Both models (mle_ols and mle_ols2) were used for Maximum Likelihood Estimation for education and income. Newton-Raphson maximisation method was used in both models. From both models 3 parameters were estimated. On slide 4.14, sigma, beta1 and beta2 were the parameters. These three parameters were estimated to understand the distribution of education and income. According to mle_ols model, education was in the X-axis and income was in the Y-axis. The result showed that the standard deviation(sigma) of the distribution was 2.53. Beta1 was the intercept of education and income, which was a negative value (0.65). Beta2 revealed that income increased by 0.37 for every one unit increase in education. On the other hand, mle_ols2 model on slide 4.18 estimated mu, theta1, and theta2 as the parameters. The result suggested the mean income of the population (mu) was 3.52. Theta1 was the intercept point of education and income, which was a positive value (1.46). Theta2 suggested that income increased by 0.11 for every one unit incraese in education. The results on the slide 4.14 suggested stronger influence of education on income compared to results suggested on the slide 4.18.
When introduce a new age variable, the relationship between age and income might be less stronger than the relationship between education and income. Becuause, when I focused on the head and tail of the dataset, it suggested that people having same level of education had almost same amount of income irespective of their age. For example: majority of the people with 12 level of education, had an income between >2.0 and <3.0, but they were in various age level such as 22, 25, 34, 67. So, the income could be better understand by the the education than age. In addition, the value of age in terms of income was much more scatter to understand the relationship. However, I think there might be a positive relationship between age and income, since the level of education increases with age and since there was a positive relationship between education and income.