6. Regression Discontinuity. A university offers scholarships to applicants base
ID: 1166445 • Letter: 6
Question
6. Regression Discontinuity. A university offers scholarships to applicants based on their high school grade point averages (GPA). In 2016, any student who earned a 3.65 GPA or higher was offered $10,000. We estimate if this program results in more students attending the university using data for 1,250 applicants. attend, = 0.38 + 0.20(GPA;-3.65) + 0.07scholari (0.09) (0.05) 0.03) (a) Interpret the coefficient on "GPA-3.65" in a sentence. Does this make sense? Explain. (b) Interpret the coefficient on "scholar" in a sentence. (c) Explain what it means for the coefficient in part b) to be called a local average treatment effect. (d) effect of the scholarship on attending the university statistically significant at the 95% level, (e) What is the probability of a student attending the university if they have a GPA of 3.64? 3.66? (f) How many GPA points are equal to the effect of the scholarship in terms of inducing attendance at the university? (g) Draw graph of this regression equation and label the slope and the discontinuityExplanation / Answer
a) By the coeffecient of 0.20,on GPA-3.65, it means 20 percent of weightage is given to the Grade Point Average in the final attendance decision. It makes sense as the the maximum Grades achievable is 3.65 which is an ideal case. The p-value is 0.05 which is lesser than significance level.
b) The Coffecient of Scholar is 0.07 i.e. there is 70% probablity that scholarship recieving candidate will attend the College .The p-value is 0.03 which is higher So we don't have enough of evidence to reject the null hypothesis.
c) Sometimes a treatment or a program is delivered but for some reason or another only some individuals or groups actually take the treatment. In this case it can be hard to estimate treatment effects for the whole population. For example maybe people for whom the treatment would have had a big effect decided not to take up the treatment. In these cases it is still possible to estimate what’s called the “Local Average Treatment Effect,” or LATE.
In the part b) above as the recieving of scholarship is highly significant factor in deciding the attendance and this turns out to be a significant Treatment group. Along with this,chosen methodology for the minimum GPA makes them compliant. And for the admission into the college the regular attendance criteria is a must The necessity for the applicant to be a scholarship holder must not holds true be a scholar and here the treatment is not applicable to them score GP So as to acdefies the non-com
d) The Effect of recieving the scholarship is not statistically significant at 95% as the probablity or the p-value turns out to be 0.03 which is greater than 0.01.
e)The Probablity of a student attending the university if their GPA turns out to be 3.64 is lesser significant than the Probablity of a student attending the university if their GPA turns out to be 3.66 which is highly significant.
P(A)Probablity of Attendance of Students with GPA 3.64 or 3.66=1- P(A')=1-0.05=0.05
f) The GPA points equivalence to the effect of the scholarship in terms of inducing attendance can be calculated by the following method GPA should lie between 3.66 to 7.00 for the full effect.
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