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The MODEL Procedure Nonlinear OLS Summary of Residual Errors Equation DF Model DF Error SSE MSE Root MSE R-Square Adj R-Sq 475 3.3486 0.00705 0.0840 0.2432 0.2368 NKErf 5 Nonlinear OLS Parameter Estimates Approx Parameter Estimate Approx Std Err t Value Pr> |t| Бо 0.008942 b1 1.055671 b2 -0.4228 0.00395 2.26 0.0240 0.0911 11.59 <.0001 0.1324 -3.19 0.0015 b3 -0.07573 b4 -0.05064 Number of Observations Used 0.1284 -0.59 0.5555 0.0905 -0.56 0.5762 Statistics for System 480 Objective 0.006976 Missing 3 Objective*N 3.3486 Equation Test Heteroscedasticity Test Statistic DF Pr> ChiSq Variables NKErf White's Test Breusch-Pagan 89.16 14 <.0001 Cross of all vars 18.82 4 0.0009 1, mktrf, smb, hml, umd Page Break The REG Procedure Model: MODEL1 Dependent Variable: NKErf Number of Observations Read Number of Observations Used Number of Observations with Missing Values Analysis of Variance Sum of Mean 483 480 3 DF Squares Square F Value Pr> F 4 1.07591 0.26898 38.15 <.0001 Source Model Error 475 Corrected Total 479 3.34860 0.00705 4.42451 Root MSE 0.08396 R-Square 0.2432 Dependent Mean 0.01607 Adj R-Sq 0.2368 Coeff Var 522.56550 Parameter Estimates Parameter Standard Heteroscedasticity Consistent Standard Variable Label DF Estimate Error t Value Pr> |t| Error t Value Pr> |t| mktrf mktrf smb smb hml hml Intercept Intercept 1 0.00894 1.05567 -0.42280 1 -0.07573 1 1 0.00395 2.26 0.0240 0.09107 11.59 <.0001 0.13243 -3.19 0.0015 0.00373 2.40 0.0169 0.09485 11.13 <.0001 0.22050 -1.92 0.0558 umd umd 1 -0.05064 0.12835 -0.59 0.5555 0.09054 -0.56 0.5762 0.14237 -0.53 0.5951 0.10444 -0.48 0.6280 Page Break The REG Procedure Model: MODEL1 Dependent Variable: NKErf Test of First and Second Moment Specification DF Chi-Square Pr> ChiSq 14 29.86 0.0080 The MODEL Procedure Nonlinear OLS Summary of Residual Errors Equation DF Model DF Error SSE MSE Root MSE R-Square Adj R-Sq NKErf 476 3.3508 0.00704 0.0839 0.2427 0.2379 4 Nonlinear OLS Parameter Estimates Approx Parameter Estimate Approx Std Err t Value Pr> [t b0 0.008575 b1 1.069264 0.00389 2.20 0.0280 0.0877 12.19 <.0001 b2 -0.42202 b3 -0.05896 Number of Observations Used Missing Heteroscedasticity Test Equation Test 0.1323 -3.19 0.0015 0.1247 -0.47 0.6366 Statistics for System 480 Objective 0.006981 3 Objective*N 3.3508 Statistic DF Pr> ChiSq Variables NKErf White's Test Breusch-Pagan 82.62 9 <.0001 Cross of all vars 0.6017 1, mktrf, smb, hml 1.86 3 Page Break The REG Procedure Model: MODEL1 Dependent Variable: NKErf Number of Observations Read Number of Observations Used 483 480 3 Source Model Number of Observations with Missing Values Analysis of Variance Sum of Mean DF Squares Square F Value Pr> F 3 1.07370 0.35790 50.84 <.0001 Error 476 Corrected Total 479 3.35081 0.00704 4.42451 Root MSE 0.08390 R-Square 0.2427 Dependent Mean 0.01607 Adj R-Sq 0.2379 Coeff Var 522.18817 Parameter Estimates Heteroscedasticity Consistent Variable Label DF Intercept Intercept 1 mktrf mktrf 1 smb smb 1 Parameter Standard Estimate 0.00858 0.00389 2.20 0.0280 1.06926 0.08771 12.19 <.0001 -0.42202 0.13233 -3.19 0.0015 Standard Error t Value Pr> |t| Error t Value Pr> \t 0.00390 2.20 0.0282 0.09337 11.45 <.0001 0.22309 -1.89 0.0591 hml hml 1 -0.05896 0.12471 -0.47 0.6366 0.13901 -0.42 0.6717 Page Break The REG Procedure Model: MODEL1 Dependent Variable: NKErf Test of First and Second Moment Specification DF Chi-Square Pr> ChiSq 9 19.82 0.0191

The MODEL Procedure Nonlinear OLS Summary of Residual Errors Equation DF Model DF Error SSE MSE Root MSE R-Square Adj R-Sq 475 3.3486 0.00705 0.0840 0.2432 0.2368 NKErf 5 Nonlinear OLS Parameter Estimates Approx Parameter Estimate Approx Std Err t Value Pr> |t| Бо 0.008942 b1 1.055671 b2 -0.4228 0.00395 2.26 0.0240 0.0911 11.59 <.0001 0.1324 -3.19 0.0015 b3 -0.07573 b4 -0.05064 Number of Observations Used 0.1284 -0.59 0.5555 0.0905 -0.56 0.5762 Statistics for System 480 Objective 0.006976 Missing 3 Objective*N 3.3486 Equation Test Heteroscedasticity Test Statistic DF Pr> ChiSq Variables NKErf White's Test Breusch-Pagan 89.16 14 <.0001 Cross of all vars 18.82 4 0.0009 1, mktrf, smb, hml, umd Page Break The REG Procedure Model: MODEL1 Dependent Variable: NKErf Number of Observations Read Number of Observations Used Number of Observations with Missing Values Analysis of Variance Sum of Mean 483 480 3 DF Squares Square F Value Pr> F 4 1.07591 0.26898 38.15 <.0001 Source Model Error 475 Corrected Total 479 3.34860 0.00705 4.42451 Root MSE 0.08396 R-Square 0.2432 Dependent Mean 0.01607 Adj R-Sq 0.2368 Coeff Var 522.56550 Parameter Estimates Parameter Standard Heteroscedasticity Consistent Standard Variable Label DF Estimate Error t Value Pr> |t| Error t Value Pr> |t| mktrf mktrf smb smb hml hml Intercept Intercept 1 0.00894 1.05567 -0.42280 1 -0.07573 1 1 0.00395 2.26 0.0240 0.09107 11.59 <.0001 0.13243 -3.19 0.0015 0.00373 2.40 0.0169 0.09485 11.13 <.0001 0.22050 -1.92 0.0558 umd umd 1 -0.05064 0.12835 -0.59 0.5555 0.09054 -0.56 0.5762 0.14237 -0.53 0.5951 0.10444 -0.48 0.6280 Page Break The REG Procedure Model: MODEL1 Dependent Variable: NKErf Test of First and Second Moment Specification DF Chi-Square Pr> ChiSq 14 29.86 0.0080 The MODEL Procedure Nonlinear OLS Summary of Residual Errors Equation DF Model DF Error SSE MSE Root MSE R-Square Adj R-Sq NKErf 476 3.3508 0.00704 0.0839 0.2427 0.2379 4 Nonlinear OLS Parameter Estimates Approx Parameter Estimate Approx Std Err t Value Pr> [t b0 0.008575 b1 1.069264 0.00389 2.20 0.0280 0.0877 12.19 <.0001 b2 -0.42202 b3 -0.05896 Number of Observations Used Missing Heteroscedasticity Test Equation Test 0.1323 -3.19 0.0015 0.1247 -0.47 0.6366 Statistics for System 480 Objective 0.006981 3 Objective*N 3.3508 Statistic DF Pr> ChiSq Variables NKErf White's Test Breusch-Pagan 82.62 9 <.0001 Cross of all vars 0.6017 1, mktrf, smb, hml 1.86 3 Page Break The REG Procedure Model: MODEL1 Dependent Variable: NKErf Number of Observations Read Number of Observations Used 483 480 3 Source Model Number of Observations with Missing Values Analysis of Variance Sum of Mean DF Squares Square F Value Pr> F 3 1.07370 0.35790 50.84 <.0001 Error 476 Corrected Total 479 3.35081 0.00704 4.42451 Root MSE 0.08390 R-Square 0.2427 Dependent Mean 0.01607 Adj R-Sq 0.2379 Coeff Var 522.18817 Parameter Estimates Heteroscedasticity Consistent Variable Label DF Intercept Intercept 1 mktrf mktrf 1 smb smb 1 Parameter Standard Estimate 0.00858 0.00389 2.20 0.0280 1.06926 0.08771 12.19 <.0001 -0.42202 0.13233 -3.19 0.0015 Standard Error t Value Pr> |t| Error t Value Pr> \t 0.00390 2.20 0.0282 0.09337 11.45 <.0001 0.22309 -1.89 0.0591 hml hml 1 -0.05896 0.12471 -0.47 0.6366 0.13901 -0.42 0.6717 Page Break The REG Procedure Model: MODEL1 Dependent Variable: NKErf Test of First and Second Moment Specification DF Chi-Square Pr> ChiSq 9 19.82 0.0191

Essentials of Business Analytics (MindTap Course List)
Essentials of Business Analytics (MindTap Course List)
2nd Edition
ISBN:9781305627734
Author:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson
Publisher:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson
Chapter8: Time Series Analysis And_forecasting
Section: Chapter Questions
Problem 18P: Consider the following time series: Construct a time series plot. What type of pattern exists in...
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  1. Comment on the SAS regression output including a-e.
  2. Compare and comment on the differences between the two regressions (3- vs. 4-factor model using either OLS or HC results depending upon the White test result)
  3. Make conclusions regarding choosing 3- vs. 4-factor model when predicting future stock returns, and explain why.
The MODEL Procedure Nonlinear OLS Summary of Residual Errors Equation DF Model DF Error SSE MSE Root MSE R-Square Adj R-Sq 475 3.3486 0.00705 0.0840 0.2432 0.2368 NKErf 5 Nonlinear OLS Parameter Estimates Approx Parameter Estimate Approx Std Err t Value Pr> |t| Бо 0.008942 b1 1.055671 b2 -0.4228 0.00395 2.26 0.0240 0.0911 11.59 <.0001 0.1324 -3.19 0.0015 b3 -0.07573 b4 -0.05064 Number of Observations Used 0.1284 -0.59 0.5555 0.0905 -0.56 0.5762 Statistics for System 480 Objective 0.006976 Missing 3 Objective*N 3.3486 Equation Test Heteroscedasticity Test Statistic DF Pr> ChiSq Variables NKErf White's Test Breusch-Pagan 89.16 14 <.0001 Cross of all vars 18.82 4 0.0009 1, mktrf, smb, hml, umd Page Break The REG Procedure Model: MODEL1 Dependent Variable: NKErf Number of Observations Read Number of Observations Used Number of Observations with Missing Values Analysis of Variance Sum of Mean 483 480 3 DF Squares Square F Value Pr> F 4 1.07591 0.26898 38.15 <.0001 Source Model Error 475 Corrected Total 479 3.34860 0.00705 4.42451 Root MSE 0.08396 R-Square 0.2432 Dependent Mean 0.01607 Adj R-Sq 0.2368 Coeff Var 522.56550 Parameter Estimates Parameter Standard Heteroscedasticity Consistent Standard Variable Label DF Estimate Error t Value Pr> |t| Error t Value Pr> |t| mktrf mktrf smb smb hml hml Intercept Intercept 1 0.00894 1.05567 -0.42280 1 -0.07573 1 1 0.00395 2.26 0.0240 0.09107 11.59 <.0001 0.13243 -3.19 0.0015 0.00373 2.40 0.0169 0.09485 11.13 <.0001 0.22050 -1.92 0.0558 umd umd 1 -0.05064 0.12835 -0.59 0.5555 0.09054 -0.56 0.5762 0.14237 -0.53 0.5951 0.10444 -0.48 0.6280 Page Break The REG Procedure Model: MODEL1 Dependent Variable: NKErf Test of First and Second Moment Specification DF Chi-Square Pr> ChiSq 14 29.86 0.0080
Transcribed Image Text:The MODEL Procedure Nonlinear OLS Summary of Residual Errors Equation DF Model DF Error SSE MSE Root MSE R-Square Adj R-Sq 475 3.3486 0.00705 0.0840 0.2432 0.2368 NKErf 5 Nonlinear OLS Parameter Estimates Approx Parameter Estimate Approx Std Err t Value Pr> |t| Бо 0.008942 b1 1.055671 b2 -0.4228 0.00395 2.26 0.0240 0.0911 11.59 <.0001 0.1324 -3.19 0.0015 b3 -0.07573 b4 -0.05064 Number of Observations Used 0.1284 -0.59 0.5555 0.0905 -0.56 0.5762 Statistics for System 480 Objective 0.006976 Missing 3 Objective*N 3.3486 Equation Test Heteroscedasticity Test Statistic DF Pr> ChiSq Variables NKErf White's Test Breusch-Pagan 89.16 14 <.0001 Cross of all vars 18.82 4 0.0009 1, mktrf, smb, hml, umd Page Break The REG Procedure Model: MODEL1 Dependent Variable: NKErf Number of Observations Read Number of Observations Used Number of Observations with Missing Values Analysis of Variance Sum of Mean 483 480 3 DF Squares Square F Value Pr> F 4 1.07591 0.26898 38.15 <.0001 Source Model Error 475 Corrected Total 479 3.34860 0.00705 4.42451 Root MSE 0.08396 R-Square 0.2432 Dependent Mean 0.01607 Adj R-Sq 0.2368 Coeff Var 522.56550 Parameter Estimates Parameter Standard Heteroscedasticity Consistent Standard Variable Label DF Estimate Error t Value Pr> |t| Error t Value Pr> |t| mktrf mktrf smb smb hml hml Intercept Intercept 1 0.00894 1.05567 -0.42280 1 -0.07573 1 1 0.00395 2.26 0.0240 0.09107 11.59 <.0001 0.13243 -3.19 0.0015 0.00373 2.40 0.0169 0.09485 11.13 <.0001 0.22050 -1.92 0.0558 umd umd 1 -0.05064 0.12835 -0.59 0.5555 0.09054 -0.56 0.5762 0.14237 -0.53 0.5951 0.10444 -0.48 0.6280 Page Break The REG Procedure Model: MODEL1 Dependent Variable: NKErf Test of First and Second Moment Specification DF Chi-Square Pr> ChiSq 14 29.86 0.0080
The MODEL Procedure Nonlinear OLS Summary of Residual Errors Equation DF Model DF Error SSE MSE Root MSE R-Square Adj R-Sq NKErf 476 3.3508 0.00704 0.0839 0.2427 0.2379 4 Nonlinear OLS Parameter Estimates Approx Parameter Estimate Approx Std Err t Value Pr> [t b0 0.008575 b1 1.069264 0.00389 2.20 0.0280 0.0877 12.19 <.0001 b2 -0.42202 b3 -0.05896 Number of Observations Used Missing Heteroscedasticity Test Equation Test 0.1323 -3.19 0.0015 0.1247 -0.47 0.6366 Statistics for System 480 Objective 0.006981 3 Objective*N 3.3508 Statistic DF Pr> ChiSq Variables NKErf White's Test Breusch-Pagan 82.62 9 <.0001 Cross of all vars 0.6017 1, mktrf, smb, hml 1.86 3 Page Break The REG Procedure Model: MODEL1 Dependent Variable: NKErf Number of Observations Read Number of Observations Used 483 480 3 Source Model Number of Observations with Missing Values Analysis of Variance Sum of Mean DF Squares Square F Value Pr> F 3 1.07370 0.35790 50.84 <.0001 Error 476 Corrected Total 479 3.35081 0.00704 4.42451 Root MSE 0.08390 R-Square 0.2427 Dependent Mean 0.01607 Adj R-Sq 0.2379 Coeff Var 522.18817 Parameter Estimates Heteroscedasticity Consistent Variable Label DF Intercept Intercept 1 mktrf mktrf 1 smb smb 1 Parameter Standard Estimate 0.00858 0.00389 2.20 0.0280 1.06926 0.08771 12.19 <.0001 -0.42202 0.13233 -3.19 0.0015 Standard Error t Value Pr> |t| Error t Value Pr> \t 0.00390 2.20 0.0282 0.09337 11.45 <.0001 0.22309 -1.89 0.0591 hml hml 1 -0.05896 0.12471 -0.47 0.6366 0.13901 -0.42 0.6717 Page Break The REG Procedure Model: MODEL1 Dependent Variable: NKErf Test of First and Second Moment Specification DF Chi-Square Pr> ChiSq 9 19.82 0.0191
Transcribed Image Text:The MODEL Procedure Nonlinear OLS Summary of Residual Errors Equation DF Model DF Error SSE MSE Root MSE R-Square Adj R-Sq NKErf 476 3.3508 0.00704 0.0839 0.2427 0.2379 4 Nonlinear OLS Parameter Estimates Approx Parameter Estimate Approx Std Err t Value Pr> [t b0 0.008575 b1 1.069264 0.00389 2.20 0.0280 0.0877 12.19 <.0001 b2 -0.42202 b3 -0.05896 Number of Observations Used Missing Heteroscedasticity Test Equation Test 0.1323 -3.19 0.0015 0.1247 -0.47 0.6366 Statistics for System 480 Objective 0.006981 3 Objective*N 3.3508 Statistic DF Pr> ChiSq Variables NKErf White's Test Breusch-Pagan 82.62 9 <.0001 Cross of all vars 0.6017 1, mktrf, smb, hml 1.86 3 Page Break The REG Procedure Model: MODEL1 Dependent Variable: NKErf Number of Observations Read Number of Observations Used 483 480 3 Source Model Number of Observations with Missing Values Analysis of Variance Sum of Mean DF Squares Square F Value Pr> F 3 1.07370 0.35790 50.84 <.0001 Error 476 Corrected Total 479 3.35081 0.00704 4.42451 Root MSE 0.08390 R-Square 0.2427 Dependent Mean 0.01607 Adj R-Sq 0.2379 Coeff Var 522.18817 Parameter Estimates Heteroscedasticity Consistent Variable Label DF Intercept Intercept 1 mktrf mktrf 1 smb smb 1 Parameter Standard Estimate 0.00858 0.00389 2.20 0.0280 1.06926 0.08771 12.19 <.0001 -0.42202 0.13233 -3.19 0.0015 Standard Error t Value Pr> |t| Error t Value Pr> \t 0.00390 2.20 0.0282 0.09337 11.45 <.0001 0.22309 -1.89 0.0591 hml hml 1 -0.05896 0.12471 -0.47 0.6366 0.13901 -0.42 0.6717 Page Break The REG Procedure Model: MODEL1 Dependent Variable: NKErf Test of First and Second Moment Specification DF Chi-Square Pr> ChiSq 9 19.82 0.0191
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