12. A model to assess the impact of student-teacher ratio on pass percentage of students in...

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12. A model to assess the impact of student-teacher ratio on pass percentage of students in their secondary school examination is estimated as below: =686.3 -1.12X2 -0.67 X3+0.0012 (X2 X3i) R²=0.422, n=420, (11.8) (0.59) (0.37) (0.019) Mean value of X₂-22 and mean value of X3-10% Y pass percentage in class 10th examination for school i. X₂ student-teacher-ratio= ratio of number of students appeared for class 10th to the total number of teachers who taught them in school i, X₁ percentage of children for whom both the parents completed graduation in school i. (3 +7 marks) (i) Specify the econometric model using the matrix structure and justify whether this model has perfect collinearity or not. (ii) You are presenting the results to the class and one of your classmate says that you cannot interpret the coefficient of X2 (teacher-student ratio) as this coefficient does not explain the variations in Y. You quickly check the regression output and find that the p-value of the overall significance of the model is very small and conclude that you can still interpret the model results. Your classmate who raised this doubt is not able to understand this, so explain what is this test of hypothesis you carried out by specifying the null and alternate hypothesis and the calculated value of the test statistic. Further give the justification as to what is the likely problem for this kind of a result and why under this condition the estimators are still BLUE. 12. A model to assess the impact of student-teacher ratio on pass percentage of students in their secondary school examination is estimated as below: =686.3 -1.12X2 -0.67 X3+0.0012 (X2 X3i) R²=0.422, n=420, (11.8) (0.59) (0.37) (0.019) Mean value of X₂-22 and mean value of X3-10% Y pass percentage in class 10th examination for school i. X₂ student-teacher-ratio= ratio of number of students appeared for class 10th to the total number of teachers who taught them in school i, X₁ percentage of children for whom both the parents completed graduation in school i. (3 +7 marks) (i) Specify the econometric model using the matrix structure and justify whether this model has perfect collinearity or not. (ii) You are presenting the results to the class and one of your classmate says that you cannot interpret the coefficient of X2 (teacher-student ratio) as this coefficient does not explain the variations in Y. You quickly check the regression output and find that the p-value of the overall significance of the model is very small and conclude that you can still interpret the model results. Your classmate who raised this doubt is not able to understand this, so explain what is this test of hypothesis you carried out by specifying the null and alternate hypothesis and the calculated value of the test statistic. Further give the justification as to what is the likely problem for this kind of a result and why under this condition the estimators are still BLUE.

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ANSWER The econometric model can be specified as Y a b1X1 b2X2 b3X3 u Where Y pass percentage in cla... View the full answer