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 your main dining hall, 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 variable:
GenderComp =

\mid ( 50 \% - \% \text { of Male Students at Table } ) \mid

Where "

| Z |

" 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 an able research assistant):

\text { h }

= 30.90 - 3.78 × Size - 8.81 × DCoed + 2.28 × DFemme +2.06 × DRoommate
(7.73)(0.63)(2.66)(2.42)(2.39)
- 0.17 × DAthlete + 1.49 × DCons - 0.81 SAT + 1.74 × SibOther, R²=0.24, SER = 15.50
(3.23)(1.10)(1.20)(1.43)
where Size is the number of persons at the table minus 3; DCoed is a binary variable, which takes on the value of 1 if you live on a coed floor; DFemme is a binary variable, which is 1 for females and zero otherwise; DRoommate is a binary variable which equals 1 if the person at the table has a roommate and is zero otherwise; DAthlete is a binary variable which is 1 if the person at the table is a member of an athletic varsity team; DCons 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; and 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 and make a decision about the exclusion of these variables based on the critical values.
(c)The Dean decides to estimate the following specification next: $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 your main dining hall, 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 variable: GenderComp = \mid ( 50 \% - \% \text { of Male Students at Table } ) \mid Where | Z | 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 an able research assistant): \text { h } = 30.90 - 3.78 × Size - 8.81 × DCoed + 2.28 × DFemme +2.06 × DRoommate (7.73)(0.63)(2.66)(2.42)(2.39) - 0.17 × DAthlete + 1.49 × DCons - 0.81 SAT + 1.74 × SibOther, R<sup>2</sup>=0.24, SER = 15.50 (3.23)(1.10)(1.20)(1.43) where Size is the number of persons at the table minus 3; DCoed is a binary variable, which takes on the value of 1 if you live on a coed floor; DFemme is a binary variable, which is 1 for females and zero otherwise; DRoommate is a binary variable which equals 1 if the person at the table has a roommate and is zero otherwise; DAthlete is a binary variable which is 1 if the person at the table is a member of an athletic varsity team; DCons 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; and 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 and make a decision about the exclusion of these variables based on the critical values. (c)The Dean decides to estimate the following specification next: = 29.07 - 3.80 × Size - 9.75 × DCoed + 1.50 × DCons + 1.97 × SibOther, (3.75)(0.62)(1.04)(1.04)(1.44) R<sup>2</sup>=0.22 SER = 15.44 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?$ = 29.07 - 3.80 × Size - 9.75 × DCoed + 1.50 × DCons + 1.97 × SibOther,
(3.75)(0.62)(1.04)(1.04)(1.44)
R²=0.22 SER = 15.44
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?

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