MAKE HTML DOCUMENT--- title: "Assignment 4" author: "Your name and ID here" date: "01/02/2020"...

Question

MAKE HTML DOCUMENT--- title: "Assignment 4" author: "Your name and ID here" date: "01/02/2020" output: html_document --- ```{r setup, include=FALSE} knitr::opts_chunk$set(echo = TRUE) # packages  library(AER) library(tidyverse) library(wooldridge) # load model summary and set options library(modelsummary) gm %    filter(complete.cases(.)) ``` Consider the generic regression: $$ y  = \beta_0 + \beta_1 x_1 + \beta_2 x_1^2 + \beta_3 x_2 + \beta_4 x_3 + \beta_5 (x_2\cdot x_3) + u $$ Here, the variable $x_1$ is entered into the regression twice -- once as a 'main' effect and once as a squared term.  Consider the partial effect of increasing $x_1$ by 1 unit. $$ \frac{\partial y}{\partial x_1} = \beta_1 + \beta_2 x_1 $$ This says that the marginal impact on $y$ from a one unit increase in $x_1$ is not a constant, but a function.  The impact depends on the value of $x_1$. For example, suppose that $\beta_1$ is positive and $\beta_2$ is negative.  This means that the relationship between $y$ and $x_1$ exhibits decreasing marginal returns.  That is, when $x_1$ increases from 0 to 1, the $\frac{\partial y}{\partial x_1}$ is higher than going from 2 to 3 and so on.  If we graph this, it would look like an inverted 'U'. For example, it might look like: ```{r} fig.data %    mutate(y = 100 + 20 * x - 1.5*x^2) ggplot(fig.data, aes(y = y, x = x)) +    geom_line() +    labs(title = "Typical diminishing marginal returns profile") ``` We can find the the point at which `x_1` turns from positive to negative (the inflection point) but setting $\frac{\partial y}{\partial x_1} = 0$ and solving for $x_1$.  This yields $$ x^*_1 = \left|\frac{\beta_1}{2\cdot \beta_2}ight|. $$ The variables $x_2$ and $x_3$ also appear twice; each as an main effect and then as an interaction.  Consider the partial effect of $x_2$ on $y$ $$ \frac{\partial y}{\partial x_2} = \beta_3 + \beta_5 x_2 $$ Again, this says that the impact of $x_2$ on $y$ is not a constant. It allows the impact to depend on the value of $x_3$.  The treatment of $x_3$ is symmetric.  We most often use these types of interactions when one term is a dummy variable. Suppose $x_3$ only takes on two values, 1 and 0.  Then $$ \frac{\partial y}{\partial x_2} = \beta_3 + \beta_5 	ext{ when } x_3 = 1 	ext{ and } \frac{\partial y}{\partial x_2} = \beta_3 	ext{ when } x_3 = 0 $$ Since dummy variables denote groups (ie, 2 groups), this allows each group to have its own intercept ($\beta_4$) and slope.  Graphically, it looks like: ```{r} ggplot(wage1 %>% filter(educ>5), aes(y = lwage, x = educ, color = factor(west))) +    geom_smooth(method = 'lm', se = F) ``` Where each line is a regression of log wages on education, with an interaction for living in the west.  The return education for workers in the western United States in this data is higher than the return for those in the rest of the country.  In `R`, we can create variables "on the fly" to use in regressions.  We use this mostly to create interaction terms and low order polynomial terms. Consider the following code that would estimate the following equation $$ y  = \beta_0 + \beta_1 x_1 + \beta_2 x_1^2 + \beta_3 x_2 + \beta_4 x_3 + \beta_5 (x_2\cdot x_3) + u $$ In the code below, each regression is exactly the same, just different ways of expressing it: ```{r, eval = F} mod %    filter(complete.cases(.)) # fit models models  Daniel S. Hamermesh, Amy Parker, Beauty in the classroom: instructors pulchritude and putative pedagogical productivity, Economics of Education Review, Volume 24, Issue 4, August 2005, Pages 369-376, ISSN 0272-7757, 10.1016/j.econedurev.2004.07.013.  [Paper link - not required to read](http://www.sciencedirect.com/science/article/pii/S0272775704001165) ```{r} data("TeachingRatings")  # load ratings data df

Mohd · Accepted Answer

Assignment 4
Assignment 4
Alain
5/12/2020
library(AER)
## Loading required package: car
## Loading required package: carData
## Loading required package: lmtest
## Loading required package: zoo
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
## Loading required package: sandwich
## Loading required package: survival
library(tidyverse)
## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──
## ✓ ggplot2 3.3.2     ✓ purrr   0.3.4
## ✓ tibble  3.0.4     ✓ dplyr   1.0.2
## ✓ tidyr   1.1.2     ✓ stringr 1.4.0
## ✓ readr   1.4.0     ✓ forcats 0.5.0
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()
## x dplyr::recode() masks car::recode()
## x purrr::some()   masks car::some()
library(wooldridge)
install.packages("modelsummary")
## Installing package into '/home/rstudio-user/R/x86_64-pc-linux-gnu-library/4.0'
## (as 'lib' is unspecified)
gm % 
  filter(complete.cases(.))
Consider the generic regression: $$
y  = \beta_0 + \beta_1 x_1 + \beta_2 x_1^2 + \beta_3 x_2 + \beta_4 x_3 + \beta_5 (x_2\cdot x_3) + u
$$ Here, the variable $x_1$ is entered into the regression twice – once as a ‘main’ effect and once as a squared term. Consider the partial effect of increasing $x_1$ by 1 unit. $$
\frac{\partial y}{\partial x_1} = \beta_1 + \beta_2 x_1
$$ This says that the marginal impact on $y$ from a one unit increase in $x_1$ is not a constant, but a function. The impact depends on the value of $x_1$. For example, suppose that $\beta_1$ is positive and $\beta_2$ is negative. This means that the relationship between $y$ and $x_1$ exhibits decreasing marginal returns. That is, when $x_1$ increases from 0 to 1, the $\frac{\partial y}{\partial x_1}$ is higher than going from 2 to 3 and so on. If we graph this, it would look like an inverted ‘U’. For example, it might look like:
library(dplyr)
library(ggplot2)
fig.data % 
  mutate(y = 100 + 20 * x - 1.5*x^2)
ggplot(fig.data, aes(y = y, x = x)) + 
  geom_line() + 
  labs(title = "Typical diminishing marginal returns profile")
 We can find the the point at which x_1 turns from positive to negative (the inflection point) but setting $\frac{\partial y}{\partial x_1} = 0$ and solving for $x_1$. This yields $$
x^*_1 = \left|\frac{\beta_1}{2\cdot \beta_2}\right|.
$$
The variables $x_2$ and $x_3$ also appear twice; each as an main effect and then as an interaction. Consider the partial effect of $x_2$ on $y$ $$
\frac{\partial y}{\partial x_2} = \beta_3 + \beta_5 x_2
$$ Again, this says that the impact of $x_2$ on $y$ is not a constant. It allows the impact to depend on the value of $x_3$. The treatment of $x_3$ is symmetric. We most often use these types of interactions when one term is a dummy variable. Suppose $x_3$ only takes on two values, 1 and 0. Then $$
\frac{\partial y}{\partial x_2} = \beta_3 + \beta_5 \text{ when } x_3 = 1 \text{ and } \frac{\partial y}{\partial x_2} = \beta_3 \text{ when } x_3 = 0
$$ Since dummy variables denote groups (ie, 2 groups), this allows each group to have its own intercept ($\beta_4$) and slope. Graphically, it looks like:
head(wage1)
##   wage educ exper tenure nonwhite female married numdep smsa northcen south
## 1 3.10   11     2      0        0      1       0      2    1        0     0
## 2 3.24   12    22      2        0      1       1      3    1        0     0
## 3 3.00   11     2      0        0      0       0      2    0        0     0
## 4 6.00    8    44     28        0      0       1      0    1        0     0
## 5 5.30   12     7      2        0      0       1      1    0        0     0
## 6 8.75   16     9      8        0      0       1      0    1        0     0
##   west construc ndurman trcommpu trade services profserv profocc clerocc
## 1    1        0       0        0     0        0        0       0       0
## 2    1        0       0        0     0        1        0       0       0
## 3    1        0       0        0     1        0        0       0       0
## 4    1        0       0        0     0        0        0       0       1
## 5    1        0       0        0     0        0        0       0       0
## 6    1        0       0        0     0        0        1       1       0
##   servocc    lwage expersq tenursq
## 1       0 1.131402       4       0
## 2       1 1.175573     484       4
## 3       0 1.098612       4       0
## 4       0 1.791759    1936     784
## 5       0 1.667707      49       4
## 6       0 2.169054      81      64
ggplot(wage1 %>% filter(educ>5), aes(y = lwage, x = educ, color = factor(west))) + 
  geom_smooth(method = 'lm', se = F)
## `geom_smooth()` using formula 'y ~ x'
Where each line is a regression of log wages on education, with an interaction for living in the west. The return education for workers in the western United States in this data is higher than the return for those in the rest of the country.
In R, we can create variables “on the fly” to use in regressions. We use this mostly to create interaction terms and low order polynomial terms. Consider the following code that would estimate the following equation $$
y  = \beta_0 + \beta_1 x_1 + \beta_2 x_1^2 + \beta_3 x_2 + \beta_4 x_3 + \beta_5 (x_2\cdot x_3) + u
$$ In the code below, each regression is exactly the same, just different ways of expressing it:
The term I() is an “insulator function”. It tells R to evaluate the expression inside first, then run the regression. The notation for x_2*x_3 says to include main effects for each variable, plus and interaction. The notation x_2:x_3 just includes an interaction. Finally, poly() constructs low order polynomials. The raw=T option is important.
wage1 % 
  filter(complete.cases(.))
# fit models
models 
## 
max(df$allstudents)
## [1] 581
#Construct a variable called frac that is the proportion of students in the class that filled out the evaluation.
mutate(df,frac=students/allstudents)
##     minority age gender credits     beauty eval division native tenure students
## 1        yes  36 female    more  0.2899157  4.3    upper    yes    yes       24
## 2         no  59   male    more -0.7377322  4.5    upper    yes    yes       17
## 3         no  51   male    more -0.5719836  3.7    upper    yes    yes       55
## 4         no  40 female    more -0.6779634  4.3    upper    yes    yes       40
## 5         no  31 female    more  1.5097940  4.4    upper    yes    yes       42
## 6         no  62   male    more  0.5885687  4.2    upper    yes    yes      182
## 7         no  33 female    more -0.1260010  4.0    upper    yes    yes       33
## 8         no  51 female    more -0.2581899  3.4    upper    yes    yes       25
## 9         no  33 female    more  0.1496926  4.5    upper    yes    yes       48
## 10        no  47   male    more  0.5409170  3.9    upper    yes     no       16
## 11       yes  35   male    more  0.2316134  3.1    upper     no    yes       18
## 12        no  37   male    more -0.0666737  4.0    upper    yes     no       30
## 13        no  42   male    more  0.2168924  3.8    upper    yes    yes       28
## 14        no  49   male    more -0.2586962  3.4    upper     no    yes       30
## 15        no  37 female    more  0.5502878  2.9    upper    yes    yes       23
## 16        no  45   male    more -0.0620358  4.5    upper    yes    yes       23
## 17        no  56 female    more -0.9823852  4.0    upper    yes     no       27
## 18        no  48   male    more -0.0543440  3.8    lower    yes     no      100
## 19        no  46 female    more -0.0680143  4.3    upper    yes    yes       25
## 20        no  57 female    more  0.0294137  3.4    upper    yes     no       17
## 21        no  52 female    more  0.2394859  3.4    upper    yes     no       19
## 22       yes  29 female    more -0.8487269  3.3    upper     no    yes       19
## 23        no  62   male    more -0.7330914  4.3    upper    yes    yes       30
## 24        no  64   male    more -0.1111221  4.4    upper    yes    yes       15
## 25        no  34 female    more  1.7755170  4.6    upper    yes    yes       20
## 26        no  58   male    more -0.3218485  4.2    upper    yes    yes       84
## 27       yes  52   male    more  0.2116939  4.0    upper     no    yes       13
## 28        no  73   male    more -0.7176450  3.3    upper    yes    yes       12
## 29        no  70   male    more -0.7326927  4.4    upper    yes    yes       47
## 30        no  41 female    more  0.4081676  2.3    upper    yes    yes       10
## 31        no  63   male    more -0.0102077  3.5    upper    yes     no       28
## 32        no  47   male    more -0.9239570  4.7    upper    yes    yes       10
## 33        no  39   male    more  0.5766805  3.9    lower    yes    yes       86
## 34       yes  47 female    more -0.0836015  4.0    lower    yes    yes       21
## 35        no  54   male    more -1.0795580  4.3    upper    yes    yes       15
## 36       yes  44 female    more  1.0409020  3.8    upper    yes    yes       30
## 37       yes  47   male    more -1.0521080  3.8    upper    yes    yes       20
## 38        no  62   male    more -0.7277681  4.0    upper    yes    yes       12
## 39        no  60   male    more -0.3953965  4.6    upper    yes    yes       25
## 40        no  37   male    more  0.9333959  3.5    upper    yes    yes       15
## 41        no  42   male    more -0.2377786  4.7    upper    yes    yes       13
## 42        no  35   male    more  0.2749080  4.2    upper    yes    yes       42
## 43        no  39 female    more  1.9700230  3.4    lower    yes     no       22
## 44        no  49   male    more  1.0509500  3.9    upper    yes    yes       28
## 45        no  61   male    more  0.2418185  4.5    lower    yes    yes       22
## 46        no  33   male    more  1.3493950  4.7    upper    yes    yes       30
## 47        no  58 female    more  0.1115635  3.5    upper    yes    yes       26
## 48        no  56 female    more -0.2577254  3.7    upper    yes    yes       12
## 49        no  50 female    more -0.6562689  4.0    lower    yes     no       22
## 50        no  52   male    more -0.6563948  4.1    upper    yes    yes       57
## 51        no  33 female    more  0.7244775  4.4    upper    yes    yes       10
## 52        no  57   male    more  0.6318343  4.2    upper    yes    yes       69
## 53        no  38 female    more  1.0709440  4.5    upper    yes    yes       46
## 54        no  34 female    more -1.4504940  3.8    lower    yes    yes       54
## 55        no  34   male    more  1.1558800  3.1    upper    yes    yes       24
## 56        no  32   male    more -0.3260148  3.7    lower    yes    yes       85
## 57        no  42 female    more  0.8846435  3.9    lower    yes    yes       44
## 58        no  43 female    more -0.5583452  4.0    lower    yes    yes       35
## 59        no  35   male    more -0.3415543  3.3    upper     no    yes       11
## 60        no  62 female    more -0.5040575  3.1    upper    yes    yes       22
## 61        no  42   male    more -0.9005804  4.0    upper    yes    yes       45
## 62        no  39   male    more  0.6430142  4.3    upper    yes    yes       22
## 63        no  52 female    more  0.7735240  3.7    upper    yes    yes       64
## 64        no  52 female    more  1.0639380  3.4    upper    yes    yes       31
## 65        no  52 female    more -1.0903890  4.3    upper    yes     no       59
## 66        no  64   male    more -1.0691620  3.7    upper    yes    yes        9
## 67        no  50   male    more  1.4156950  4.2    upper    yes    yes       15
## 68        no  60   male    more -1.4229190  2.2    upper    yes    yes       23
## 69        no  51 female    more  0.3918222  3.0    upper    yes    yes       47
## 70        no  43   male    more -0.4899626  4.3    lower    yes    yes       19
## 71       yes  50   male  single -0.5835869  4.6    lower    yes     no       17
## 72        no  52   male    more  0.7566829  3.5    upper    yes    yes       46
## 73        no  51   male    more  0.8808186  4.6    lower    yes    yes      348
## 74        no  38   male    more -0.5665014  3.7    lower    yes    yes       44
## 75        no  47 female    more  0.3394037  3.8    lower    yes    yes       19
## 76       yes  43 female    more -0.1513687  3.6    lower    yes    yes       47
## 77        no  38 female    more -1.0249970  4.4    lower    yes     no       33
## 78        no  43   male    more -0.0252444  4.1    lower    yes    yes       10
## 79        no  57   male    more -0.7467875  4.3    upper    yes    yes        7
## 80        no  51 female    more  0.9889485  4.0    upper    yes    yes        9
## 81        no  45   male  single -0.5324199  4.8    lower    yes     no       12
## 82        no  57   male    more -0.7668921  3.5    lower    yes    yes       13
## 83        no  47 female    more  1.1542560  3.6    lower    yes     no       16
## 84       yes  54 female    more  1.2326020  3.8    lower    yes    yes       18
## 85        no  58   male    more  1.7743340  4.7    lower    yes     no       16
## 86        no  42   male    more  1.7731510  4.9    lower    yes    yes       15
## 87        no  33   male    more  0.7245926  4.3    lower    yes    yes       85
## 88        no  62   male    more -1.1816260  3.3    lower    yes    yes       11
## 89       yes  35 female    more  1.7694520  3.4    lower    yes    yes       60
## 90        no  61   male    more -0.5872612  3.6    lower    yes    yes       27
## 91        no  52 female    more -0.0018324  4.0    lower    yes    yes       61
## 92        no  60 female    more -0.0566766  3.9    upper     no    yes       23
## 93        no  32   male    more  1.2313940  4.3    lower    yes    yes       98
## 94       yes  42 female    more  0.4203998  3.3    upper     no    yes       48
## 95       yes  36 female    more  0.2899157  3.7    upper    yes    yes       86
## 96       yes  36 female    more  0.2899157  3.6    upper    yes    yes       76
## 97       yes  36 female    more  0.2899157  4.4    upper    yes    yes       77
## 98        no  59   male    more -0.7377322  4.0    upper    yes    yes       35
## 99        no  59   male    more -0.7377322  2.1    upper    yes    yes       39
## 100       no  51   male    more -0.5719836  3.2    upper    yes    yes      111
## 101       no  40 female    more -0.6779634  3.5    upper    yes    yes       24
## 102       no  40 female    more -0.6779634  4.1    upper    yes    yes       24
## 103       no  40 female    more -0.6779634  4.6    upper    yes    yes       17
## 104       no  40 female    more -0.6779634  3.8    upper    yes    yes       14
## 105       no  40 female    more -0.6779634  3.8    upper    yes    yes       37
## 106       no  40 female    more -0.6779634  3.8    upper    yes    yes       18
## 107       no  40 female    more -0.6779634  4.2    upper    yes    yes       15
## 108       no  31 female    more  1.5097940  3.9    upper    yes    yes       40
## 109       no  31 female    more  1.5097940  4.5    upper    yes    yes       38
## 110       no  31 female    more  1.5097940  4.5    upper    yes    yes       40
## 111       no  31 female    more  1.5097940  4.4    upper    yes    yes       52
## 112       no  31 female    more  1.5097940  4.4    upper    yes    yes       49
## 113       no  62   male    more  0.5885687  4.4    upper    yes    yes      160
## 114       no  62   male    more  0.5885687  4.5    upper    yes    yes       79
## 115       no  62   male    more  0.5885687  4.3    upper    yes    yes      176
## 116       no  62   male    more  0.5885687  4.6    upper    yes    yes      155
## 117       no  62   male    more  0.5885687  4.8    upper    yes    yes      166
## 118       no  62   male    more  0.5885687  4.3    upper    yes    yes      186
## 119       no  33 female    more -0.1260010  4.0    upper    yes    yes       29
## 120       no  33 female    more -0.1260010  4.0    upper    yes    yes       37
## 121       no  33 female    more -0.1260010  3.9    upper    yes    yes       29
## 122       no  33 female    more -0.1260010  3.3    upper    yes    yes       28
## 123       no  51 female    more -0.2581899  4.5    upper    yes    yes       21
## 124       no  51 female    more -0.2581899  4.5    upper    yes    yes       13
## 125       no  51 female    more -0.2581899  4.5    upper    yes    yes       16
## 126       no  51 female    more -0.2581899  2.5    lower    yes    yes       24
## 127       no  51 female    more -0.2581899  4.3    upper    yes    yes       23
## 128       no  51 female    more -0.2581899  4.5    upper    yes    yes       20
## 129       no  33 female    more  0.1496926  4.7    upper    yes    yes       29
## 130       no  33 female    more  0.1496926  3.5    upper    yes    yes       11
## 131       no  33 female    more  0.1496926  4.5    upper    yes    yes       29
## 132       no  33 female    more  0.1496926  3.8    upper    yes    yes       25
## 133       no  33 female    more  0.1496926  4.5    upper    yes    yes       42
## 134       no  33 female    more  0.1496926  4.3    upper    yes    yes       34
## 135       no  47   male    more  0.5409170  3.9    upper    yes     no       12
## 136       no  47   male    more  0.5409170  4.3    upper    yes     no       14
## 137       no  47   male    more  0.5409170  4.2    upper    yes     no       22
## 138       no  47   male    more  0.5409170  5.0    lower    yes     no       10
## 139       no  47   male    more  0.5409170  5.0    lower    yes     no       17
## 140       no  47   male    more  0.5409170  4.6    upper    yes     no       16
## 141       no  47   male    more  0.5409170  5.0    lower    yes     no       15
## 142       no  47   male    more  0.5409170  4.7    upper    yes     no       16
## 143       no  47   male    more  0.5409170  5.0    lower    yes     no       16
## 144      yes  35   male    more  0.2316134  2.7    upper     no    yes       30
## 145      yes  35   male    more  0.2316134  4.0    upper     no    yes       23
## 146       no  37   male    more -0.0666737  4.4    upper    yes     no       13
## 147       no  37   male    more -0.0666737  4.4    upper    yes     no       24
## 148       no  37   male    more -0.0666737  4.3    upper    yes     no       24
## 149       no  37   male    more -0.0666737  3.5    upper    yes     no       25
## 150       no  42   male    more  0.2168924  3.8    upper    yes    yes       18
## 151       no  42   male    more  0.2168924  3.9    upper    yes    yes       28
## 152       no  42   male    more  0.2168924  3.7    upper    yes    yes       25
## 153       no  42   male    more  0.2168924  3.3    upper    yes    yes       40
## 154       no  42   male    more  0.2168924  4.0    upper    yes    yes       40
## 155       no  42   male    more  0.2168924  3.8    upper    yes    yes       18
## 156       no  49   male    more -0.2586962  4.2    upper     no    yes       31
## 157       no  49   male    more -0.2586962  3.1    upper     no    yes       15
## 158       no  49   male    more -0.2586962  3.6    upper     no    yes       23
## 159       no  37 female    more  0.5502878  3.3    upper    yes    yes       34
## 160       no  37 female    more  0.5502878  2.9    upper    yes    yes       21
## 161       no  37 female    more  0.5502878  3.1    upper    yes    yes       29
## 162       no  45   male    more -0.0620358  4.0    lower    yes    yes       45
## 163       no  45   male    more -0.0620358  4.0    lower    yes    yes       90
## 164       no  45   male    more -0.0620358  4.2    upper    yes    yes       27
## 165       no  45   male    more -0.0620358  3.8    upper    yes    yes       35
## 166       no  45   male    more -0.0620358  4.3    lower    yes    yes      120
## 167       no  56 female    more -0.9823852  4.6    upper    yes     no       39
## 168       no  56 female    more -0.9823852  4.3    upper    yes     no       35
## 169       no  56 female    more -0.9823852  3.6    upper    yes     no       34
## 170       no  56 female    more -0.9823852  4.2    upper    yes     no       27
## 171       no  48   male    more -0.0543440  3.9    upper    yes     no       20
## 172       no  48   male    more -0.0543440  4.1    upper    yes     no       14
## 173       no  48   male    more -0.0543440  4.0    lower    yes     no       65
## 174       no  48   male    more -0.0543440  4.3    lower    yes     no       95
## 175       no  48   male    more -0.0543440  3.9    upper    yes     no       18
## 176       no  48   male    more -0.0543440  4.2    lower    yes     no       85
## 177       no  48   male    more -0.0543440  4.2    lower    yes     no      113
## 178       no  46 female    more -0.0680143  4.9    lower    yes    yes       14
## 179       no  46 female    more -0.0680143  4.0    upper    yes    yes       23
## 180       no  46 female    more -0.0680143  4.3    upper    yes    yes       23
## 181       no  46 female    more -0.0680143  4.9    upper    yes    yes        9
## 182       no  46 female    more -0.0680143  3.9    upper    yes    yes       30
## 183       no  46 female    more -0.0680143  4.9    lower    yes    yes       15
## 184       no  46 female    more -0.0680143  3.9    upper    yes    yes       31
## 185       no  46 female    more -0.0680143  4.0    lower    yes    yes       12
## 186       no  57 female    more  0.0294137  3.5    upper    yes     no       10
## 187       no  57 female    more  0.0294137  3.9    upper    yes     no       15
## 188       no  57 female    more  0.0294137  4.0    upper    yes     no        7
## 189       no  57 female    more  0.0294137  3.6    upper    yes     no        7
## 190       no  57 female    more  0.0294137  3.0    upper    yes     no       14
## 191       no  57 female    more  0.0294137  3.0    upper    yes     no        8
## 192       no  57 female    more  0.0294137  3.6    upper    yes     no       17
## 193       no  57 female    more  0.0294137  3.6    upper    yes     no       10
## 194       no  57 female    more  0.0294137  3.2    upper    yes     no       12
## 195       no  52 female    more  0.2394859  3.9    upper    yes     no       27
## 196       no  52 female    more  0.2394859  3.5    upper    yes     no       20
## 197       no  52 female    more  0.2394859  3.5    upper    yes     no       31
## 198       no  52 female  single  0.2394859  3.1    upper    yes     no       17
## 199       no  52 female    more  0.2394859  4.2    upper    yes     no       23
## 200       no  62   male    more -0.7330914  3.6    lower    yes    yes       94
## 201       no  62   male    more -0.7330914  4.5    upper    yes    yes       46
## 202       no  62   male    more -0.7330914  3.7    lower    yes    yes       80
## 203       no  62   male    more -0.7330914  3.4    lower    yes    yes       61
## 204       no  64   male    more -0.1111221  4.5    upper    yes    yes       51
## 205       no  64   male    more -0.1111221  4.6    upper    yes    yes       22
## 206       no  64   male    more -0.1111221  4.8    upper    yes    yes       10
## 207       no  64   male    more -0.1111221  4.5    upper    yes    yes       11
## 208       no  64   male    more -0.1111221  4.4    upper    yes    yes       15
## 209       no  64   male    more -0.1111221  4.1    upper    yes    yes       21
## 210       no  34 female    more  1.7755170  3.9    upper    yes    yes       33
## 211       no  58   male    more -0.3218485  4.3    upper    yes    yes       71
## 212       no  58   male    more -0.3218485  3.5    lower    yes    yes       36
## 213       no  58   male    more -0.3218485  4.0    upper    yes    yes       73
## 214       no  58   male    more -0.3218485  4.0    lower    yes    yes       31
## 215      yes  52   male    more  0.2116939  4.6    upper     no    yes       23
## 216      yes  52   male    more  0.2116939  4.6    upper     no    yes       12
## 217      yes  52   male    more  0.2116939  3.7    upper     no    yes       15
## 218      yes  52   male    more  0.2116939  3.5    upper     no    yes       11
## 219      yes  52   male    more  0.2116939  3.6    upper     no    yes       12
## 220      yes  52   male    more  0.2116939  3.9    upper     no    yes       18
## 221       no  73   male    more -0.7176450  4.2    upper    yes    yes       10
## 222       no  73   male    more -0.7176450  3.2    upper    yes    yes       16
## 223       no  73   male    more -0.7176450  4.9    upper    yes    yes       13
## 224       no  70   male    more -0.7326927  4.0    upper    yes    yes        5
## 225       no  70   male    more -0.7326927  3.5    upper    yes    yes       34
## 226       no  70   male    more -0.7326927  3.4    upper    yes    yes       24
## 227       no  63   male    more -0.0102077  4.2    upper    yes     no       11
## 228       no  63   male    more -0.0102077  3.5    upper    yes     no       10
## 229       no  63   male    more -0.0102077  4.4    upper    yes     no       14
## 230       no  63   male    more -0.0102077  3.7    upper    yes     no       12
## 231       no  63   male    more -0.0102077  3.4    upper    yes     no        8
## 232       no  63   male    more -0.0102077  3.0    upper    yes     no       23
## 233       no  47   male    more -0.9239570  3.9    upper    yes    yes       10
## 234       no  47   male    more -0.9239570  2.8    upper    yes    yes       10
## 235       no  39   male    more  0.5766805  3.7    lower    yes    yes      154
## 236       no  39   male    more  0.5766805  4.6    upper    yes    yes       12
## 237       no  39   male    more  0.5766805  4.2    upper    yes    yes       14
## 238       no  39   male    more  0.5766805  4.4    upper    yes    yes       27
## 239      yes  47 female    more -0.0836015  3.8    upper    yes    yes        8
## 240      yes  47 female  single -0.0836015  4.1    lower    yes    yes       16
## 241      yes  47 female    more -0.0836015  3.7    lower    yes    yes       24
## 242      yes  47 female    more -0.0836015  4.1    upper    yes    yes        7
## 243      yes  47 female    more -0.0836015  3.0    lower    yes    yes       25
## 244      yes  47 female    more -0.0836015  3.2    lower    yes    yes       24
## 245      yes  47 female    more -0.0836015  2.8    lower    yes    yes       24
## 246      yes  47 female  single -0.0836015  4.7    lower    yes    yes       20
## 247      yes  47 female    more -0.0836015  4.2    lower    yes    yes       12
## 248      yes  47 female    more -0.0836015  3.2    lower    yes    yes       25
## 249      yes  47 female    more -0.0836015  3.1    lower    yes    yes       26
## 250      yes  47 female    more -0.0836015  4.0    lower    yes    yes       24
## 251       no  54   male    more -1.0795580  4.2    upper    yes    yes       10
## 252       no  54   male    more -1.0795580  4.3    upper    yes    yes       16
## 253      yes  44 female    more  1.0409020  3.3    upper    yes    yes       35
## 254      yes  44 female    more  1.0409020  4.1    upper    yes    yes       21
## 255      yes  44 female    more  1.0409020  3.7    upper    yes    yes       35
## 256      yes  47   male    more -1.0521080  3.3    upper    yes    yes        9
## 257      yes  47   male    more -1.0521080  3.8    upper    yes    yes       21
## 258      yes  47   male    more -1.0521080  3.4    upper    yes    yes       13
## 259      yes  47   male    more -1.0521080  4.2    upper    yes    yes       13
## 260      yes  47   male    more -1.0521080  3.8    upper    yes    yes       12
## 261      yes  47   male    more -1.0521080  3.5    upper    yes    yes       14
## 262      yes  47   male    more -1.0521080  3.3    upper    yes    yes       15
## 263       no  62   male    more -0.7277681  4.3    upper    yes    yes       13
## 264       no  62   male    more -0.7277681  4.1    upper    yes    yes        7
## 265       no  60   male    more -0.3953965  4.5    upper    yes    yes       12
## 266       no  60   male    more -0.3953965  4.5    upper    yes    yes       11
## 267       no  60   male    more -0.3953965  4.6    upper    yes    yes        8
## 268       no  60   male    more -0.3953965  4.4    upper    yes    yes       24
## 269       no  60   male    more -0.3953965  4.1    upper    yes    yes       15
## 270       no  60   male    more -0.3953965  4.5    upper    yes    yes       31
## 271       no  60   male    more -0.3953965  4.3    lower    yes    yes       36
## 272       no  42   male    more -0.2377786  4.4    upper    yes    yes       14
## 273       no  42   male    more -0.2377786  4.9    upper    yes    yes       13
## 274       no  42   male    more -0.2377786  4.7    upper    yes    yes       12
## 275       no  42   male    more -0.2377786  4.6    upper    yes    yes       13
## 276       no  35   male    more  0.2749080  4.8    lower    yes    yes       21
## 277       no  35   male    more  0.2749080  4.2    upper    yes    yes       49
## 278       no  35   male    more  0.2749080  4.6    lower    yes    yes       44
## 279       no  39 female    more  1.9700230  4.7    upper    yes     no       18
## 280       no  39 female    more  1.9700230  4.6    upper    yes     no       20
## 281       no  39 female    more  1.9700230  3.6    lower    yes     no       27
## 282       no  49   male    more  1.0509500  3.9    upper    yes    yes       27
## 283       no  49   male    more  1.0509500  4.0    upper    yes    yes       49
## 284       no  61   male    more  0.2418185  4.4    upper    yes    yes       31
## 285       no  61   male    more  0.2418185  4.5    lower    yes    yes       19
## 286       no  61   male    more  0.2418185  4.4    upper    yes    yes       27
## 287       no  33   male    more  1.3493950  3.0    upper    yes    yes       12
## 288       no  33   male    more  1.3493950  3.7    upper    yes    yes       13
## 289       no  56 female    more -0.2577254  3.6    upper    yes    yes       16
## 290       no  56 female    more -0.2577254  3.1    upper    yes    yes       17
## 291       no  50 female  single -0.6562689  3.8    lower    yes     no       24
## 292       no  50 female  single -0.6562689  4.7    lower    yes     no       14
## 293       no  50 female    more -0.6562689  3.8    upper    yes     no       23
## 294       no  50 female    more -0.6562689  3.8    upper    yes     no       19
## 295       no  50 female    more -0.6562689  2.8    upper    yes     no       18
## 296       no  50 female    more -0.6562689  4.0    upper    yes     no       23
## 297       no  52   male    more -0.6563948  4.0    upper    yes    yes       81
## 298       no  52   male    more -0.6563948  3.5    upper    yes    yes       74
## 299       no  52   male    more -0.6563948  3.4    upper    yes    yes      102
## 300       no  52   male    more -0.6563948  4.0    upper    yes    yes       94
## 301       no  52   male    more -0.6563948  3.5    upper    yes    yes       89
## 302       no  52   male    more -0.6563948  3.8    upper    yes    yes      133
## 303       no  52   male    more -0.6563948  4.7    upper    yes    yes       22
## 304       no  52   male    more -0.6563948  3.9    upper    yes    yes       78
## 305       no  52   male    more -0.6563948  4.5    upper    yes    yes       22
## 306       no  52   male    more -0.6563948  4.2    upper    yes    yes       27
## 307       no  52   male    more -0.6563948  4.7    upper    yes    yes       27
## 308       no  52   male    more -0.6563948  4.0    upper    yes    yes       60
## 309       no  33 female    more  0.7244775  4.8    upper    yes    yes       10
## 310       no  33 female    more  0.7244775  4.8    upper    yes    yes       10
## 311       no  33 female    more  0.7244775  4.4    upper    yes    yes       10
## 312       no  33 female    more  0.7244775  4.7    upper    yes    yes        7
## 313       no  33 female    more  0.7244775  4.5    upper    yes    yes       14
## 314       no  57   male    more  0.6318343  4.2    upper    yes    yes       36
## 315       no  57   male    more  0.6318343  4.4    upper    yes    yes       72
## 316       no  57   male    more  0.6318343  4.1    upper    yes    yes       63
## 317       no  38 female    more  1.0709440  4.2    lower    yes    yes      109
## 318       no  38 female    more  1.0709440  4.8    upper    yes    yes       54
## 319       no  38 female    more  1.0709440  4.4    upper    yes    yes       51
## 320       no  38 female    more  1.0709440  4.7    upper    yes    yes       61
## 321       no  38 female    more  1.0709440  4.2    lower    yes    yes      102
## 322       no  38 female    more  1.0709440  4.5    upper    yes    yes       58
## 323       no  34 female    more -1.4504940  3.4    lower    yes    yes       46
## 324       no  34 female    more -1.4504940  3.7    lower    yes    yes       53
## 325       no  34 female    more -1.4504940  3.6    upper    yes    yes       19
## 326       no  34 female    more -1.4504940  3.9    upper    yes    yes       41
## 327       no  34 female    more -1.4504940  3.9    upper    yes    yes       25
## 328       no  34   male    more  1.1558800  3.7    upper    yes    yes       16
## 329       no  34   male    more  1.1558800  3.0    lower    yes    yes       20
## 330       no  32   male    more -0.3260148  3.6    lower    yes    yes       69
## 331       no  32   male    more -0.3260148  3.6    lower    yes    yes       98
## 332       no  32   male    more -0.3260148  4.3    upper    yes    yes       20
## 333       no  32   male    more -0.3260148  4.5    upper    yes    yes       72
## 334       no  42 female    more  0.8846435  3.9    upper    yes    yes       51
## 335       no  43 female    more -0.5583452  4.6    upper    yes    yes       18
## 336       no  43 female    more -0.5583452  4.1    lower    yes    yes       26
## 337       no  43 female    more -0.5583452  4.

--- title: "Assignment 4" author: "Your name and ID here" date: "01/02/2020" output: html_document --- ```{r setup, include=FALSE} knitr::opts_chunk$set(echo = TRUE) # packages library(AER)...

Answer To: --- title: "Assignment 4" author: "Your name and ID here" date: "01/02/2020" output: html_document...

Answer To This Question Is Available To Download

Related Questions & Answers

Submit New Assignment