Solution to Technical Exercise 4 of Exercise Set 06

rm(list=ls())
library(foreign)
college <- read.dta("https://www.princeton.edu/~mwatson/Stock-Watson_3u/Students/EE_Datasets/CollegeDistance.dta")
names(college)

 [1] "female"   "black"    "hispanic" "bytest"   "dadcoll"  "momcoll" 
 [7] "ownhome"  "urban"    "cue80"    "stwmfg80" "dist"     "tuition" 
[13] "incomehi" "ed"      

apply(college, 2, mean)

    female      black   hispanic     bytest    dadcoll    momcoll    ownhome 
 0.5453109  0.1925711  0.1498946 51.0019310  0.2020548  0.1393572  0.8192835 
     urban      cue80   stwmfg80       dist    tuition   incomehi         ed 
 0.2439410  7.6548735  9.5564989  1.7249210  0.9131396  0.2863541 13.8292940 

apply(college[, c("ed", "bytest", "cue80", "stwmfg80", "dist", "tuition")], 2, sd)

       ed    bytest     cue80  stwmfg80      dist   tuition 
1.8139688 8.8192514 2.8657700 1.3644112 2.1338357 0.2835778 

college$c.dist <- college$dist - 1
college$c.cue80 <- college$cue80 - mean(college$cue80)
college$c.tuition <- college$tuition - mean(college$tuition)
lm(ed ~ c.dist + c.cue80 + c.tuition + black + dadcoll + momcoll + dadcoll:momcoll + black:c.tuition, data = college)

Call:
lm(formula = ed ~ c.dist + c.cue80 + c.tuition + black + dadcoll + 
    momcoll + dadcoll:momcoll + black:c.tuition, data = college)

Coefficients:
    (Intercept)           c.dist          c.cue80        c.tuition  
       13.62648         -0.05305          0.01760          0.16000  
          black          dadcoll          momcoll  dadcoll:momcoll  
       -0.36653          1.11807          0.92463         -0.48436  
c.tuition:black  
       -0.31440  

Interpretations

1. Intercept: The average number of years of completed education is 13.6 years for non-black students whose mother and father are not college graduates, who live 10 miles away from a 4 year college, and residing in a county whose unemployment rate is 7.65 percent and average state 4 year college tuition is 913 dollars.

2. Coefficient on c.dist: When we look at students having the same demographic characteristics (black, dadcoll, momcoll) and the same county characteristics (cue80, tuition), students who live 30 miles from a 4 year college have on average 1 year less completed education than students who live 10 miles from a 4 year college.

3. Coefficient of c.cue80: When we look at students having the same demographic characteristics (black, dadcoll, momcoll), living in counties with the same average state 4 year college tuition, and are equally far from a 4 year college, but living in counties whose unemployment rates differ by about 5 percentage points, their average completed years of education will differ by roughly a month (0.088 years).

4. Coefficient of c.tuition: When we look at non-black students having the same demographic characteristics (dadcoll, momcoll), living in counties with the same unemployment rate, and are equally far from a 4 year college, but living in counties whose average state 4 year college tuition differ by about 10000 dollars, their average completed years of education will differ by 1.6 years.

5. Coefficient of black: When we compare black and non-black students having the same demographic characteristics (dadcoll, momcoll), living in counties with the same unemployment rate and the same average state 4 year college tuition equal to 913 dollars, and are equally far from a 4 year college, we find that black students have on average about 4.5 less months (0.37 years) of completed education compared to non-black students.

6. Coefficient of dadcoll: When we look at black students who have mothers who are not college graduates, living in counties with the same unemployment rate and the same average state 4 year college tuition, and are equally far from a 4 year college, we find that students whose fathers are college graduates have on average 1.12 years of completed education compared to students whose fathers are not college graduates.

7. Coefficient of dadcoll:momcoll: When we look at black students living in counties with the same unemployment rate and the same average state 4 year college tuition, and are equally far from a 4 year college, we find that students whose fathers and mothers are both college graduates have on average 1.56 years of completed education compared to students whose fathers and mothers are both not college graduates.

8. Coefficient of c.tuition:black: When we compare students having the same demographic characteristics (dadcoll, momcoll), living in counties with the same unemployment rate and average state 4 year college tuition equal to 1000 dollars, and are equally far from a 4 year college, black students have on average 0.39 years less completed education than non-black students.

Remarks

1. Another interpretation for dadcoll: When we look at non-black students who have mothers who are not college graduates, living in counties with the same unemployment rate and the same average state 4 year college tuition, and are equally far from a 4 year college, we find that students whose fathers are college graduates have on average 1.11 years of completed education compared to students whose fathers are not college graduates.

2. I leave interpreting the coefficient of momcoll to you.

3. For the coefficient of c.dist for example, you can make this very specific and still obtain an interpretation. When we look at non-black students whose mothers and fathers are not college graduates and are living in a state whose county employment rate is 7.65 percent and the average state tuition is 913 dollars, students who live 30 miles from a 4 year college have on average 1 year less completed education than students who live 10 miles from a 4 year college.