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Model Selection & Functional Form: Female (takes a value for 1 if female, 0 if not female) and Non-White (and value of 1 if NonWhite, 0 if white) are dummy variables. Age is measured continuously in years, and Age Squared is the square of Age. Education is measured in years, Earnings measured in dollars, and Log Earnings are the log transformation of earnings. Are the predictor variables in Models A & B statistically significant at the 5% significance level? Carefully interpret and explain the coefficients for Female, Non-White, Age Squared and Education in models A and B. Compare Model A to Model B. Which model would use for purposes of prediction and why? In your preferred model, should we add Age Squared? Is your chosen model a good model? Explain why or why not.

Model Selection & Functional Form: Female (takes a value for 1 if female, 0 if not female) and Non-White (and value of 1 if NonWhite, 0 if white) are dummy variables. Age is measured continuously in years, and Age Squared is the square of Age. Education is measured in years, Earnings measured in dollars, and Log Earnings are the log transformation of earnings. Are the predictor variables in Models A & B statistically significant at the 5% significance level? Carefully interpret and explain the coefficients for Female, Non-White, Age Squared and Education in models A and B. Compare Model A to Model B. Which model would use for purposes of prediction and why? In your preferred model, should we add Age Squared? Is your chosen model a good model? Explain why or why not.

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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  1. Model Selection & Functional Form:

Female (takes a value for 1 if female, 0 if not female) and Non-White (and value of 1 if NonWhite, 0 if white) are dummy variables. Age is measured continuously in years, and Age Squared is the square of Age. Education is measured in years, Earnings measured in dollars, and Log Earnings are the log transformation of earnings.

  1. Are the predictor variables in Models A & B statistically significant at the 5% significance level?
  2. Carefully interpret and explain the coefficients for Female, Non-White, Age Squared and Education in models A and B.
  3. Compare Model A to Model B. Which model would use for purposes of prediction and why? In your preferred model, should we add Age Squared? Is your chosen model a good model? Explain why or why not.
### Regression Model B Summary (from R) #### Coefficients: - **(Intercept):** - Estimate: 8.6956410 - Std. Error: 0.5913211 - t value: 14.705 - Pr(>|t|): < 2e-16 *** - **Female:** - Estimate: -0.3720635 - Std. Error: 0.1455393 - t value: -3.931 - Pr(>|t|): 0.000088 *** - **Non-White:** - Estimate: 0.3627136 - Std. Error: 0.2222849 - t value: 2.082 - Pr(>|t|): 0.0375 * - **Female * Age:** - Estimate: 0.0854627 - Std. Error: 0.0524483 - t value: 1.629 - Pr(>|t|): 0.1034 - **Age:** - Estimate: 0.0540141 - Std. Error: 0.0200741 - t value: 2.691 - Pr(>|t|): 0.0072 ** - **Age Squared:** - Estimate: -0.0003535 - Std. Error: 0.0001883 - t value: -1.877 - Pr(>|t|): 0.0606 . - **Education:** - Estimate: 0.0399288 - Std. Error: 0.0170229 - t value: 2.346 - Pr(>|t|): 0.0191 * #### Model Summary: - **Residual standard error:** 1.733 on 1755 degrees of freedom - (802 observations deleted due to missingness) - **Multiple R-squared:** 0.03378 - **Adjusted R-squared:** 0.03048 - **F-statistic:** 10.23 on 6 and 1755 DF - **p-value:** 3.779e-11 #### Note: - Significant codes: - `
Transcribed Image Text:### Regression Model B Summary (from R) #### Coefficients: - **(Intercept):** - Estimate: 8.6956410 - Std. Error: 0.5913211 - t value: 14.705 - Pr(>|t|): < 2e-16 *** - **Female:** - Estimate: -0.3720635 - Std. Error: 0.1455393 - t value: -3.931 - Pr(>|t|): 0.000088 *** - **Non-White:** - Estimate: 0.3627136 - Std. Error: 0.2222849 - t value: 2.082 - Pr(>|t|): 0.0375 * - **Female * Age:** - Estimate: 0.0854627 - Std. Error: 0.0524483 - t value: 1.629 - Pr(>|t|): 0.1034 - **Age:** - Estimate: 0.0540141 - Std. Error: 0.0200741 - t value: 2.691 - Pr(>|t|): 0.0072 ** - **Age Squared:** - Estimate: -0.0003535 - Std. Error: 0.0001883 - t value: -1.877 - Pr(>|t|): 0.0606 . - **Education:** - Estimate: 0.0399288 - Std. Error: 0.0170229 - t value: 2.346 - Pr(>|t|): 0.0191 * #### Model Summary: - **Residual standard error:** 1.733 on 1755 degrees of freedom - (802 observations deleted due to missingness) - **Multiple R-squared:** 0.03378 - **Adjusted R-squared:** 0.03048 - **F-statistic:** 10.23 on 6 and 1755 DF - **p-value:** 3.779e-11 #### Note: - Significant codes: - `
**Regression Model A (from R)** **Coefficients:** | Variable | Estimate | Std. Error | t value | Pr(>|t|) | |----------------|-----------|------------|---------|--------------------| | (Intercept) | 24156.63 | 8943.25 | 2.701 | 0.00697 ** | | Female | -24134.88 | 2397.93 | -10.065 | < 2e-16 *** | | Non-White | -4924.83 | 3629.86 | -1.357 | 0.17503 | | Female * Age | 1877.77 | 857.37 | 2.190 | 0.02864 * | | Age | 1718.91 | 336.42 | 5.109 | 0.0000003570 *** | | Age Squared | -18.13 | 3.17 | -5.718 | 0.00000000126 *** | | Education | 3860.943 | 263.590 | 14.648 | < 2e-16 *** | **Additional Information:** - Residual standard error: 1.735 on 1758 degrees of freedom (800 observations deleted due to missingness) - Multiple R-squared: 0.03073 - Adjusted R-squared: 0.02797 - F-statistic: 11.15 on 5 and 1758 DF, p-value: 1.361e-10 **Explanation:** - The model examines the relationship between various factors and an outcome measured by the coefficients. - Significant predictors (marked by ** or ***) include Female, Age, Age Squared, and Education, suggesting strong effects on the outcome. - The p-value indicates the probability that the observed relationship occurred by chance, with smaller values suggesting stronger evidence against the null hypothesis. - The Multiple R-squared and Adjusted R-squared indicate how well the model explains the variability in the data, with higher values representing better fits. This analysis is useful for understanding the impact of these variables on the outcome of interest in the context studied.
Transcribed Image Text:**Regression Model A (from R)** **Coefficients:** | Variable | Estimate | Std. Error | t value | Pr(>|t|) | |----------------|-----------|------------|---------|--------------------| | (Intercept) | 24156.63 | 8943.25 | 2.701 | 0.00697 ** | | Female | -24134.88 | 2397.93 | -10.065 | < 2e-16 *** | | Non-White | -4924.83 | 3629.86 | -1.357 | 0.17503 | | Female * Age | 1877.77 | 857.37 | 2.190 | 0.02864 * | | Age | 1718.91 | 336.42 | 5.109 | 0.0000003570 *** | | Age Squared | -18.13 | 3.17 | -5.718 | 0.00000000126 *** | | Education | 3860.943 | 263.590 | 14.648 | < 2e-16 *** | **Additional Information:** - Residual standard error: 1.735 on 1758 degrees of freedom (800 observations deleted due to missingness) - Multiple R-squared: 0.03073 - Adjusted R-squared: 0.02797 - F-statistic: 11.15 on 5 and 1758 DF, p-value: 1.361e-10 **Explanation:** - The model examines the relationship between various factors and an outcome measured by the coefficients. - Significant predictors (marked by ** or ***) include Female, Age, Age Squared, and Education, suggesting strong effects on the outcome. - The p-value indicates the probability that the observed relationship occurred by chance, with smaller values suggesting stronger evidence against the null hypothesis. - The Multiple R-squared and Adjusted R-squared indicate how well the model explains the variability in the data, with higher values representing better fits. This analysis is useful for understanding the impact of these variables on the outcome of interest in the context studied.
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