This document provides an in-depth analysis of the results obtained from a multiple regression exercise in econometrics, focusing on the relationship between household expenditures and pass rates at a math test.
Extract
[...] Econometrics - Multiple Regression I. Exercise 1 There were 2017 one-person households. ii) (0,059) (0,092) n = 2017 R2 = 0,119 Are there any surprises in the estimates of some of the loss parameters? iii) The constant allows for the consideration of very young households (age close to and having very little annual income (inc close to 0). In this case, the model's prediction, thanks to the negative constant, is that this type of household will have a net financial wealth that is negative, that is to say a debt, which is consistent with economic intuition. [...]
[...] iv) The R-squared increases significantly in this specification, rising from 0.0297 to 0.1893: the inclusion of two additional variables allows for a better explanation of the pass rate at this math test. It would, however, be interesting to calculate the adjusted R-squared because the inclusion of new variables mechanically increases the R-squared. Other variables could be added to account for this score at this math test, such as the teachers' remuneration. We can think that better-paid teachers would be more motivated and therefore motivating for their students. Similarly, we could add variables on the school environment itself: quantity of non-teaching staff, class size, etc. [...]
[...] The estimated constant is negative, which means that a certain level of expenditures is necessary before a strictly positive pass rate can be obtained. Indeed, the low value of the coefficient of determination seems to indicate that expenditures are strongly correlated with other factors influencing the pass rate at the exam. In particular, expenditures per student are not decided at an individual level (at the level of each child), but at a larger geographical scale: the R-squared is thus relatively low in this first specification. [...]
