Final Project
Olivia Ogutu
2025-12-09
Introduction
To what extent do work-related variables and demographics predict one’s annual income?
The dataset I chose is called American Community Survey, 2012 which I got from the OpenIntro website. The dataset contains 2000 observations and 13 variables. The reason I chose this topic is because I feel that as a college student or for high school students who are about to graduate, as we plan for our future, it is important to know the factors that can affect our annual income. This will help us plan accordingly and be aware of how our income is predicted and the biases and inequalities that come with it based on factual data. The dataset had variables such as: age, gender, employment status, income, citizen, language spoken, disability, hours worked, age, education level and more. The specific variables that I chose to work with were:
- income
- hrs_work
- age
- gender
- income
- edu
Data Analysis
I start by creating a dataframe with the CSV file and look through my data using the structure function to see the kind of data I will be working with if they are characters, numeric or integers. This will also let me know if I may need to factor any of the variables.
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.1 ✔ stringr 1.5.2
## ✔ ggplot2 4.0.0 ✔ tibble 3.3.0
## ✔ lubridate 1.9.4 ✔ tidyr 1.3.1
## ✔ purrr 1.1.0
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## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(dplyr)
library(tibble)
library(car)## Warning: package 'car' was built under R version 4.5.2## Loading required package: carData## Warning: package 'carData' was built under R version 4.5.2##
## Attaching package: 'car'
##
## The following object is masked from 'package:dplyr':
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## recode
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## The following object is masked from 'package:purrr':
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## someAmerican_survey_data <- read.csv("acs12.csv")
str(American_survey_data)## 'data.frame': 2000 obs. of 13 variables:
## $ income : int 60000 0 NA 0 0 1700 NA NA NA 45000 ...
## $ employment : chr "not in labor force" "not in labor force" NA "not in labor force" ...
## $ hrs_work : int 40 NA NA NA NA 40 NA NA NA 84 ...
## $ race : chr "white" "white" "white" "white" ...
## $ age : int 68 88 12 17 77 35 11 7 6 27 ...
## $ gender : chr "female" "male" "female" "male" ...
## $ citizen : chr "yes" "yes" "yes" "yes" ...
## $ time_to_work: int NA NA NA NA NA 15 NA NA NA 40 ...
## $ lang : chr "english" "english" "english" "other" ...
## $ married : chr "no" "no" "no" "no" ...
## $ edu : chr "college" "hs or lower" "hs or lower" "hs or lower" ...
## $ disability : chr "no" "yes" "no" "no" ...
## $ birth_qrtr : chr "jul thru sep" "jan thru mar" "oct thru dec" "oct thru dec" ...head(American_survey_data)## income employment hrs_work race age gender citizen time_to_work
## 1 60000 not in labor force 40 white 68 female yes NA
## 2 0 not in labor force NA white 88 male yes NA
## 3 NA <NA> NA white 12 female yes NA
## 4 0 not in labor force NA white 17 male yes NA
## 5 0 not in labor force NA white 77 female yes NA
## 6 1700 employed 40 other 35 female yes 15
## lang married edu disability birth_qrtr
## 1 english no college no jul thru sep
## 2 english no hs or lower yes jan thru mar
## 3 english no hs or lower no oct thru dec
## 4 other no hs or lower no oct thru dec
## 5 other no hs or lower yes jul thru sep
## 6 other yes hs or lower yes jul thru septail(American_survey_data)## income employment hrs_work race age gender citizen time_to_work
## 1995 65000 employed 48 white 53 male yes 45
## 1996 0 not in labor force NA white 71 female yes NA
## 1997 0 not in labor force NA other 50 female no NA
## 1998 70000 employed 40 asian 63 male yes 30
## 1999 105000 employed 50 asian 36 male yes 30
## 2000 0 unemployed NA black 22 male yes NA
## lang married edu disability birth_qrtr
## 1995 english yes hs or lower yes oct thru dec
## 1996 english yes hs or lower no oct thru dec
## 1997 other yes hs or lower no jul thru sep
## 1998 english no college no jan thru mar
## 1999 english yes college no apr thru jun
## 2000 english no college no oct thru decI then check the dataframe for any missing values using the ColSums function. However, since I am doing a multiple regression, any variable with NA’s is dropped in the model. Though it is still important to know.
colSums(is.na(American_survey_data))## income employment hrs_work race age gender
## 377 395 1041 0 0 0
## citizen time_to_work lang married edu disability
## 0 1217 105 0 58 0
## birth_qrtr
## 0Next, I create a subset from the main dataframe where I will select only the columns that I need which will makes the work cleaner and easier to follow. I did this by using the select function.
survey_data <- American_survey_data |>
select(income, hrs_work, race, gender, edu, age)
survey_data## income hrs_work race gender edu age
## 1 60000 40 white female college 68
## 2 0 NA white male hs or lower 88
## 3 NA NA white female hs or lower 12
## 4 0 NA white male hs or lower 17
## 5 0 NA white female hs or lower 77
## 6 1700 40 other female hs or lower 35
## 7 NA NA white male hs or lower 11
## 8 NA NA other male hs or lower 7
## 9 NA NA asian male hs or lower 6
## 10 45000 84 white male hs or lower 27
## 11 NA NA white female hs or lower 8
## 12 8600 23 white female hs or lower 69
## 13 0 NA white male college 69
## 14 0 NA black male hs or lower 17
## 15 NA NA white male hs or lower 10
## 16 33500 55 white male hs or lower 52
## 17 4000 8 white female hs or lower 67
## 18 19000 35 white female college 36
## 19 NA NA white female hs or lower 12
## 20 3400 25 white male hs or lower 40
## 21 0 NA black male hs or lower 27
## 22 1200 12 white female hs or lower 18
## 23 140000 40 white female hs or lower 35
## 24 0 8 white female college 31
## 25 12000 23 asian female hs or lower 32
## 26 45000 72 black male hs or lower 35
## 27 150000 40 white male college 51
## 28 0 NA white female grad 37
## 29 0 NA white female hs or lower 47
## 30 70000 50 black male college 50
## 31 12000 35 asian female hs or lower 20
## 32 24500 40 white male hs or lower 61
## 33 45000 40 white female college 61
## 34 0 NA asian male hs or lower 70
## 35 70000 35 white female college 43
## 36 35000 40 white male hs or lower 27
## 37 0 NA white female hs or lower 60
## 38 15000 8 white female hs or lower 20
## 39 31000 40 white female hs or lower 32
## 40 NA NA black female hs or lower 3
## 41 0 NA white female hs or lower 63
## 42 19000 70 white male hs or lower 28
## 43 50000 45 asian male grad 48
## 44 85000 50 white male college 33
## 45 100000 40 white male college 27
## 46 0 NA white female hs or lower 21
## 47 49000 55 white male grad 32
## 48 0 NA black male hs or lower 34
## 49 9600 24 white female hs or lower 33
## 50 0 NA white male hs or lower 83
## 51 333000 55 white male grad 75
## 52 NA NA white female hs or lower 14
## 53 0 NA white male college 65
## 54 0 NA black female hs or lower 18
## 55 NA NA white male hs or lower 4
## 56 NA NA white female hs or lower 14
## 57 NA NA white female hs or lower 6
## 58 0 NA white female hs or lower 33
## 59 70000 50 white male college 37
## 60 NA NA white male hs or lower 11
## 61 NA NA white male <NA> 2
## 62 15000 20 white female grad 64
## 63 NA NA white female hs or lower 13
## 64 NA NA white male <NA> 2
## 65 6500 10 white male hs or lower 22
## 66 0 NA black male hs or lower 61
## 67 0 NA white female hs or lower 70
## 68 0 NA white female hs or lower 65
## 69 0 NA black male hs or lower 27
## 70 0 NA black female hs or lower 56
## 71 NA NA white male hs or lower 7
## 72 0 NA white female grad 77
## 73 0 NA black male hs or lower 30
## 74 1200 25 white male hs or lower 31
## 75 5000 20 asian female college 44
## 76 0 NA white female grad 77
## 77 60000 40 black male hs or lower 50
## 78 0 NA white male grad 63
## 79 0 NA white female hs or lower 74
## 80 0 50 white male hs or lower 54
## 81 33000 45 white female college 28
## 82 60000 50 white male hs or lower 56
## 83 0 NA white male hs or lower 36
## 84 NA NA white female hs or lower 11
## 85 0 NA white male hs or lower 68
## 86 NA NA white female hs or lower 3
## 87 31000 38 white female hs or lower 62
## 88 35000 40 white female hs or lower 50
## 89 70000 50 white male grad 38
## 90 NA NA black male hs or lower 9
## 91 0 NA other female hs or lower 20
## 92 42000 40 white female hs or lower 50
## 93 8000 35 white female hs or lower 43
## 94 NA NA white female <NA> 0
## 95 18000 50 asian male hs or lower 50
## 96 0 50 white female grad 46
## 97 NA NA white female hs or lower 7
## 98 0 NA white female hs or lower 36
## 99 10800 29 white female college 41
## 100 0 NA white female grad 71
## 101 2000 10 white male hs or lower 16
## 102 0 NA white female hs or lower 65
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## 105 NA NA white male hs or lower 9
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## 107 NA NA white male hs or lower 13
## 108 0 NA white female hs or lower 79
## 109 9000 42 white female hs or lower 48
## 110 3000 20 white female hs or lower 33
## 111 37000 60 white female college 26
## 112 0 NA black male hs or lower 78
## 113 NA NA white female hs or lower 12
## 114 0 NA white female hs or lower 15
## 115 12800 25 white male college 22
## 116 1500 24 white male hs or lower 44
## 117 0 NA white female hs or lower 16
## 118 0 NA white female college 43
## 119 1200 20 white female hs or lower 21
## 120 0 NA white female hs or lower 58
## 121 0 NA white male hs or lower 67
## 122 1200 5 white male college 25
## 123 0 NA white female college 65
## 124 0 NA white male grad 93
## 125 33000 40 white male grad 49
## 126 NA NA white female hs or lower 12
## 127 24000 40 white female hs or lower 35
## 128 32000 40 white female college 33
## 129 6300 25 white female hs or lower 69
## 130 NA NA white male hs or lower 11
## 131 2000 10 white male hs or lower 20
## 132 NA NA other male hs or lower 11
## 133 NA NA white female <NA> 1
## 134 0 NA white male hs or lower 84
## 135 168000 60 white male college 51
## 136 4400 20 black male hs or lower 18
## 137 0 NA white female hs or lower 76
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## 139 NA NA white male hs or lower 14
## 140 1500 16 white female hs or lower 18
## 141 NA NA white female hs or lower 10
## 142 22800 35 white female college 26
## 143 NA NA asian male hs or lower 11
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## 146 0 NA white female hs or lower 61
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## 157 45000 36 white female hs or lower 60
## 158 600 15 other male hs or lower 17
## 159 23000 40 black female hs or lower 49
## 160 45000 30 white male hs or lower 45
## 161 NA NA other female hs or lower 3
## 162 0 NA white female hs or lower 16
## 163 0 NA white female college 34
## 164 43000 70 white male hs or lower 53
## 165 NA NA white female <NA> 0
## 166 37000 37 white male hs or lower 55
## 167 55000 60 white male grad 66
## 168 58000 50 white male college 59
## 169 0 NA white male college 24
## 170 0 NA white male hs or lower 77
## 171 360000 40 white male college 50
## 172 127000 40 other female grad 32
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## 174 20000 40 white female hs or lower 27
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## 176 19600 35 white female college 42
## 177 0 NA white male college 42
## 178 0 NA white female grad 63
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## 195 31000 38 white female college 69
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## 205 0 NA white male grad 70
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## 209 100000 40 white male college 40
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## 216 323000 45 white female grad 43
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## 218 NA NA white female hs or lower 5
## 219 0 NA white male hs or lower 39
## 220 6000 30 white female college 34
## 221 0 NA white male hs or lower 81
## 222 0 NA other male grad 67
## 223 54000 48 white male college 42
## 224 85000 40 white female grad 42
## 225 1900 25 white female college 37
## 226 NA NA white female hs or lower 8
## 227 55000 60 white female college 26
## 228 0 NA white female hs or lower 18
## 229 1800 8 white female hs or lower 22
## 230 0 NA white male hs or lower 73
## 231 398000 40 asian male grad 51
## 232 104000 50 white male college 33
## 233 0 NA white male hs or lower 43
## 234 NA NA white female <NA> 0
## 235 35000 40 white male hs or lower 43
## 236 0 NA white female college 27
## 237 52000 48 white male hs or lower 61
## 238 0 NA white male hs or lower 78
## 239 NA NA white male hs or lower 4
## 240 38000 45 white female hs or lower 68
## 241 0 NA white male hs or lower 60
## 242 0 NA white female hs or lower 64
## 243 NA NA white male <NA> 2
## 244 33500 40 white male hs or lower 29
## 245 0 NA white male hs or lower 52
## 246 NA NA black female <NA> 2
## 247 NA NA white male hs or lower 11
## 248 0 NA white female hs or lower 61
## 249 0 25 white female college 48
## 250 43000 40 asian female hs or lower 47
## 251 0 NA black male hs or lower 24
## 252 333000 50 white male grad 37
## 253 NA NA white female <NA> 0
## 254 0 NA white male hs or lower 65
## 255 0 NA white female hs or lower 18
## 256 34700 40 white female hs or lower 59
## 257 NA NA white male hs or lower 4
## 258 NA NA other male hs or lower 6
## 259 270 20 black female hs or lower 48
## 260 0 NA white female hs or lower 39
## 261 2000 16 white female grad 37
## 262 15000 25 white female hs or lower 36
## 263 NA NA asian male hs or lower 7
## 264 40000 40 white male hs or lower 51
## 265 0 40 other female hs or lower 62
## 266 0 NA white female hs or lower 29
## 267 0 NA white female hs or lower 63
## 268 0 NA black male hs or lower 64
## 269 360000 50 white male hs or lower 52
## 270 0 NA white male college 76
## 271 89000 55 white male hs or lower 43
## 272 40000 40 white male college 50
## 273 0 NA white female hs or lower 58
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## 290 NA NA asian male hs or lower 7
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## 299 46000 40 white female grad 27
## 300 0 NA other female college 52
## 301 0 50 white male grad 63
## 302 16000 40 white female hs or lower 56
## 303 NA NA other male hs or lower 5
## 304 39000 35 white female college 63
## 305 4000 30 white male college 36
## 306 0 NA white female hs or lower 73
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## 312 NA NA white male hs or lower 6
## 313 0 NA asian female hs or lower 19
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## 319 85000 40 white female college 51
## 320 NA NA other male hs or lower 7
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## 324 NA NA black female hs or lower 7
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## 330 19200 50 other male hs or lower 23
## 331 27000 40 asian male hs or lower 35
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## 334 NA NA white male hs or lower 14
## 335 NA NA white female hs or lower 6
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## 341 48000 40 white female college 28
## 342 NA NA white male <NA> 0
## 343 19000 37 white female hs or lower 31
## 344 NA NA white female hs or lower 13
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## 347 30000 40 white male hs or lower 38
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## 349 0 NA black female hs or lower 66
## 350 0 52 white female college 55
## 351 NA NA other male <NA> 1
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## 353 40000 50 white female college 52
## 354 38000 40 white male grad 35
## 355 50000 40 white male hs or lower 66
## 356 NA NA black female hs or lower 4
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## 362 NA NA white male hs or lower 10
## 363 10000 40 white male hs or lower 20
## 364 24000 30 white female hs or lower 69
## 365 60000 68 white male hs or lower 20
## 366 0 NA white female hs or lower 48
## 367 0 NA white female college 51
## 368 150000 42 other male hs or lower 46
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## 370 0 NA white female hs or lower 61
## 371 0 NA white female hs or lower 66
## 372 0 NA black male hs or lower 24
## 373 50000 40 asian male college 64
## 374 108000 45 white male college 61
## 375 0 NA black female college 50
## 376 NA NA white female hs or lower 10
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## 378 0 NA white male college 64
## 379 0 NA other male hs or lower 40
## 380 0 NA white female hs or lower 69
## 381 27900 40 white female hs or lower 57
## 382 NA NA asian male hs or lower 3
## 383 NA NA white male hs or lower 3
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## 385 0 NA white female hs or lower 48
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## 387 0 NA white female college 62
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## 389 30000 40 white female college 28
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## 391 0 40 white male hs or lower 48
## 392 16000 30 white female hs or lower 20
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## 394 NA NA white male hs or lower 6
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## 398 NA NA other female hs or lower 11
## 399 0 NA white male college 59
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## 401 29600 37 white female college 54
## 402 0 NA other female hs or lower 60
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## 405 NA NA white male hs or lower 14
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## 407 0 NA white male hs or lower 46
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## 409 NA NA white female hs or lower 12
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## 419 0 NA white female hs or lower 77
## 420 0 NA white male hs or lower 78
## 421 NA NA white male hs or lower 13
## 422 NA NA asian female hs or lower 12
## 423 NA NA white female <NA> 0
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## 425 NA NA black male hs or lower 14
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## 429 0 NA asian female hs or lower 55
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## 432 18000 49 black female hs or lower 43
## 433 0 NA other male hs or lower 44
## 434 0 30 black female hs or lower 37
## 435 NA NA other female <NA> 1
## 436 NA NA white male <NA> 0
## 437 18000 30 white female college 25
## 438 27000 40 white female hs or lower 42
## 439 0 NA white female hs or lower 59
## 440 0 NA white male hs or lower 78
## 441 12000 24 white female hs or lower 26
## 442 5000 40 asian female hs or lower 20
## 443 41000 40 white female college 38
## 444 0 NA white female hs or lower 66
## 445 0 NA other male hs or lower 16
## 446 0 NA asian female hs or lower 76
## 447 90000 40 white male college 38
## 448 60000 45 white male hs or lower 49
## 449 30000 40 white female college 35
## 450 0 NA white male hs or lower 64
## 451 10000 40 white female hs or lower 23
## 452 0 NA white female grad 75
## 453 50000 80 white female college 48
## 454 0 NA white male hs or lower 79
## 455 24000 40 white female hs or lower 30
## 456 88000 40 white male college 27
## 457 18000 40 other female hs or lower 54
## 458 0 NA black male hs or lower 15
## 459 15600 40 white female hs or lower 47
## 460 12000 30 white female hs or lower 60
## 461 30000 60 other female grad 27
## 462 0 40 white male hs or lower 58
## 463 80000 40 asian male college 51
## 464 0 NA white female hs or lower 28
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## 466 NA NA other male hs or lower 8
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## 469 10000 36 black female hs or lower 21
## 470 0 45 white male grad 57
## 471 0 NA white female college 69
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## 486 4500 20 white male hs or lower 58
## 487 0 NA asian male college 63
## 488 0 NA other female hs or lower 33
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## 490 0 NA white female hs or lower 74
## 491 5300 40 black female hs or lower 52
## 492 16800 40 white female hs or lower 67
## 493 32000 40 black male hs or lower 50
## 494 0 NA white female hs or lower 77
## 495 0 NA white female hs or lower 93
## 496 NA NA white female hs or lower 14
## 497 NA NA white male <NA> 0
## 498 0 NA white female hs or lower 56
## 499 0 NA white female hs or lower 61
## 500 110 2 black male hs or lower 24
## 501 NA NA white male hs or lower 8
## 502 0 NA black male hs or lower 24
## 503 NA NA white male hs or lower 12
## 504 0 NA white female hs or lower 68
## 505 NA NA white male hs or lower 12
## 506 0 NA white female hs or lower 81
## 507 45000 40 black male hs or lower 57
## 508 0 NA white female hs or lower 82
## 509 0 NA white female college 33
## 510 125000 60 white male hs or lower 61
## 511 0 NA white female hs or lower 66
## 512 90000 40 white female hs or lower 62
## 513 0 50 white female hs or lower 27
## 514 0 NA white male hs or lower 39
## 515 NA NA other male hs or lower 5
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## 517 0 NA white male grad 67
## 518 0 NA white male hs or lower 74
## 519 NA NA white male hs or lower 5
## 520 20000 40 white male college 28
## 521 26000 40 white female hs or lower 31
## 522 32000 40 black female hs or lower 57
## 523 6000 16 asian male college 26
## 524 0 NA white male hs or lower 17
## 525 5000 35 white female hs or lower 70
## 526 0 NA asian male grad 67
## 527 39000 40 black male hs or lower 42
## 528 0 NA white male hs or lower 60
## 529 NA NA white male hs or lower 8
## 530 52000 40 white male hs or lower 52
## 531 40000 40 white male hs or lower 37
## 532 42500 40 white female college 36
## 533 NA NA asian male hs or lower 11
## 534 44000 40 white female college 33
## 535 0 NA white female hs or lower 39
## 536 0 NA white male hs or lower 57
## 537 NA NA white male hs or lower 11
## 538 58000 53 white male grad 32
## 539 3500 40 white male hs or lower 34
## 540 0 NA white male hs or lower 88
## 541 NA NA white male hs or lower 9
## 542 24000 40 white male hs or lower 33
## 543 56000 40 black female grad 52
## 544 NA NA white male hs or lower 7
## 545 0 NA white male hs or lower 74
## 546 NA NA other female hs or lower 7
## 547 80000 40 white male college 68
## 548 0 NA white female hs or lower 64
## 549 0 60 white male hs or lower 49
## 550 0 NA asian female hs or lower 53
## 551 24300 40 white female hs or lower 60
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## 1826 0 NA white male college 52
## 1827 0 NA asian female hs or lower 65
## 1828 3300 9 white female hs or lower 51
## 1829 7000 38 white male hs or lower 20
## 1830 12900 16 white female hs or lower 56
## 1831 44000 48 white male hs or lower 34
## 1832 NA NA white male hs or lower 14
## 1833 90000 70 white male college 32
## 1834 6600 40 white female hs or lower 40
## 1835 0 NA black male hs or lower 74
## 1836 0 30 white male college 35
## 1837 24000 40 other female college 26
## 1838 28000 40 white female hs or lower 49
## 1839 0 NA white female grad 88
## 1840 0 NA other male hs or lower 59
## 1841 40000 40 white male college 36
## 1842 1000 6 other female college 64
## 1843 20000 40 black male hs or lower 37
## 1844 NA NA white male hs or lower 3
## 1845 30000 40 white male hs or lower 34
## 1846 0 NA white male hs or lower 43
## 1847 NA NA other male hs or lower 3
## 1848 0 NA white female hs or lower 49
## 1849 NA NA other female hs or lower 6
## 1850 0 NA white female hs or lower 15
## 1851 NA NA black male <NA> 0
## 1852 NA NA black male hs or lower 13
## 1853 18000 40 white female hs or lower 32
## 1854 NA NA white male hs or lower 3
## 1855 29000 40 white male hs or lower 23
## 1856 13000 40 white female grad 22
## 1857 0 NA white male hs or lower 24
## 1858 16800 40 other female hs or lower 22
## 1859 NA NA white female hs or lower 9
## 1860 0 NA white female hs or lower 71
## 1861 0 NA white male hs or lower 74
## 1862 40000 50 white female grad 31
## 1863 28600 40 white male hs or lower 53
## 1864 7800 12 white female college 30
## 1865 0 NA white male college 72
## 1866 200 15 white male hs or lower 21
## 1867 NA NA black female <NA> 2
## 1868 0 NA white male college 46
## 1869 0 NA white male hs or lower 20
## 1870 0 NA white male hs or lower 90
## 1871 65000 50 white female college 30
## 1872 35000 40 white male hs or lower 55
## 1873 6000 8 white female hs or lower 33
## 1874 55000 40 white male hs or lower 53
## 1875 NA NA white male <NA> 1
## 1876 59000 40 white female college 65
## 1877 NA NA other female hs or lower 9
## 1878 0 NA black male hs or lower 70
## 1879 0 NA black female hs or lower 64
## 1880 NA NA white male hs or lower 12
## 1881 12900 25 white female hs or lower 54
## 1882 5500 37 white female hs or lower 69
## 1883 NA NA other female hs or lower 12
## 1884 NA NA white male hs or lower 14
## 1885 0 NA white female hs or lower 69
## 1886 42000 40 white male hs or lower 47
## 1887 72000 40 white female hs or lower 51
## 1888 NA NA white male hs or lower 11
## 1889 400 20 white female college 28
## 1890 0 NA white male hs or lower 32
## 1891 0 NA white male hs or lower 25
## 1892 180000 60 white male grad 64
## 1893 133000 40 asian male college 39
## 1894 0 10 white male college 29
## 1895 0 NA white female hs or lower 61
## 1896 92000 40 white male hs or lower 39
## 1897 0 NA white male grad 72
## 1898 0 NA white male hs or lower 17
## 1899 75000 45 white male grad 30
## 1900 0 40 white male college 51
## 1901 NA NA white female hs or lower 13
## 1902 NA NA white female <NA> 2
## 1903 60000 84 white male hs or lower 43
## 1904 35000 56 white male college 34
## 1905 0 NA white male hs or lower 67
## 1906 92000 40 white female college 46
## 1907 0 NA white male hs or lower 46
## 1908 40000 40 white male college 30
## 1909 0 NA black female hs or lower 45
## 1910 0 NA black female grad 87
## 1911 0 NA white female hs or lower 29
## 1912 NA NA white male hs or lower 10
## 1913 18000 99 white male hs or lower 39
## 1914 0 NA white male hs or lower 80
## 1915 0 NA white female hs or lower 86
## 1916 NA NA white female hs or lower 8
## 1917 NA NA white male hs or lower 9
## 1918 0 NA white female hs or lower 34
## 1919 20400 40 white female college 40
## 1920 88000 50 asian female grad 34
## 1921 NA NA black male hs or lower 13
## 1922 NA NA white male hs or lower 5
## 1923 9100 30 other female hs or lower 63
## 1924 0 NA white male hs or lower 88
## 1925 0 NA black male hs or lower 18
## 1926 55000 40 black female grad 27
## 1927 50000 27 white female college 33
## 1928 NA NA white male hs or lower 11
## 1929 0 NA white male college 63
## 1930 NA NA white male <NA> 1
## 1931 8900 40 white female hs or lower 50
## 1932 0 NA black male college 22
## 1933 0 NA white male hs or lower 85
## 1934 30000 30 white female college 38
## 1935 5000 15 white female college 22
## 1936 26000 45 white female hs or lower 39
## 1937 0 NA white female hs or lower 76
## 1938 21500 40 white female hs or lower 44
## 1939 600 5 white male college 23
## 1940 0 NA white female hs or lower 72
## 1941 0 NA white male grad 70
## 1942 25000 40 other female hs or lower 56
## 1943 0 NA white male hs or lower 56
## 1944 62000 68 white female college 49
## 1945 NA NA black female hs or lower 13
## 1946 NA NA black male hs or lower 4
## 1947 NA NA white male hs or lower 5
## 1948 0 NA white female college 63
## 1949 NA NA white female <NA> 0
## 1950 3500 15 white female hs or lower 22
## 1951 NA NA white female hs or lower 9
## 1952 60000 40 black female hs or lower 54
## 1953 0 NA black male hs or lower 86
## 1954 NA NA white male hs or lower 14
## 1955 0 NA white male hs or lower 68
## 1956 40000 40 other female grad 30
## 1957 49000 40 white male hs or lower 48
## 1958 NA NA other female hs or lower 3
## 1959 65000 40 white female hs or lower 39
## 1960 0 NA other female hs or lower 31
## 1961 9400 40 white female hs or lower 25
## 1962 190000 50 white male grad 48
## 1963 18000 40 other female hs or lower 56
## 1964 10000 10 white male hs or lower 73
## 1965 30000 40 white male hs or lower 66
## 1966 78000 40 white male grad 45
## 1967 0 NA white male college 86
## 1968 NA NA white male <NA> 1
## 1969 0 NA asian male hs or lower 24
## 1970 13000 15 white female hs or lower 27
## 1971 0 NA white male hs or lower 72
## 1972 6200 35 black female hs or lower 20
## 1973 7000 15 white male hs or lower 22
## 1974 63000 50 white male college 24
## 1975 1600 15 black female hs or lower 22
## 1976 0 NA white female hs or lower 38
## 1977 0 NA white female hs or lower 22
## 1978 0 NA white male hs or lower 22
## 1979 0 NA white male college 48
## 1980 0 NA white male college 47
## 1981 NA NA white male <NA> 2
## 1982 NA NA white male hs or lower 10
## 1983 48900 40 white male college 43
## 1984 3500 40 white female hs or lower 49
## 1985 5000 25 white female hs or lower 48
## 1986 28000 40 white female college 25
## 1987 12000 38 white female hs or lower 62
## 1988 0 NA white female hs or lower 80
## 1989 33300 40 white female hs or lower 54
## 1990 NA NA other male hs or lower 11
## 1991 NA NA white male <NA> 1
## 1992 NA NA other male hs or lower 11
## 1993 85000 40 white male college 52
## 1994 0 NA black male hs or lower 17
## 1995 65000 48 white male hs or lower 53
## 1996 0 NA white female hs or lower 71
## 1997 0 NA other female hs or lower 50
## 1998 70000 40 asian male college 63
## 1999 105000 50 asian male college 36
## 2000 0 NA black male college 22Statistical Analysis
For my statistical analysis, I chose to do a multiple regression model to explain how income is affected by the variables I chose. The reason I chose this model is because I feel that it does a thorough analysis and creates a better understanding of how multiple predictors can affect an outcome. I also chose this model because of the ability to use both quantitative and categorical variables which is more realistic to answer my research question.
multiple_regression_model <- lm(income ~ hrs_work + race + gender + edu + age, data = survey_data)
summary(multiple_regression_model)##
## Call:
## lm(formula = income ~ hrs_work + race + gender + edu + age, data = survey_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -117322 -20066 -3452 10282 330071
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9746.4 9310.5 1.047 0.295450
## hrs_work 988.8 116.4 8.497 < 2e-16 ***
## raceblack -32533.4 8721.9 -3.730 0.000203 ***
## raceother -35822.6 9071.4 -3.949 8.43e-05 ***
## racewhite -27904.3 7292.1 -3.827 0.000138 ***
## gendermale 17313.0 3124.1 5.542 3.88e-08 ***
## edugrad 39661.9 5439.7 7.291 6.47e-13 ***
## eduhs or lower -17820.7 3494.4 -5.100 4.10e-07 ***
## age 411.2 102.3 4.020 6.28e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 46610 on 950 degrees of freedom
## (1041 observations deleted due to missingness)
## Multiple R-squared: 0.2864, Adjusted R-squared: 0.2803
## F-statistic: 47.65 on 8 and 950 DF, p-value: < 2.2e-16In this model, the annual income is being explained using hours worked, race, gender, education level and age. The predicted annual income when all these factors are 0 is the intercept we see as (9746.4).
hrs_work: (988.8) per hours worked and the p-value = (<2e-16) meaning hours worked is a highly significant predictor for this model.
age: (411.2) meaning that the older an individual is per unit, the higher their pay will be and since the p-value = 0.0000628, this means that age is a significant predictor for this model in determining an individuals annual income.
For the categorical variables:
Race: This will be compared to an individual who is Asian as the baseline to determine the difference between the other races.
Race (Black): (-32533.4) Race(Other): (-35822.6) Race(White): (-27904.3)
With all their p-values being less than 0.01, this shows that they are all significant. The values above are telling us that Black individuals earn $32,533.40 less than Asians, White individuals earn $35,822 less than Asians and individuals from other races earn $27,904 less than Asians.
Gender: R set the baseline to be Female hence we will compare the differentiate between Males.
Gender(Male): (17313.0)
The male gender has a p-value of (3.88e-08) which is very small compared to 0.01 meaning that gender is significant. With the coefficient being positive, the model is telling us that the male gender earns $17,313.0 more than females.
Edu: R set the baseline to college hence we will use this to differentiate between the different education levels achieved.
Edu(Grad): (39661.9) Edu(Hs or lower): (-17820.7)
Both education levels have a very small p-value that is less than 0.01 which means that education level is a significant predictor for annual income. For education level, the model is telling us that compared to individuals who have attained a college degree, individuals who have a graduate degree earn $39,661.90 more than college degree holders and individuals who have completed high school or lower earn $17,820.70 less than college degree holders.
The adjusted R-squared for the model is 0.2803 which means that the model explains about 28% of variation in income.
To test for linearity:
crPlots(multiple_regression_model)
The visuals above are explaining the linearity, meaning the relationship
between the annual income and the predictors.
Hrs_work: We can see that there is a positive relationship between hours worked and annual income which is shown by the pink line. The blue line serves as the line of best fit and the pink line shows the actual trend. Since there is a slight bend in the pink line towards the end, this means that there is some minor non-linearity but it is not severe.
Age: The pink line is mostly flat and the loess line (blue dotted line) follows it closely which means that linearity looks good.
As for gender, edu and race, being categorical variables, linearity does not apply to them because they are treated as a factor.
To test for independence:
plot(resid(multiple_regression_model), type="b",
main="Residuals vs Order", ylab="Residuals"); abline(h=0, lty=2)
The independence of the predictors is determined using the Residual vs Order plot to show that each predictor is independent and not affected by other predictors. As shown in the plot above, most of the residuals are scattered around 0 without showing any abnormal trends meaning that the residuals are not correlated hence reducing bias in the model.
par(mfrow=c(2,2)); plot(multiple_regression_model); par(mfrow=c(1,1))
Residuals vs Fitted: This checks for linearity. The plot shows a fairly straight line with some slight deviation hence showing linearity.
Q-Q Residuals: There is a strong upper right tail which means that the residuals are not normally distributed and are more skewed to the right.
Scale-Location: There appears to be an upward trend as seen by the red line which shows that there is no equal variance of the residuals hence showing heteroscedasticity.
Residuals vs Leverage: There are some few leverage points however, they may not influence the data in the model.
To check for multicollinearity between hrs_work and age as they are the only quantitative predictors:
cor(survey_data[, c("hrs_work", "age")], use = "complete.obs")## hrs_work age
## hrs_work 1.0000000 0.1106824
## age 0.1106824 1.0000000I used the hours worked and age predictors to test for multicollineraity and |r| came to about 0.1107 which indicates that there is a weak correlation between hours worked and age hence showing no evidence of multicollinearity.
Conclusion and Future Directions
In conclusion, this multiple regression model has proven to significant and was able to explain 28% of the variance in income. The model was able to show that the predictors hrs_work, age, gender, race, edu were all highly significant in determining the annual income of an individual. From the analysis done, it showed us how age and hours worked were associated with higher income. In addition, the model also shows us how when it comes to categorical variables, the differences between the different categories and how it impacts their income. When it comes to race, it is evident that Asians were earning significantly higher income compared to the other races. In terms of education level, the model showed us that having a graduate degree makes an individual more likely to have a higher income and finally, we also got to see that the male gender earns significantly higher annual income as compared to females.
From this model, it is evident that there is some form of inequality when it comes to annual income especially with regard to race and gender which should be looked into further. For future research, it would be important to add other predictors like work experience and the different job types to analyze annual income as I think that these would be very highly significant factors in determining an individuals annual income.