Question

1. In an effort to determine whether going to class improved student academic performance, David Romer[1] developed the following equation:

Where:   G_i = the grade of the ith student in Romer’s class (A=4, B=3, etc).

                  ATT_i = the percent of class lectures that the ith student attended

                  PS_i = the percent of the problem sets that the ith student completed

1. What signs do you expect for the coefficients of the independent variables in this equation?  Explain your reasoning.
2. Romer then estimated the equation:

Do the estimated results agree with your expectations?

3. It’s usually easier to develop expectations about the signs of coefficients than about the size of those coefficients.  To get an insight into the size of the coefficients, let’s assume that there are 25 hours of lectures in a semester and that it takes the average student approximately 50 hours to complete all of the problem sets in a semester.  If a student in one of Romer’s classes had only one more hour to devote to class and wanted to maximize the impact on his or her grade, should the student go to class for an extra hour or work on problem sets for an extra hour?  (HINT:  Convert the extra hour to percentage terms and then multiply those percentages by the estimated coefficients.)
4. From the given information, it would be easy to draw the conclusion that the bigger a variable’s coefficient, the greater its impact on the dependent variable.  To test this conclusion, what would your answer to part c have been if there had been 50 hours of lecture in a semester and if it had taken 10 hours for the average student to complete the problem sets?  Were we right to conclude that the larger the estimated coefficient the more important the variable?
5. What’s the real world meaning of R² = 0.33?  For this specific equation does 0.33 seem high, low or about right?
6. Is it reasonable to think that only class attendance and problem set completion affect your grade in a class?  If you could add just one more variable to the equation, what would it be?  Explain your reasoning.  What should adding your variable to the equation do to R²? To adjusted-R²?

Answer 1

Sol:

(a).

The coefficient of ATT and PS are both expected to have a positive sign. This is so because it is assumed that higher the number of classes a students attends and greater the number of problem sets he or she solves,higher would be the students grades.

(b).

The coefficient of ATT is 1.74 and the coefficient of PS is 0.60. Both coefficients have a positive sign.An increase in ATT and PS will increase a students grades according to the equation estimated by Romer. The result confirms to our expectations.

(c).

For a one percent increase in the number of lectures that a student attends, Grade rises by 1.74. For a one percent rise in PS,Grade rises by 0.60.

If the student has one extra hour,as a percent of ATT, the student has or 3.85% more time to be devoted to ATT.This will lead to a rise in grade by

If the student has one extra hour,as a percent of PS, the student has or 1.96% more time to be devoted to PS.This will lead to a rise in grade by

Therefore an hour spent in class will cause the students grade to rise by a greater amount.With an extra hour in hand,the student should attend class.

If the student has one extra hour,as a percent of ATT, the student has or 1.96% more time to be devoted to ATT. This will lead to a rise in grade by

If the student has one extra hour,as a percent of PS, the student has or 9.09% more time to be devoted to PS.This will lead to a rise in grade by

Here,An hour devoted to solving problem sets would be more beneficial to the student. His grade increase by a greater amount.We thus cannot conclude that the bigger an independent variables coefficient higher is its impact on the independent variable.and thus it is not right to conclude that the larger the coefficient,more important is my independent variable.

(d).

Both Class attendance and problem set solving only explain 33% of the variation in Grades(as given by R^2).A major part of variation in grades thus remain unexplained.Therefore there must be other factors affecting Grades.

It can be access to resources(say tutorials,books) which may indirectly depend upon income of the individual student.

No matter what variable we introduce, the R^2 will always increase ,significantly, or insignificantly. Adjusted R^2 may increase,decrease or remain constant depending upon the relevance of the variable introduced.