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Sagot :
a. The misspecification error is due to a redundancy in the model specification. Since age and the year of birth go hand in hand in a cross-sectional dataset one of these two related variables should be removed.
The possible solution is just to remove year of birth from the model. Alternatively we could remove age, but it is better to retain age because the regression coefficient for age is more easily interpretable than the coefficient for year of birth.
Thus the corrected formula is:
⇒ [tex]Wealth_{i}=\alpha _{0}+ \alpha_{1} educ_{i} +\alpha_{2}male_{i}+\alpha_{3}age_{i}+\alpha_{4}married_{i}+\in_{i}[/tex]
b. Even after correcting the misspecification error, [tex]\alpha _{1}[/tex] cannot be interpreted as the causal effect of education on wealth. The coefficient [tex]\alpha _{1}[/tex] represents just that portion of variation in Wealth that is uniquely explained by education.
The correlation of education with the other predictors, such as the categorical predictor male, the numeric variable age, etc. that are not captured in the model also explain the variation in Wealth.
What is regression?
⇒ Regression is a group of statistical procedures used in statistical modeling to determine the relationships between a dependent variable (often referred to as the "outcome" or "response" variable, or a "label" in machine learning jargon), and one or more independent variables (often referred to as "predictors," "covariates," "explanatory variables," or "features"). In linear regression, the most typical type of regression analysis, the line (or a more complicated linear combination) that most closely matches the data in terms of a given mathematical criterion is found. When using the ordinary least squares method, for instance, the specific line (or hyperplane) that minimizes the sum of squared differences between the genuine data and that line is computed (or hyperplane).
To learn more about regression, visit:
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