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# Do Athletes Perform Poorly during the Semester Using the GAP Data? (Math Problem Sample)

Instructions:

Do athletes perform poorly during the semester using the GAP data?
a) Factor that would be taken up by time effect include; term, SAT score, and term GAP.
While those that could be taken by individual effect include; total hours prior to term, colour,
and gender.
b) Using the pooled OLS as shown below, the season variable is not statistically significant.
Therefore it does not have an effect on the term GAP.

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Content:

3.1: Do athletes perform poorly during the semester using the GAP data?
a) Factor that would be taken up by time effect include; term, SAT score, and term GAP. While those that could be taken by individual effect include; total hours prior to term, colour, and gender.
b) Using the pooled OLS as shown below, the season variable is not statistically significant. Therefore it does not have an effect on the term GAP.
c) If the SAT score does not give all explanation to ability, it would mean that since ability is not observable, there would be a measurement error and some of the variable element would be in the error term resulting to endogeneity problem. Also there would be a heterogeneity problem since there would be correlation between the error terms. In addition, the model does not take individual account into consideration therefore would be inappropriate to predict the full ability.
d) After testing the model with term difference, term other than spring dropped out, female=0, black=0, and white= 0. They were dropped since they would be used as the reference category for making interpretations. For instance we would say that being in season 1 decreases the likelihood of achieving a higher GAP. However, the season variable is not significant thus has no effect on the level of GAP.
e) One of the factors that have been omitted and varies with time is the class grade rank since it keeps changing over time though affecting the same people.
3.2: making use of cigarettes data in US
To measure the responsiveness of per capita cigarettes consumption to real cigarettes price.
a) Using the pooled regression we realise a negative relationship between consumption and price. An indication that elasticity is less than one hence presenting an inelastic demand for cigarettes with changes in price as shown below.
The effect is significant thus an increase in prices would reduce consumption by 72.1% at % level of significance.
B) Time effect captures impact for a variable that affects all individuals alike in a given time period but can vary over time. On the other hand the individual effect vary across individuals but are constant over time. Therefore factors that vary across states but constant over time represent the individual effect, while those that vary over years represent the time effect. Therefore from our survey, the real price in adjoining states and states would be a good example for an individual effect while disposable income and years would be used for time effect.
c) Adding state fixed effect. We realise that our variable of interest is significant. The effect using the state fixed effect is higher since it is 78% change while without the effect its 72%.
Making use of roubust errors, the factors remain significant and thus an in crease in price leads to a 78% decrease in consumption.
d) Adding the time effect the change increases though in both cases the effect is significant. Using the time effect the change is 105.7% while without it is 72.1%.
e) Controlling for both state and year fixed effect results lead to an increase effect. An increase in prices would lead to a decrease in consumption by 143%. The absolute value is positive an indication that the price is elastic.
f) The results would be biased and inconsistent. The results would be invalid due to loss of degrees of freedom and could suffer from heterogeneity problem.
3.3: Estimating return to education for working women
a) Running a regression of the wage received by women on education, experience, and experience squared. The analysis revealed that the overall model parsimony was fit and thus the model was able to fit the data. Education was significant at 1%. An indication that an increase in the number of schooling years increase wage by 10.7%.
b) Using instrumental variables has been highly accepted especially in cases that

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