Homework 6

Loading libraries and IPUMS data.

library(haven)
library(readr)
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(ggplot2)
library(broom)
ipums<-read_dta("https://github.com/coreysparks/data/blob/master/usa_00045.dta?raw=true")
mySE<-function(x){sd(x,na.rm=T)/length(x)}

1 and 2) clear up missing values for Travel Time and remove poputaltion not in a metro area

myPositiveTravel<-subset(ipums,age>17)
myPositiveTravel<-subset(myPositiveTravel,trantime>0)
myPositiveTravel<-subset(myPositiveTravel,met2013>0)
#subset only takes 2 manipulations at a time

2)Mutating the database to reduce the observations to Texas Metro Areas and labeling the areas

The Metro List:

Code Metro Area

11100 Amarillo

12420 Austin-Round Rock

13140 Beaumont - Port Arthur

15180 Brownsville - Harlingen

17780 College Station - Bryan

18580 Corpus Christi

19100 Dallas - Fort Worth - Arlington

21340 El Paso

26420 Houston - The Woodlands - Sugar Land

28660 Killeen - Temple

29700 Laredo

31180 Lubbock

32580 McAllen - Edinburg - Mission

33260 Midland

36220 Odessa

41660 San Angelo

41700 San Antonio - New Braunfels

46340 Tyler

47380 Waco

48660 Wichita Falls

myTXMetros<-myPositiveTravel%>%
  filter(statefip==48)%>%
  mutate(TXmet2013 = case_when
    (
      .$met2013 ==11100 ~"Amarillo", 
      .$met2013 ==12420 ~"Austin-Round Rock",
      .$met2013 ==13140 ~"Beaumont - Port Arthur",
      .$met2013 ==15180 ~"Brownsville - Harlingen",
      .$met2013 ==17780 ~"College Station - Bryan",
      .$met2013 ==18580 ~"Corpus Christi",
      .$met2013 ==19100 ~"Dallas - Fort Worth - Arlington",
      .$met2013 ==21340 ~"El Paso",
      .$met2013 ==26420 ~"Houston - The Woodlands - Sugar Land",
      .$met2013 ==28660 ~"Killeen - Temple",
      .$met2013 ==29700 ~"Laredo",
      .$met2013 ==31180 ~"Lubbock",
      .$met2013 ==32580 ~"McAllen - Edinburg - Mission",
      .$met2013 ==33260 ~"Midland",
      .$met2013 ==36220 ~"Odessa",
      .$met2013 ==41660 ~"San Angelo",
      .$met2013 ==41700 ~"San Antonio - New Braunfels",
      .$met2013 ==46340 ~"Tyler",
      .$met2013 ==47380 ~"Waco",
      .$met2013 ==48660 ~"Wichita Falls"
    ))

The new database contains 14,863 observations.

3) Descriptive Statistics

General Summary:

myTXMetros%>%
  group_by(TXmet2013) %>%
  summarise(mean(trantime), sd(trantime), mySE(trantime))

## # A tibble: 19 x 4
##                               TXmet2013 `mean(trantime)` `sd(trantime)`
##                                   <chr>            <dbl>          <dbl>
##  1                             Amarillo         18.42975      22.160335
##  2                    Austin-Round Rock         25.89784      18.036476
##  3               Beaumont - Port Arthur         23.85714      22.312567
##  4              Brownsville - Harlingen         18.22034      10.647527
##  5              College Station - Bryan         21.43750      24.918314
##  6                       Corpus Christi         21.36453      23.844486
##  7      Dallas - Fort Worth - Arlington         27.95233      22.545452
##  8                              El Paso         24.07719      25.014806
##  9 Houston - The Woodlands - Sugar Land         29.52089      21.717294
## 10                               Laredo         21.27778      20.361358
## 11                              Lubbock         16.47727      17.345376
## 12         McAllen - Edinburg - Mission         23.05917      22.180994
## 13                              Midland         20.23404      16.808658
## 14                               Odessa         19.07895      12.101779
## 15                           San Angelo         27.55000      33.576510
## 16          San Antonio - New Braunfels         27.54078      21.971427
## 17                                Tyler         24.20225      27.622940
## 18                                 Waco         22.22314      18.555542
## 19                        Wichita Falls         13.43939       9.907462
## # ... with 1 more variables: `mySE(trantime)` <dbl>

Summary using the Linear Model

myPlot1<-lm(trantime~TXmet2013,data=myTXMetros)
tidy(myPlot1)

##                                             term   estimate std.error
## 1                                    (Intercept) 18.4297521  1.974511
## 2                     TXmet2013Austin-Round Rock  7.4680845  2.113218
## 3                TXmet2013Beaumont - Port Arthur  5.4273908  2.728667
## 4               TXmet2013Brownsville - Harlingen -0.2094131  2.810072
## 5               TXmet2013College Station - Bryan  3.0077479  2.968614
## 6                        TXmet2013Corpus Christi  2.9347800  2.494503
## 7       TXmet2013Dallas - Fort Worth - Arlington  9.5225792  2.015647
## 8                               TXmet2013El Paso  5.6474409  2.356677
## 9  TXmet2013Houston - The Woodlands - Sugar Land 11.0911380  2.028035
## 10                               TXmet2013Laredo  2.8480257  3.023288
## 11                              TXmet2013Lubbock -1.9524793  2.733586
## 12         TXmet2013McAllen - Edinburg - Mission  4.6294195  2.586516
## 13                              TXmet2013Midland  1.8042905  3.733062
## 14                               TXmet2013Odessa  0.6491953  4.038929
## 15                           TXmet2013San Angelo  9.1202479  3.961343
## 16          TXmet2013San Antonio - New Braunfels  9.1110259  2.119101
## 17                                TXmet2013Tyler  5.7724951  3.033012
## 18                                 TXmet2013Waco  3.7933884  2.792380
## 19                        TXmet2013Wichita Falls -4.9903581  3.323597
##      statistic      p.value
## 1   9.33383222 1.283309e-20
## 2   3.53398687 4.115336e-04
## 3   1.98902642 4.673054e-02
## 4  -0.07452232 9.405965e-01
## 5   1.01318251 3.110021e-01
## 6   1.17649898 2.394287e-01
## 7   4.72432818 2.346104e-06
## 8   2.39635749 1.658058e-02
## 9   5.46890853 4.657666e-08
## 10  0.94202934 3.462046e-01
## 11 -0.71425559 4.750889e-01
## 12  1.78982838 7.351737e-02
## 13  0.48332721 6.288760e-01
## 14  0.16073450 8.723064e-01
## 15  2.30231212 2.134181e-02
## 16  4.29947667 1.731281e-05
## 17  1.90322191 5.704561e-02
## 18  1.35847864 1.743482e-01
## 19 -1.50149322 1.332655e-01

Box Plot

myTXMetros%>%
  ggplot(.)+
  geom_boxplot(aes(TXmet2013,trantime))+
  ggtitle("Box Plot for Comute Time in Texas Metro Areas")+
  coord_flip()+
  xlab("Metro Area")+
  ylab("Commute Time")

Graph (Linear Model) of Commute Times in Texas Metros

qqnorm(rstudent(myPlot1), main="Q-Q Plot for Commute Times in Texas")
qqline(rstudent(myPlot1), col=2)

Transforamtion using Square Root

myPlot2<-lm(sqrt(trantime)~TXmet2013,data=myTXMetros)
tidy(myPlot2)

##                                             term   estimate std.error
## 1                                    (Intercept)  3.9106054 0.1622638
## 2                     TXmet2013Austin-Round Rock  0.9066938 0.1736627
## 3                TXmet2013Beaumont - Port Arthur  0.6255438 0.2242398
## 4               TXmet2013Brownsville - Harlingen  0.1821689 0.2309296
## 5               TXmet2013College Station - Bryan  0.3218004 0.2439585
## 6                        TXmet2013Corpus Christi  0.3252899 0.2049963
## 7       TXmet2013Dallas - Fort Worth - Arlington  1.0467210 0.1656444
## 8                               TXmet2013El Paso  0.6395462 0.1936699
## 9  TXmet2013Houston - The Woodlands - Sugar Land  1.2051111 0.1666624
## 10                               TXmet2013Laredo  0.4110962 0.2484515
## 11                              TXmet2013Lubbock -0.1202756 0.2246441
## 12         TXmet2013McAllen - Edinburg - Mission  0.5671799 0.2125579
## 13                              TXmet2013Midland  0.2600347 0.3067802
## 14                               TXmet2013Odessa  0.2291389 0.3319162
## 15                           TXmet2013San Angelo  0.8106906 0.3255402
## 16          TXmet2013San Antonio - New Braunfels  1.0427744 0.1741461
## 17                                TXmet2013Tyler  0.5974084 0.2492506
## 18                                 TXmet2013Waco  0.5251029 0.2294757
## 19                        TXmet2013Wichita Falls -0.4050950 0.2731307
##     statistic       p.value
## 1  24.1002949 3.651938e-124
## 2   5.2210060  1.821977e-07
## 3   2.7896198  5.288838e-03
## 4   0.7888505  4.302215e-01
## 5   1.3190787  1.871786e-01
## 6   1.5868082  1.125936e-01
## 7   6.3190862  2.764530e-10
## 8   3.3022478  9.631228e-04
## 9   7.2308525  5.219080e-13
## 10  1.6546336  9.803605e-02
## 11 -0.5354051  5.923839e-01
## 12  2.6683546  7.636956e-03
## 13  0.8476253  3.966708e-01
## 14  0.6903519  4.899919e-01
## 15  2.4902935  1.278286e-02
## 16  5.9879277  2.212265e-09
## 17  2.3968178  1.655978e-02
## 18  2.2882725  2.214628e-02
## 19 -1.4831544  1.380708e-01

Square Root Graph

qqnorm(rstudent(myPlot2), main="Q-Q Plot")
qqline(rstudent(myPlot2), col=2)

Reciprocal Transformation

myPlot3<-lm(I(1/trantime)~TXmet2013,data=myTXMetros)
tidy(myPlot3)

##                                             term     estimate   std.error
## 1                                    (Intercept)  0.114731096 0.008114440
## 2                     TXmet2013Austin-Round Rock -0.047199567 0.008684471
## 3                TXmet2013Beaumont - Port Arthur -0.027517223 0.011213717
## 4               TXmet2013Brownsville - Harlingen -0.029813151 0.011548259
## 5               TXmet2013College Station - Bryan -0.030526691 0.012199803
## 6                        TXmet2013Corpus Christi -0.023422716 0.010251397
## 7       TXmet2013Dallas - Fort Worth - Arlington -0.047936517 0.008283495
## 8                               TXmet2013El Paso -0.043197705 0.009684989
## 9  TXmet2013Houston - The Woodlands - Sugar Land -0.051231649 0.008334403
## 10                               TXmet2013Laredo -0.042261031 0.012424489
## 11                              TXmet2013Lubbock -0.015041440 0.011233934
## 12         TXmet2013McAllen - Edinburg - Mission -0.039115915 0.010629534
## 13                              TXmet2013Midland -0.025465939 0.015341375
## 14                               TXmet2013Odessa -0.020480887 0.016598366
## 15                           TXmet2013San Angelo -0.041898073 0.016279517
## 16          TXmet2013San Antonio - New Braunfels -0.052562620 0.008708648
## 17                                TXmet2013Tyler -0.037161573 0.012464453
## 18                                 TXmet2013Waco -0.040610033 0.011475551
## 19                        TXmet2013Wichita Falls -0.009730824 0.013658638
##     statistic      p.value
## 1  14.1391263 7.079216e-45
## 2  -5.4349388 5.634515e-08
## 3  -2.4538895 1.415212e-02
## 4  -2.5816144 9.850657e-03
## 5  -2.5022282 1.236022e-02
## 6  -2.2848316 2.234742e-02
## 7  -5.7869919 7.421893e-09
## 8  -4.4602739 8.291528e-06
## 9  -6.1470087 8.254306e-10
## 10 -3.4014301 6.734553e-04
## 11 -1.3389290 1.806299e-01
## 12 -3.6799276 2.347544e-04
## 13 -1.6599515 9.696138e-02
## 14 -1.2339099 2.172709e-01
## 15 -2.5736681 1.007959e-02
## 16 -6.0356807 1.649776e-09
## 17 -2.9814043 2.877492e-03
## 18 -3.5388306 4.040670e-04
## 19 -0.7124301 4.762182e-01

Reciprocal Graph

qqnorm(rstudent(myPlot3), main="Q-Q Plot for Reciprocal Family Size")

Histogram

myTXMetros%>%
   ggplot(.)+geom_histogram(aes(trantime))+facet_wrap(~TXmet2013)+ggtitle(label = "Histogram Texas Metros Commute Times")

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

4)ANOVA

The ANOVA itself:

anova(myPlot1)

## Analysis of Variance Table
## 
## Response: trantime
##             Df  Sum Sq Mean Sq F value    Pr(>F)    
## TXmet2013   18   88806  4933.7  10.458 < 2.2e-16 ***
## Residuals 8434 3978670   471.7                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

t-Test for lowest (Wichita Falls) and highest (Houston Area), finding a true difference:

myWF<-subset(myTXMetros,TXmet2013=="Wichita Falls")
myHou<-subset(myTXMetros,TXmet2013=="Houston - The Woodlands - Sugar Land")

t.test(myHou$trantime,myWF$trantime)

## 
##  Welch Two Sample t-test
## 
## data:  myHou$trantime and myWF$trantime
## t = 12.329, df = 85.018, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  13.48803 18.67496
## sample estimates:
## mean of x mean of y 
##  29.52089  13.43939

Homework 6

Tobias Kuhn

October 4, 2017

Loading libraries and IPUMS data.

1 and 2) clear up missing values for Travel Time and remove poputaltion not in a metro area

2)Mutating the database to reduce the observations to Texas Metro Areas and labeling the areas

The Metro List:

Code Metro Area

11100 Amarillo

12420 Austin-Round Rock

13140 Beaumont - Port Arthur

15180 Brownsville - Harlingen

17780 College Station - Bryan

18580 Corpus Christi

19100 Dallas - Fort Worth - Arlington

21340 El Paso

26420 Houston - The Woodlands - Sugar Land

28660 Killeen - Temple

29700 Laredo

31180 Lubbock

32580 McAllen - Edinburg - Mission

33260 Midland

36220 Odessa

41660 San Angelo

41700 San Antonio - New Braunfels

46340 Tyler

47380 Waco

48660 Wichita Falls

The new database contains 14,863 observations.

3) Descriptive Statistics

General Summary:

Summary using the Linear Model

Box Plot

Graph (Linear Model) of Commute Times in Texas Metros

Transforamtion using Square Root

Square Root Graph

Reciprocal Transformation

Reciprocal Graph

Histogram

4)ANOVA

The ANOVA itself:

t-Test for lowest (Wichita Falls) and highest (Houston Area), finding a true difference: