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2. In an experiment involving one dependent variable y and four explanatory variables 1₁, 12, 13 and 14, all possible regressions are fit to the data set consisting of n = 13 cases. A constant term is routinely included in all models. The results are summarizes as follows: Regressors in Model Residual Sum of Squares None 4073.6 I1 1898.5 I2 1359.5 2909.1 I3 IA I1, I2 X1, X3 I1, I4 I2, I3 I2, Is 1325.8 86.9 1840.6 112.1 623.1 1303.3

2. In an experiment involving one dependent variable y and four explanatory variables 1₁, 12, 13 and 14, all possible regressions are fit to the data set consisting of n = 13 cases. A constant term is routinely included in all models. The results are summarizes as follows: Regressors in Model Residual Sum of Squares None 4073.6 I1 1898.5 I2 1359.5 2909.1 I3 IA I1, I2 X1, X3 I1, I4 I2, I3 I2, Is 1325.8 86.9 1840.6 112.1 623.1 1303.3

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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2. In an experiment involving one dependent variable y and four explanatory variables ₁, 2, 3 and 4, all possible regressions are fit to the data set consisting of n = 13 cases. A constant term is routinely included in all models. The results are summarizes as follows: Regressors in Model Residual Sum of Squares None 4073.6 1898.5 1359.5 2909.1 1325.8 86.9 1840.6 112.1 623.1 1303.3 263.6 72.2 72.0 76.2 110.7 71.8 x1 X2 I3 XA X1, X2 X1, X3 I1, I4 I2, I3 X2, X4 x3, x4 X1, X2, I3 X1, X2, X4 X1, X3, 4 X2, X3, x4 X1, X2, X3, X₁ (a) What model will result from automatic forward selection with a significance level of 0.1 (a to enter)? Show all your work and how you obtained this model. (b) What model will result from automatic backward selection with a significance level of 0.1 (a to drop)? Show all your work and how you obtained this model. (c) Compare the value of the C, statistic for the model you found in part (b) to the model that includes all four x's.
Transcribed Image Text:2. In an experiment involving one dependent variable y and four explanatory variables ₁, 2, 3 and 4, all possible regressions are fit to the data set consisting of n = 13 cases. A constant term is routinely included in all models. The results are summarizes as follows: Regressors in Model Residual Sum of Squares None 4073.6 1898.5 1359.5 2909.1 1325.8 86.9 1840.6 112.1 623.1 1303.3 263.6 72.2 72.0 76.2 110.7 71.8 x1 X2 I3 XA X1, X2 X1, X3 I1, I4 I2, I3 X2, X4 x3, x4 X1, X2, I3 X1, X2, X4 X1, X3, 4 X2, X3, x4 X1, X2, X3, X₁ (a) What model will result from automatic forward selection with a significance level of 0.1 (a to enter)? Show all your work and how you obtained this model. (b) What model will result from automatic backward selection with a significance level of 0.1 (a to drop)? Show all your work and how you obtained this model. (c) Compare the value of the C, statistic for the model you found in part (b) to the model that includes all four x's.
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