OLS estimation Assignment Example | Topics and Well Written Essays - 2500 words

OLS estimation - Assignment ExampleThe respective means of these variables ar 82.38, 80.77 and 44.66 and signifi flowerpott variability among the values taken by these variables is observed, implying a possibility that variations in attention can potentially cause variations in marks. Other variables that can potentially affect performances in the course have to be accounted for to ensure a proper evaluation and so, ability, age, hrss, i,e., study hours are in like manner explored. All these variables reflect strong variability and thus are all potential candidates as controls. (For details, see table 1 in appendix). Apart from hardly looking at individual descriptive statistics, in order to obtain some idea about the interrelationships and potential causations, a table of scatter plots are also explored where smarks is the plotted as the y variable while ability, age, hrss, alevelsa attl as well as squared forms of ability and attl as the x variables. From the plots (figure 2 i n appendix), we find that both ability and its square seem to be positively correlated with marks. The variables age and alevelsa seem to have no associative patterns with marks. For attendance, our primary variable of interest, we find that there is evidence of clustering of values greater than the mean marks at the higher values of attl implying that higher chat attendance rate is associated with better performances on average on the course. Further, it seems that there is some clustering at higher values of the squared lecture attendance rates. No correlation seems to be present between smarks and hrss from the last graph in the table. The interrelationships between these variables are important for regression specifications, since high correlations among independent variables whitethorn lead to multicollinearity. So, a scatterplot matrix is presented as figure 2 in the appendix. Therefore, the summary statistics and the scatter plots, show that there is a strong possibility tha t rank attendance influences performance along with other factors such as ability. Further, since some evidence of possible positive correlation between class performance as measured by smarks and the squares of ability and attendance, represented by attl were observed, the possibility of nonlinear dependence cannot be ignored. 2. Basic OLS estimation a) From the simple regression of smarks on an lay off and the variable attl, we find that attendance has a significant positive impact on performance1. The coefficient on attendance is close to 0.15 and has a t-stat value of 4.331.96, which is the 5% detailed value for the t distribution under the null hypothesis that the coefficient is insignificant, i.e., is not statistically significantly different from zero. Additionally the intercept takes a value of 52.91 implying that the conditional mean of smarks is 52.91 for students who have a zero attendance rate for lectures. This value is significant at the 5% level as well (t-stat val ue 19.061.96). However, the correct R-squared value is only 0.06 implying that only 6% of the variation of performance can be explained in terms of variations in lecture attendance rates. Therefore, the model last is poor. b) Inclusion of ability and hours studied (hrss) leads to the impact of attendance rate falling to approximately 0.13 from 0.15, but the