BU Econometrics with Applications Worksheet

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variable:
GenderComp
[2] = 150% – % of Male students at table]
Where “Zl” stands for absolute value of Z. The variable can take on values from zero to fifty.
After considering various explanatory variables, the Dean settles for an initial list of eight, and estimates
the following relationship, using heteroskedasticity-robust standard errors (this Dean obviously has
taken an econometrics course earlier in her career and/or has a capable research assistant):
GenderComp = 30.90 – 3.78 Size – 8.81 D[Coed] + 2.28 D[Femme] + 2.06 D[Roommate]
– 0.17 D[Athlete] + 1.49 D[Cons] – 0.81 SAT + 1.74 SibOther
R2=0.24 , SER=15.50

Standard Errors:
Intercept=7.73
Size=0.63
D[Coed]=2.66
D[Femme]=2.42
D[Roommate]=2.39
D[Athlete]=3.23
D[Cons]=1.10
SAT=1.20
SibOther=1.43
Where:
Size is the number of persons at the table minus 3;
D[Coed) is a binary variable, which takes on the value of 1 if you live on a coed floor;
D[Femme) is a binary variable, which is 1 for females and zero otherwise;
D[Roommate] is a binary variable which equals 1 if the person at the table has a roommate and is zero
otherwise;
D[Athlete) is a binary variable which is 1 if the person at the table is a member of an athletic varsity team;
D[Cons) is a variable which measures the political tendency of the person at the table on a seven-point
scale, ranging from 1 being “liberal” to 7 being “conservative”;
SAT is the SAT score of the person at the table measured on a seven-point scale, ranging from 1 for the
category “900-1000” to 7 for the category “1510 and above”; and increasing by one for 100 point increases;
SibOther is the number of siblings from the opposite gender in the family the person at the table grew up
with.
(a) Indicate which of the coefficients are statistically significant.
(b) Based on the above results, the Dean decides to specify a more parsimonious form by eliminating the
least significant variables. Using the F-statistic for the null hypothesis that there is no relationship
between the gender composition at the table and DFemme, DRoommate, DAthlete, and SAT, the regression
package returns a value of 1.10.
What are the degrees of freedom for the statistic? Look up the 1% and 5% critical values from the F-table
4. Assume that the pandemic is over, and university campuses are accepting students in their
dorms.
The administration of your university/college is thinking about implementing a policy of coed floors only
in dormitories. Currently there are only single gender floors. One reason behind such a policy might be to
generate an atmosphere of better “understanding” between the sexes. The Dean of Students (DoS) has
decided to investigate if such a behavior results in more “togetherness” by attempting to find the
determinants of the gender composition at the dinner table in the main dining hall of your dorm, and in
that of a neighboring university, which only allows for coed floors in their dorms. The survey includes
176 students, 63 from your university/college, and 113 from a neighboring institution.
The Dean’s first problem is how to define gender composition. To begin with, the survey excludes single
persons’ tables, since the study is to focus on group behavior. The Dean also eliminates sports teams from
the analysis, since a large number of single-gender students will sit at the same table.
Finally, the Dean decides to only analyze tables with three or more students, since she worries about
“couples” distorting the results. The Dean finally settles for the following specification of the dependent
and make a decision about the exclusion of these variables based on the critical values.
(c) Next, the Dean decides to estimate the following specification:
==

GenderComp = 29.07 – 3.80 Size – 9.75 D[Coed] + 1.50 D[Cons] + 1.97 SibOther
R2 = 0.22 SER = 15.44
Standard errors:
Intercept-3.75
Size=0.62
D[Coed]=1.04
D[Cons]=1.04
SibOther=1.44
Calculate the t-statistics for the coefficients and discuss whether or not the Dean should attempt to
simplify the specification further. Based on the results, what might some of the comments be that she will
write up for the other senior administrators of your college? What are some of the potential flaws in her
analysis? What other variables do you think she should have considered as explanatory factors in terms
of impacting “gender” role on education?
(b) Based on the above results, the Dean decides to specify a more parsimonious form by eliminating the
least significant variables. Using the F-statistic for the null hypothesis that there is no relationship
between the gender composition at the table and DFemme, DRoommate, DAthlete, and SAT, the regression
package returns a value of 1.10.
What are the degrees of freedom for the statistic? Look up the 1% and 5% critical values from the F-table
and make a decision about the exclusion of these variables based on the critical values.
In the original model 8 variables were considered. Dean has
eliminated 4 variables (D[Femme), D[Roommate], D[Athlete), and SAT).
(
His new model has variables. The same 176 observations (students) are
used.
Considering the F statistic the degrees of freedom are:
With this new regression model, we obtain an F-statistic of 1.10.
We will now consider the critical values for 1% and 5% significance
levels.
For 1% significance, the critical value is:
For 5% significance, the critical value is:
Note that the F-value returned from the regression package 1.10 is less
than both of the critical values. That is, for both the 1% and 5%
significance level the model is not significant. The exclusion of the
variables did not help the model be significant/useful.

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Tags:
degrees of freedom

coefficients

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