 63 countries, a model was estimated by least squares. After the independent variable x₁ was dropped from the model, the regression of growth rate in real gross domestic product on x2 was estimated and the new fitted model was found. i Click the icon to see the regression models and variable descriptions. Comment on the change in the coefficient of x2 as x₁ is removed from the model. Choose the correct answer below. A. The change in the coefficient of x2 indicates neither a presence nor a lack of multicollinearity in the original model. Changes in the estimates of the coefficients could be the result of many factors and there is not enough information given to say that this change resulted from multicollinearity. B. The large change in the coefficient of x2 as x₁ is removed from the model is an indicator of the likely presence of multicollinearity in the original model. When there is multicollinearity in a model, the coefficients of the collinear variables often change drastically from their true values and can even change signs. C. The large change in the coefficient of x2 as x₁ is removed from the model is an indicator that there is no multicollinearity in the original model. Whenever an independent variable is removed from a regression equation, the coefficients of the remaining variables often change drastically.
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