Problem Set 5

Analytically Problems

  1. \[ GPA_i = \beta_0 + \beta_1 Black_i + \beta_2 Female_i + \beta_3 Dorms_i+\beta_4Pysch_i + u_i\]

  2. Who forms the reference group group in this regression? The reference group would be White Males who don’t live in the dorms and are not majoring in Psych.

  3. \[\beta_0\] divided by the number of students is the average GPA of the reference group.

  1. \[ Y_i = \beta_0 + \beta_1 X_{1i} + \beta_2 X_{2i} + \beta_3 X_{3i}+\beta_4X_{4i} + u_i\]
  1. What restricted model would allow you to test the null hypothesis thatβ1=β2= 0? How many restrictions do you have?

\[ Y_i = \beta_0 + \beta_3 X_{3i}+\beta_4X_{4i} + u_i\] There are 2 restrictions.

  1. What restricted model would allow you to test the null hypothesis thatβ1=β2? How many restrictions do you have?

\[ Y_i = \beta_0 + \beta_1 X_{1i} + \beta_1 X_{2i} + \beta_3 X_{3i}+\beta_4X_{4i} + u_i\] There are 4 restrictions.

  1. What restricted model would allow you to test the null hypothesis thatβ1+β2= 0? How many restrictions do you have? \[ Y_i = \beta_0 + \beta_1 X_{1i} - \beta_1 X_{2i} + \beta_3 X_{3i}+\beta_4X_{4i} + u_i\] There are 2 restrictions.

Computational Problems

\[ hsgrad_i = \beta_0 + \beta_1 lowincome_i + \beta_2 teenbirth_i + \beta_3 lowincome_i*teenbirth_i + u_i\]

## 
## ================================================
##                          Dependent variable:    
##                      ---------------------------
##                                hs_grad          
## ------------------------------------------------
## lowincome                     -0.035***         
##                                (0.003)          
##                                                 
## teen_birth                    -0.326***         
##                                (0.008)          
##                                                 
## lowincome:teen_birth          -0.062***         
##                                (0.012)          
##                                                 
## Constant                      0.943***          
##                                (0.001)          
##                                                 
## ------------------------------------------------
## Observations                    9,294           
## R2                              0.605           
## Adjusted R2                     0.605           
## Residual Std. Error       0.043 (df = 9290)     
## F Statistic          4,742.620*** (df = 3; 9290)
## ================================================
## Note:                *p<0.1; **p<0.05; ***p<0.01

  1. The reference group is lowincome variable. If lowincome is Zero, then that means they have a higher income than “Low”. The \[\beta_0\] is 0.943, which means that if you didn’t have a kid during your teens and weren’t in the “Low” income category then you have 0.943 change of graduating High School.

  2. If you don’t have any teen births, then we look at the coefficient for lowincome, which is -0.035. This means that if you are born in the low income level, then you have 0.035 less of a chance of graduating high school. This makes sense considering if you are poorer than you have less access to things like tutoring or even necessary school supplies.

  3. The coefficient for lowincome:teen_birth is -0.062. This means that there is a 0.062 less chance for high school degree for a single percentage change in lowincome:teen_birth.

  5. It can be seen that there is a much higher concentration of teen age pregnancy in the South, especially for low income individuals. This doesn’t surprise me that much at all. I would say there is a lot of uneducated people in the South. Many rural communities, which typically don’t value education as much as cities do. Rural communities also tend to have less money on average.