w <- c(-5,2,-3)
L1 <- sum(abs(w))
L1[1] 10L2 <- sqrt(sum(w^2))
L2[1] 6.164414Activity 1.1 - vector basics
SUBMISSION INSTRUCTIONS:
- Complete this activity, rendering periodically to html to view your output. Make sure you have this .qmd file in a folder with the Activity subdirectories!
- When complete, publish to either Posit Connect Cloud or Rpubs
- Submit a link to your rendered html and your .qmd to D2L.
Question 1
Consider the 3-dimensional vector \(w = c(-5, 2, -3)\).
A)
Find \(||w||_1\), the L1 (aka taxicab or Manhattan) norm of this vector. Show your work!
L1 = |-5| + |2| + |-3| = 10
B)
Find \(||w||_2\), the L2 (aka Euclidean) norm of this vector. Show your work!
L2 = sqrt((-5)2 + (2)2 + (-3)2)
= sqrt(25 + 4 + 9)
= sqrt(38)
= 6.16
C)
Create the vector in R. Use R to verify your computations above.
Question 2
Consider the iris data set, which comes packaged with a standard R installation. In the code below I have selected only the numeric variables from this data set:
library(tidyverse)
(iris_use <- iris
%>% select(-Species)
) %>% head() Sepal.Length Sepal.Width Petal.Length Petal.Width
1 5.1 3.5 1.4 0.2
2 4.9 3.0 1.4 0.2
3 4.7 3.2 1.3 0.2
4 4.6 3.1 1.5 0.2
5 5.0 3.6 1.4 0.2
6 5.4 3.9 1.7 0.4A)
How many vectors are there in this new data set, and what is the dimension of each vector?
There are 150 4-dimensional vectors in this data set. ## B)
B)
Find the mean and standard deviation vectors.
(mean_vector <- iris_use
%>% summarise(across(.cols = c(1:4), .fns = mean))
) Sepal.Length Sepal.Width Petal.Length Petal.Width
1 5.843333 3.057333 3.758 1.199333(sd_vector <- iris_use
%>% summarise(across(.cols = c(1:4), .fns = sd))
) Sepal.Length Sepal.Width Petal.Length Petal.Width
1 0.8280661 0.4358663 1.765298 0.7622377C)
Mean-center and scale the data set. Verify that the mean and standard deviation vectors of the scaled data set are \(\vec 0\) and \(\vec 1\), respectively.
(iris_scaled <- scale(iris_use, center = TRUE, scale = TRUE)) Sepal.Length Sepal.Width Petal.Length Petal.Width
[1,] -0.89767388 1.01560199 -1.33575163 -1.3110521482
[2,] -1.13920048 -0.13153881 -1.33575163 -1.3110521482
[3,] -1.38072709 0.32731751 -1.39239929 -1.3110521482
[4,] -1.50149039 0.09788935 -1.27910398 -1.3110521482
[5,] -1.01843718 1.24503015 -1.33575163 -1.3110521482
[6,] -0.53538397 1.93331463 -1.16580868 -1.0486667950
[7,] -1.50149039 0.78617383 -1.33575163 -1.1798594716
[8,] -1.01843718 0.78617383 -1.27910398 -1.3110521482
[9,] -1.74301699 -0.36096697 -1.33575163 -1.3110521482
[10,] -1.13920048 0.09788935 -1.27910398 -1.4422448248
[11,] -0.53538397 1.47445831 -1.27910398 -1.3110521482
[12,] -1.25996379 0.78617383 -1.22245633 -1.3110521482
[13,] -1.25996379 -0.13153881 -1.33575163 -1.4422448248
[14,] -1.86378030 -0.13153881 -1.50569459 -1.4422448248
[15,] -0.05233076 2.16274279 -1.44904694 -1.3110521482
[16,] -0.17309407 3.08045544 -1.27910398 -1.0486667950
[17,] -0.53538397 1.93331463 -1.39239929 -1.0486667950
[18,] -0.89767388 1.01560199 -1.33575163 -1.1798594716
[19,] -0.17309407 1.70388647 -1.16580868 -1.1798594716
[20,] -0.89767388 1.70388647 -1.27910398 -1.1798594716
[21,] -0.53538397 0.78617383 -1.16580868 -1.3110521482
[22,] -0.89767388 1.47445831 -1.27910398 -1.0486667950
[23,] -1.50149039 1.24503015 -1.56234224 -1.3110521482
[24,] -0.89767388 0.55674567 -1.16580868 -0.9174741184
[25,] -1.25996379 0.78617383 -1.05251337 -1.3110521482
[26,] -1.01843718 -0.13153881 -1.22245633 -1.3110521482
[27,] -1.01843718 0.78617383 -1.22245633 -1.0486667950
[28,] -0.77691058 1.01560199 -1.27910398 -1.3110521482
[29,] -0.77691058 0.78617383 -1.33575163 -1.3110521482
[30,] -1.38072709 0.32731751 -1.22245633 -1.3110521482
[31,] -1.25996379 0.09788935 -1.22245633 -1.3110521482
[32,] -0.53538397 0.78617383 -1.27910398 -1.0486667950
[33,] -0.77691058 2.39217095 -1.27910398 -1.4422448248
[34,] -0.41462067 2.62159911 -1.33575163 -1.3110521482
[35,] -1.13920048 0.09788935 -1.27910398 -1.3110521482
[36,] -1.01843718 0.32731751 -1.44904694 -1.3110521482
[37,] -0.41462067 1.01560199 -1.39239929 -1.3110521482
[38,] -1.13920048 1.24503015 -1.33575163 -1.4422448248
[39,] -1.74301699 -0.13153881 -1.39239929 -1.3110521482
[40,] -0.89767388 0.78617383 -1.27910398 -1.3110521482
[41,] -1.01843718 1.01560199 -1.39239929 -1.1798594716
[42,] -1.62225369 -1.73753594 -1.39239929 -1.1798594716
[43,] -1.74301699 0.32731751 -1.39239929 -1.3110521482
[44,] -1.01843718 1.01560199 -1.22245633 -0.7862814418
[45,] -0.89767388 1.70388647 -1.05251337 -1.0486667950
[46,] -1.25996379 -0.13153881 -1.33575163 -1.1798594716
[47,] -0.89767388 1.70388647 -1.22245633 -1.3110521482
[48,] -1.50149039 0.32731751 -1.33575163 -1.3110521482
[49,] -0.65614727 1.47445831 -1.27910398 -1.3110521482
[50,] -1.01843718 0.55674567 -1.33575163 -1.3110521482
[51,] 1.39682886 0.32731751 0.53362088 0.2632599711
[52,] 0.67224905 0.32731751 0.42032558 0.3944526477
[53,] 1.27606556 0.09788935 0.64691619 0.3944526477
[54,] -0.41462067 -1.73753594 0.13708732 0.1320672944
[55,] 0.79301235 -0.59039513 0.47697323 0.3944526477
[56,] -0.17309407 -0.59039513 0.42032558 0.1320672944
[57,] 0.55148575 0.55674567 0.53362088 0.5256453243
[58,] -1.13920048 -1.50810778 -0.25944625 -0.2615107354
[59,] 0.91377565 -0.36096697 0.47697323 0.1320672944
[60,] -0.77691058 -0.81982329 0.08043967 0.2632599711
[61,] -1.01843718 -2.42582042 -0.14615094 -0.2615107354
[62,] 0.06843254 -0.13153881 0.25038262 0.3944526477
[63,] 0.18919584 -1.96696410 0.13708732 -0.2615107354
[64,] 0.30995914 -0.36096697 0.53362088 0.2632599711
[65,] -0.29385737 -0.36096697 -0.08950329 0.1320672944
[66,] 1.03453895 0.09788935 0.36367793 0.2632599711
[67,] -0.29385737 -0.13153881 0.42032558 0.3944526477
[68,] -0.05233076 -0.81982329 0.19373497 -0.2615107354
[69,] 0.43072244 -1.96696410 0.42032558 0.3944526477
[70,] -0.29385737 -1.27867961 0.08043967 -0.1303180588
[71,] 0.06843254 0.32731751 0.59026853 0.7880306775
[72,] 0.30995914 -0.59039513 0.13708732 0.1320672944
[73,] 0.55148575 -1.27867961 0.64691619 0.3944526477
[74,] 0.30995914 -0.59039513 0.53362088 0.0008746178
[75,] 0.67224905 -0.36096697 0.30703027 0.1320672944
[76,] 0.91377565 -0.13153881 0.36367793 0.2632599711
[77,] 1.15530226 -0.59039513 0.59026853 0.2632599711
[78,] 1.03453895 -0.13153881 0.70356384 0.6568380009
[79,] 0.18919584 -0.36096697 0.42032558 0.3944526477
[80,] -0.17309407 -1.04925145 -0.14615094 -0.2615107354
[81,] -0.41462067 -1.50810778 0.02379201 -0.1303180588
[82,] -0.41462067 -1.50810778 -0.03285564 -0.2615107354
[83,] -0.05233076 -0.81982329 0.08043967 0.0008746178
[84,] 0.18919584 -0.81982329 0.76021149 0.5256453243
[85,] -0.53538397 -0.13153881 0.42032558 0.3944526477
[86,] 0.18919584 0.78617383 0.42032558 0.5256453243
[87,] 1.03453895 0.09788935 0.53362088 0.3944526477
[88,] 0.55148575 -1.73753594 0.36367793 0.1320672944
[89,] -0.29385737 -0.13153881 0.19373497 0.1320672944
[90,] -0.41462067 -1.27867961 0.13708732 0.1320672944
[91,] -0.41462067 -1.04925145 0.36367793 0.0008746178
[92,] 0.30995914 -0.13153881 0.47697323 0.2632599711
[93,] -0.05233076 -1.04925145 0.13708732 0.0008746178
[94,] -1.01843718 -1.73753594 -0.25944625 -0.2615107354
[95,] -0.29385737 -0.81982329 0.25038262 0.1320672944
[96,] -0.17309407 -0.13153881 0.25038262 0.0008746178
[97,] -0.17309407 -0.36096697 0.25038262 0.1320672944
[98,] 0.43072244 -0.36096697 0.30703027 0.1320672944
[99,] -0.89767388 -1.27867961 -0.42938920 -0.1303180588
[100,] -0.17309407 -0.59039513 0.19373497 0.1320672944
[101,] 0.55148575 0.55674567 1.27004036 1.7063794137
[102,] -0.05233076 -0.81982329 0.76021149 0.9192233541
[103,] 1.51759216 -0.13153881 1.21339271 1.1816087073
[104,] 0.55148575 -0.36096697 1.04344975 0.7880306775
[105,] 0.79301235 -0.13153881 1.15674505 1.3128013839
[106,] 2.12140867 -0.13153881 1.60992627 1.1816087073
[107,] -1.13920048 -1.27867961 0.42032558 0.6568380009
[108,] 1.75911877 -0.36096697 1.43998331 0.7880306775
[109,] 1.03453895 -1.27867961 1.15674505 0.7880306775
[110,] 1.63835547 1.24503015 1.32668801 1.7063794137
[111,] 0.79301235 0.32731751 0.76021149 1.0504160307
[112,] 0.67224905 -0.81982329 0.87350679 0.9192233541
[113,] 1.15530226 -0.13153881 0.98680210 1.1816087073
[114,] -0.17309407 -1.27867961 0.70356384 1.0504160307
[115,] -0.05233076 -0.59039513 0.76021149 1.5751867371
[116,] 0.67224905 0.32731751 0.87350679 1.4439940605
[117,] 0.79301235 -0.13153881 0.98680210 0.7880306775
[118,] 2.24217198 1.70388647 1.66657392 1.3128013839
[119,] 2.24217198 -1.04925145 1.77986923 1.4439940605
[120,] 0.18919584 -1.96696410 0.70356384 0.3944526477
[121,] 1.27606556 0.32731751 1.10009740 1.4439940605
[122,] -0.29385737 -0.59039513 0.64691619 1.0504160307
[123,] 2.24217198 -0.59039513 1.66657392 1.0504160307
[124,] 0.55148575 -0.81982329 0.64691619 0.7880306775
[125,] 1.03453895 0.55674567 1.10009740 1.1816087073
[126,] 1.63835547 0.32731751 1.27004036 0.7880306775
[127,] 0.43072244 -0.59039513 0.59026853 0.7880306775
[128,] 0.30995914 -0.13153881 0.64691619 0.7880306775
[129,] 0.67224905 -0.59039513 1.04344975 1.1816087073
[130,] 1.63835547 -0.13153881 1.15674505 0.5256453243
[131,] 1.87988207 -0.59039513 1.32668801 0.9192233541
[132,] 2.48369858 1.70388647 1.49663097 1.0504160307
[133,] 0.67224905 -0.59039513 1.04344975 1.3128013839
[134,] 0.55148575 -0.59039513 0.76021149 0.3944526477
[135,] 0.30995914 -1.04925145 1.04344975 0.2632599711
[136,] 2.24217198 -0.13153881 1.32668801 1.4439940605
[137,] 0.55148575 0.78617383 1.04344975 1.5751867371
[138,] 0.67224905 0.09788935 0.98680210 0.7880306775
[139,] 0.18919584 -0.13153881 0.59026853 0.7880306775
[140,] 1.27606556 0.09788935 0.93015445 1.1816087073
[141,] 1.03453895 0.09788935 1.04344975 1.5751867371
[142,] 1.27606556 0.09788935 0.76021149 1.4439940605
[143,] -0.05233076 -0.81982329 0.76021149 0.9192233541
[144,] 1.15530226 0.32731751 1.21339271 1.4439940605
[145,] 1.03453895 0.55674567 1.10009740 1.7063794137
[146,] 1.03453895 -0.13153881 0.81685914 1.4439940605
[147,] 0.55148575 -1.27867961 0.70356384 0.9192233541
[148,] 0.79301235 -0.13153881 0.81685914 1.0504160307
[149,] 0.43072244 0.78617383 0.93015445 1.4439940605
[150,] 0.06843254 -0.13153881 0.76021149 0.7880306775
attr(,"scaled:center")
Sepal.Length Sepal.Width Petal.Length Petal.Width
5.843333 3.057333 3.758000 1.199333
attr(,"scaled:scale")
Sepal.Length Sepal.Width Petal.Length Petal.Width
0.8280661 0.4358663 1.7652982 0.7622377 (iris_scaled
%>% data.frame()
%>% summarise(across(everything(.), \(x) round(mean(x),1)))
) Sepal.Length Sepal.Width Petal.Length Petal.Width
1 0 0 0 0(iris_scaled
%>% data.frame()
%>% summarise(across(everything(.), \(x) round(sd(x),1)))
) Sepal.Length Sepal.Width Petal.Length Petal.Width
1 1 1 1 1D)
Find the centered/scaled vectors for the first two irises. Find the L1 and L2 distances between these two irises “from scratch,” then verify your answer using dist.
(iris_1and2 <- iris_scaled[1:2,]) Sepal.Length Sepal.Width Petal.Length Petal.Width
[1,] -0.8976739 1.0156020 -1.335752 -1.311052
[2,] -1.1392005 -0.1315388 -1.335752 -1.311052L1 = |-1.139 + 0.898| + |-0.132 - 1.016| + |-1.336 + 1.336| + |-1.311 + 1.311|
= 0.241 + 1.148 + 0 + 0
= 1.389
L2 = sqrt[(-1.139 + 0.898)2 + (-0.132 - 1.016)2 + (-1.336 + 1.366)2 + (-1.311 + 1.311)2]
= sqrt(0.058 + 1.318 + 0 + 0)
= sqrt(1.376)
= 1.173
(L1_dist <- dist(iris_1and2, method = 'manhattan')) 1
2 1.388667(L2_dist <- dist(iris_1and2, method = 'euclidean')) 1
2 1.172291Question 3
Reconsider the USairpollution data. If you don’t have the HSAUR2 package installed, run install.packages(HSAUR2) once in your console to install the package. Do not insert this code in your .qmd, as you only need to install the package once, not every time you compile the html.
library(HSAUR2)
data("USairpollution")
head(USairpollution) SO2 temp manu popul wind precip predays
Albany 46 47.6 44 116 8.8 33.36 135
Albuquerque 11 56.8 46 244 8.9 7.77 58
Atlanta 24 61.5 368 497 9.1 48.34 115
Baltimore 47 55.0 625 905 9.6 41.31 111
Buffalo 11 47.1 391 463 12.4 36.11 166
Charleston 31 55.2 35 71 6.5 40.75 148A)
GOAL: Find the cities that are most and least similar with respect to their pollution. Use dist to find L2 distances between the cities. Then use wrangling approaches (i.e., DSCI 210/325 techniques) to find the two cities that are most similar, and two cities that are most dissimilar.
(pollution_dist <- dist(USairpollution, method = 'euclidean')) Albany Albuquerque Atlanta Baltimore Buffalo
Albuquerque 155.82522
Atlanta 501.43664 415.66700
Baltimore 980.19264 881.70044 482.85600
Buffalo 492.97543 423.74461 69.44655 504.51788
Charleston 51.16309 199.11303 541.85520 1022.39472 530.32627
Chicago 4634.25147 4545.00583 4136.75219 3669.93381 4144.49044
Cincinnati 537.50080 472.59485 105.87134 481.56246 80.77924
Cleveland 1153.84855 1092.56137 690.24539 414.69232 682.23696
Columbus 479.05070 378.02137 113.34293 512.94029 151.12118
Dallas 944.12289 845.76292 443.52124 81.64537 464.51705
Denver 575.30696 490.68916 99.77285 428.57935 116.96147
Des Moines 112.71211 88.72889 397.45636 876.45249 393.76480
Detroit 1729.79153 1628.76911 1231.83872 750.32418 1247.96380
Hartford 370.74855 386.60660 343.80732 777.01635 311.57707
Houston 1307.29324 1198.98115 816.51863 344.20195 840.47232
Indianapolis 705.66341 597.04860 249.55793 308.95292 288.69404
Jacksonville 425.78900 308.24253 234.59386 618.03267 269.61777
Kansas City 518.49040 428.88797 28.34441 468.17944 81.21153
Little Rock 72.03295 134.22255 458.58597 940.24037 451.97993
Louisville 537.67770 433.20055 123.72471 457.53502 171.02064
Memphis 588.68744 482.72383 131.85825 404.24548 181.51647
Miami 278.12322 205.32857 229.90725 708.55098 230.35698
Milwaukee 798.68706 708.58543 299.26120 199.56490 313.25051
Minneapolis 907.62168 826.73087 414.61670 181.01516 418.46102
Nashville 406.10937 315.11314 105.41976 576.45316 127.31203
New Orleans 297.41331 210.27482 213.86630 689.23315 221.53617
Norfolk 201.05291 108.31199 331.32384 797.84826 337.89869
Omaha 273.04346 176.00369 241.43534 714.06990 249.49103
Philadelphia 2465.86330 2372.21512 1966.29819 1493.65862 1977.32488
Phoenix 507.96589 377.90102 198.69301 531.49581 253.31736
Pittsburgh 505.38142 421.95807 60.27599 476.49565 89.81037
Providence 309.63070 324.16775 326.97821 780.40571 302.63136
Richmond 240.60065 174.68578 261.72123 742.21997 259.87982
Salt Lake City 122.60280 119.34588 397.87518 878.14014 391.88057
San Francisco 730.27742 623.44302 241.70929 262.48071 279.28400
Seattle 534.43624 453.66616 62.46961 451.16139 71.61133
St. Louis 889.64756 824.22746 427.29910 320.52488 422.57413
Washington 750.97997 646.38600 268.52185 242.32259 302.91150
Wichita 191.93472 91.92266 330.37310 804.28434 335.46672
Wilmington 56.75801 181.31685 507.05001 988.82884 496.80510
Charleston Chicago Cincinnati Cleveland Columbus
Albuquerque
Atlanta
Baltimore
Buffalo
Charleston
Chicago 4672.60936
Cincinnati 573.21700 4100.81609
Cleveland 1186.79054 3509.78751 623.03397
Columbus 523.04406 4181.45138 214.50086 771.73610
Dallas 985.04441 3700.56980 433.82818 389.79886 486.50645
Denver 614.43224 4062.98246 82.15052 607.50655 197.31499
Des Moines 155.05012 4532.42210 438.92355 1059.68614 377.17099
Detroit 1771.64299 2940.88808 1219.11775 765.17052 1258.44365
Hartford 388.34820 4348.58252 301.14012 840.60288 410.16505
Houston 1350.39532 3384.30349 822.68489 566.03170 830.01421
Indianapolis 750.10779 3973.05485 310.17050 647.98786 227.24182
Jacksonville 470.79270 4285.65475 335.91269 901.54344 134.46004
Kansas City 559.04276 4120.70139 103.24641 676.14857 125.27554
Little Rock 97.88719 4590.24860 491.88015 1108.27074 445.68699
Louisville 581.94069 4127.16496 221.34038 734.83094 60.20889
Memphis 631.99760 4072.80006 214.30673 686.21978 115.94196
Miami 317.65113 4365.45829 282.89722 904.48592 216.54917
Milwaukee 838.79483 3839.61206 285.42141 443.25710 351.37718
Minneapolis 945.68654 3727.40643 375.77268 310.89135 478.86694
Nashville 448.09169 4237.88772 187.79308 794.58310 94.75083
New Orleans 338.82423 4349.57031 275.87231 895.89931 193.10033
Norfolk 246.90700 4463.81928 394.17401 1014.41271 288.43833
Omaha 316.90026 4375.71299 302.54452 922.69625 214.39669
Philadelphia 2505.76009 2178.17396 1938.12316 1381.48185 2005.94246
Phoenix 554.21471 4193.93415 298.85993 823.05043 125.26293
Pittsburgh 547.62941 4135.43712 139.31691 699.31771 91.41922
Providence 333.27744 4379.77573 307.19540 877.42886 375.49194
Richmond 281.69728 4397.24233 307.02816 929.33270 251.54488
Salt Lake City 159.98693 4526.39872 429.89456 1045.77692 389.41398
San Francisco 773.35742 3925.44889 271.92586 564.75941 266.31630
Seattle 574.65212 4105.33971 118.51904 666.46804 117.31568
St. Louis 923.96326 3761.51645 358.28382 270.34646 517.26920
Washington 794.47197 3911.18804 306.09272 575.91018 275.47897
Wichita 235.72193 4464.80517 383.90063 1005.60842 303.58222
Wilmington 57.40157 4634.30731 534.36979 1145.48757 496.70203
Dallas Denver Des Moines Detroit Hartford
Albuquerque
Atlanta
Baltimore
Buffalo
Charleston
Chicago
Cincinnati
Cleveland
Columbus
Dallas
Denver 379.57165
Des Moines 838.34888 470.87011
Detroit 793.76201 1170.72908 1626.02153
Hartford 726.63486 365.16875 314.59752 1503.90487
Houston 398.12606 767.25817 1202.68817 444.98131 1119.91808
Indianapolis 300.69335 253.02524 602.98789 1040.51788 590.92907
Jacksonville 596.71736 322.83928 331.24919 1353.12478 464.97069
Kansas City 426.34941 78.46759 412.86743 1216.52113 354.09142
Little Rock 900.07588 529.16791 73.62220 1689.86691 326.28787
Louisville 433.74823 187.38945 435.20602 1201.73764 452.32821
Memphis 376.48803 165.47191 483.49439 1149.13783 474.94223
Miami 671.26552 313.00780 175.45425 1457.47978 276.47406
Milwaukee 154.45147 236.01935 694.90749 937.58312 582.21121
Minneapolis 133.64273 339.78355 806.36761 851.32392 653.40013
Nashville 541.00873 196.90039 301.42258 1325.69087 323.25101
New Orleans 652.63125 298.66120 191.87542 1438.27800 295.67983
Norfolk 765.75002 416.14074 110.34364 1545.80427 351.01327
Omaha 677.70441 321.25791 165.18411 1463.09631 303.10121
Philadelphia 1527.40243 1896.35165 2362.98738 766.03381 2202.27597
Phoenix 504.44866 255.93235 403.27059 1265.40138 481.19807
Pittsburgh 446.23869 132.94699 405.85224 1225.22096 368.43856
Providence 735.37195 365.46027 253.30016 1517.57480 81.57055
Richmond 704.23339 338.44098 136.77071 1491.96713 259.28413
Salt Lake City 837.48986 464.26913 47.82376 1627.51329 281.02658
San Francisco 228.44380 202.16472 623.31082 1006.50747 564.93769
Seattle 417.90834 113.03763 434.12060 1197.86194 377.28124
St. Louis 265.11517 341.92761 793.14747 937.27246 589.61974
Washington 228.02954 245.83558 646.82389 984.33444 600.29776
Wichita 766.73733 406.60619 82.45655 1553.19245 317.95051
Wilmington 949.00634 575.32226 125.76645 1738.41172 341.92213
Houston Indianapolis Jacksonville Kansas City Little Rock
Albuquerque
Atlanta
Baltimore
Buffalo
Charleston
Chicago
Cincinnati
Cleveland
Columbus
Dallas
Denver
Des Moines
Detroit
Hartford
Houston
Indianapolis 606.45121
Jacksonville 915.46146 313.75540
Kansas City 801.89851 241.26533 247.58403
Little Rock 1268.53785 671.36844 399.97690 474.24171
Louisville 771.69226 168.37146 169.46722 127.94308 503.38597
Memphis 719.99839 127.41299 222.79640 125.99389 550.10517
Miami 1035.08772 440.44552 207.16143 248.35225 236.21204
Milwaukee 539.16678 210.69997 473.34496 283.13877 756.22242
Minneapolis 492.20145 338.74340 604.39822 399.00587 864.09193
Nashville 903.08607 310.50017 161.43281 123.46020 366.20623
New Orleans 1013.83122 416.99133 181.34900 231.19224 255.96170
Norfolk 1116.67566 512.04306 225.63664 348.54897 177.77625
Omaha 1037.91335 438.63579 190.66469 256.23685 234.01687
Philadelphia 1208.64766 1795.24392 2108.03356 1950.45117 2423.18029
Phoenix 829.50075 240.18940 131.96252 197.47568 472.54639
Pittsburgh 808.25088 230.31945 220.06686 76.52306 469.95541
Providence 1123.26615 571.14550 415.10138 340.81912 270.29438
Richmond 1071.21278 476.22944 238.79057 278.51014 198.90894
Salt Lake City 1208.40396 613.72489 356.90651 412.16925 74.90309
San Francisco 584.22954 113.50439 373.01879 223.97885 688.46563
Seattle 783.74560 220.00121 249.25391 71.02904 496.68010
St. Louis 615.36898 433.39719 647.57776 412.63112 842.62519
Washington 556.41109 74.67384 376.03749 256.30041 713.27319
Wichita 1126.97028 526.94599 256.01207 344.69395 151.29922
Wilmington 1319.61180 722.93545 453.46952 523.11644 60.56429
Louisville Memphis Miami Milwaukee Minneapolis
Albuquerque
Atlanta
Baltimore
Buffalo
Charleston
Chicago
Cincinnati
Cleveland
Columbus
Dallas
Denver
Des Moines
Detroit
Hartford
Houston
Indianapolis
Jacksonville
Kansas City
Little Rock
Louisville
Memphis 62.23898
Miami 273.34970 318.21021
Milwaukee 305.22677 251.97970 528.08069
Minneapolis 435.78493 384.31101 641.84115 134.20163
Nashville 146.50581 187.33964 134.12256 399.13221 518.16938
New Orleans 249.56341 295.00400 31.18302 511.27254 627.90156
Norfolk 345.42936 398.15297 118.86385 625.87065 744.81597
Omaha 271.45489 318.73636 56.50623 536.75756 654.03445
Philadelphia 1950.85822 1896.84350 2194.97881 1668.68001 1562.97439
Phoenix 125.28250 154.12700 268.93792 392.03275 523.54392
Pittsburgh 100.38786 124.78932 240.77622 301.28553 418.75856
Providence 422.18098 453.53483 225.47841 588.91007 671.30829
Richmond 308.80026 354.45787 49.31971 560.01682 671.57480
Salt Lake City 446.72918 492.49148 186.05961 693.42333 800.59281
San Francisco 212.92809 155.56701 459.66017 129.65469 258.25323
Seattle 115.36950 120.29791 265.88332 269.58375 385.64533
St. Louis 485.95335 440.64848 639.21366 231.38894 150.55555
Washington 217.97178 166.18587 480.65742 142.74187 267.26360
Wichita 360.21433 407.75758 115.89956 626.58032 742.44767
Wilmington 554.81369 602.39366 287.87229 803.47540 908.26901
Nashville New Orleans Norfolk Omaha Philadelphia
Albuquerque
Atlanta
Baltimore
Buffalo
Charleston
Chicago
Cincinnati
Cleveland
Columbus
Dallas
Denver
Des Moines
Detroit
Hartford
Houston
Indianapolis
Jacksonville
Kansas City
Little Rock
Louisville
Memphis
Miami
Milwaukee
Minneapolis
Nashville
New Orleans 113.67697
Norfolk 227.65773 123.28020
Omaha 140.76819 44.39052 98.13348
Philadelphia 2065.56839 2177.87551 2290.16826 2203.66748
Phoenix 174.33451 239.44485 311.71169 247.02519 2017.40614
Pittsburgh 114.80374 224.35176 331.59949 249.26881 1963.42671
Providence 287.92918 245.66296 285.98989 248.51025 2226.43147
Richmond 168.46150 67.06685 101.60521 56.54722 2227.71100
Salt Lake City 308.30130 204.15910 144.17469 178.00110 2359.67897
San Francisco 326.95267 437.70947 545.21769 459.60038 1750.37326
Seattle 141.32984 251.28892 363.63357 278.77866 1934.30726
St. Louis 531.06781 630.09995 748.64747 655.99384 1613.92689
Washington 347.85618 458.86981 562.06158 482.30184 1734.19649
Wichita 231.25453 122.88326 60.80715 91.41887 2293.32271
Wilmington 416.96694 309.10315 228.73407 286.95168 2469.11620
Phoenix Pittsburgh Providence Richmond Salt Lake City
Albuquerque
Atlanta
Baltimore
Buffalo
Charleston
Chicago
Cincinnati
Cleveland
Columbus
Dallas
Denver
Des Moines
Detroit
Hartford
Houston
Indianapolis
Jacksonville
Kansas City
Little Rock
Louisville
Memphis
Miami
Milwaukee
Minneapolis
Nashville
New Orleans
Norfolk
Omaha
Philadelphia
Phoenix
Pittsburgh 194.88576
Providence 442.71180 343.38643
Richmond 297.09241 271.45640 201.27063
Salt Lake City 417.36161 409.06351 221.04811 142.15592
San Francisco 277.30576 242.35365 557.75754 492.34982 626.30554
Seattle 219.74901 49.64972 361.88994 299.03272 436.77615
St. Louis 570.41420 442.04906 620.32256 662.92165 779.39333
Washington 294.35638 257.12400 588.94472 515.72748 653.34347
Wichita 321.98640 339.77660 258.00984 85.16273 105.25601
Wilmington 527.09575 516.36456 287.19298 248.54150 117.43976
San Francisco Seattle St. Louis Washington Wichita
Albuquerque
Atlanta
Baltimore
Buffalo
Charleston
Chicago
Cincinnati
Cleveland
Columbus
Dallas
Denver
Des Moines
Detroit
Hartford
Houston
Indianapolis
Jacksonville
Kansas City
Little Rock
Louisville
Memphis
Miami
Milwaukee
Minneapolis
Nashville
New Orleans
Norfolk
Omaha
Philadelphia
Phoenix
Pittsburgh
Providence
Richmond
Salt Lake City
San Francisco
Seattle 223.06848
St. Louis 340.78326 411.50755
Washington 67.82369 238.63876 367.80701
Wichita 548.32510 369.19581 737.83259 572.05254
Wilmington 739.46004 543.47190 881.64214 764.01298 206.77514(distance_df <- pollution_dist
%>% as.matrix
%>% data.frame(check.names = FALSE) #handles the issue of replacing spaces with periods
%>% rownames_to_column('CityA')
%>% pivot_longer(cols = -CityA,
names_to = 'CityB',
values_to = 'Distance'
)
%>% filter(CityA != CityB) #remove the distances betwen a city and itself
#remove duplicate rows
%>% rowwise()
%>% mutate(City1 = min(CityA, CityB),
City2 = max(CityA, CityB))
%>% ungroup()
%>% distinct(City1, City2, .keep_all = TRUE)
%>% select(-c(CityA, CityB))
%>% arrange(desc(Distance))
)# A tibble: 820 × 3
Distance City1 City2
<dbl> <chr> <chr>
1 4673. Charleston Chicago
2 4634. Chicago Wilmington
3 4634. Albany Chicago
4 4590. Chicago Little Rock
5 4545. Albuquerque Chicago
6 4532. Chicago Des Moines
7 4526. Chicago Salt Lake City
8 4465. Chicago Wichita
9 4464. Chicago Norfolk
10 4397. Chicago Richmond
# ℹ 810 more rows(most_dissimilar <- distance_df[1,])# A tibble: 1 × 3
Distance City1 City2
<dbl> <chr> <chr>
1 4673. Charleston Chicago# Charleston and Chicago
(most_similar <- distance_df
%>% arrange(desc(-Distance))
)[1,]# A tibble: 1 × 3
Distance City1 City2
<dbl> <chr> <chr>
1 28.3 Atlanta Kansas City# Atlanta and Kansas CityB)
Assess how scaling the data before computing distance impacts your answer to the previous question.
(scaled_pollution <- scale(USairpollution, center = FALSE, scale = TRUE)) SO2 temp manu popul wind precip
Albany 1.1971497 0.8363065 0.06002535 0.13718084 0.9102788 0.8544499
Albuquerque 0.2862749 0.9979456 0.06275377 0.28855281 0.9206229 0.1990131
Atlanta 0.6245998 1.0805220 0.50203016 0.58774895 0.9413110 1.2381327
Baltimore 1.2231747 0.9663205 0.85263275 1.07024709 0.9930314 1.0580733
Buffalo 0.2862749 0.8275218 0.53340705 0.54754078 1.2826656 0.9248857
Charleston 0.8067748 0.9698344 0.04774743 0.08396414 0.6723650 1.0437300
Chicago 2.8627493 0.8890149 4.56192625 3.98415740 1.0757840 0.8821120
Cincinnati 0.5985748 0.9487511 0.63026613 0.53571484 0.7344295 0.9999318
Cleveland 1.6916246 0.8732024 1.37376188 0.88812770 1.1275044 0.8961991
Columbus 0.6766498 0.9048274 0.36288050 0.63860047 0.8895907 0.9479374
Dallas 0.2342249 1.1630985 0.87446015 0.99810889 1.1275044 0.9205315
Denver 0.4424249 0.9118552 0.61935243 0.60903564 0.9309670 0.3316884
Des Moines 0.4424249 0.8609037 0.14187809 0.23770129 1.1585367 0.7901613
Detroit 0.9108748 0.8767163 1.45152199 1.78926392 1.0447518 0.7929787
Hartford 1.4573996 0.8626607 0.56205551 0.18684977 0.9309670 1.1108361
Houston 0.2602499 1.2105361 0.98359714 1.45813775 1.1171604 1.2342908
Indianapolis 0.7286998 0.9188830 0.49248068 0.88221473 1.0033755 0.9922479
Jacksonville 0.3643499 1.2017513 0.18553289 0.62559195 0.9102788 1.3951405
Kansas City 0.3643499 0.9575358 0.51976492 0.59957489 1.0344077 0.9476812
Little Rock 0.3383249 1.0717373 0.12414333 0.15610234 0.8482143 1.2427431
Louisville 0.7807498 0.9768622 0.39698581 0.70127793 0.8585584 1.1041767
Memphis 0.2602499 1.0822790 0.45973958 0.73793833 0.9516551 1.2575986
Miami 0.2602499 1.3264945 0.28239197 0.39616881 0.9309670 1.5316578
Milwaukee 0.4163999 0.8029245 0.77623685 0.84791952 1.2206011 0.7445701
Minneapolis 0.7547248 0.7642717 0.95358447 0.87984954 1.0964722 0.6644014
Nashville 0.4684499 1.0436262 0.37515841 0.52980187 0.8171821 1.1781983
New Orleans 0.2342249 1.1999944 0.27829933 0.42691624 0.8689025 1.4540504
Norfolk 0.8067748 1.0418692 0.13096439 0.36423879 1.0964722 1.1443891
Omaha 0.3643499 0.9048274 0.24692244 0.41035993 1.1275044 0.7730005
Philadelphia 1.7957245 0.9592927 2.30824737 2.30605727 0.9930314 1.0227274
Phoenix 0.2602499 1.2351333 0.29057724 0.68826940 0.6206446 0.1805717
Pittsburgh 1.5875246 0.8855010 0.47338170 0.61494860 0.9723433 0.9277031
Providence 2.4463494 0.8784732 0.46792485 0.21168423 1.0964722 1.0949560
Richmond 0.6766498 1.0155150 0.26874984 0.35359545 0.7861499 1.0908580
Salt Lake City 0.7286998 0.8960427 0.18689710 0.20813645 0.8999347 0.3885493
San Francisco 0.3122999 0.9961886 0.61798822 0.84673692 0.8999347 0.5291647
Seattle 0.7547248 0.8977996 0.51703650 0.62795713 0.9723433 0.9935285
St. Louis 1.4573996 0.9821330 1.05726461 0.73557314 0.9826873 0.9192508
Washington 0.7547248 1.0067303 0.59206818 0.89522326 0.9619992 0.9960898
Wichita 0.2081999 0.9944317 0.17052655 0.32757839 1.3136978 0.7832457
Wilmington 0.9368998 0.9487511 0.10913699 0.09460748 0.9309670 1.0309235
predays
Albany 1.1409297
Albuquerque 0.4901772
Atlanta 0.9719031
Baltimore 0.9380978
Buffalo 1.4029210
Charleston 1.2507970
Chicago 1.0310624
Cincinnati 1.1155757
Cleveland 1.3099563
Columbus 1.1324784
Dallas 0.6592038
Denver 0.7268145
Des Moines 0.8704871
Detroit 1.0902217
Hartford 1.0733191
Houston 0.8704871
Indianapolis 1.0226111
Jacksonville 0.9803544
Kansas City 0.8366818
Little Rock 0.8451331
Louisville 1.0395137
Memphis 0.8873898
Miami 1.0817704
Milwaukee 1.0395137
Minneapolis 1.1578324
Nashville 1.0057084
New Orleans 0.9550004
Norfolk 0.9803544
Omaha 0.8282305
Philadelphia 0.9719031
Phoenix 0.3042479
Pittsburgh 1.2423457
Providence 1.0564164
Richmond 0.9719031
Salt Lake City 0.7521685
San Francisco 0.5662392
Seattle 1.3860183
St. Louis 0.8873898
Washington 0.9380978
Wichita 0.6930092
Wilmington 0.9634518
attr(,"scaled:scale")
SO2 temp manu popul wind precip predays
38.424601 56.916933 733.023687 845.599122 9.667368 39.042663 118.324554 (pollution_dist <- dist(scaled_pollution, method = 'euclidean')) Albany Albuquerque Atlanta Baltimore Buffalo Charleston
Albuquerque 1.3160259
Atlanta 0.9811116 1.3099703
Baltimore 1.2672298 1.7485984 0.8736702
Buffalo 1.1977179 1.3448794 0.7625596 1.2608968
Charleston 0.5269780 1.2913223 0.8327770 1.4123771 1.0731608
Chicago 6.1549629 6.4291048 5.7630433 4.9990364 5.9045923 6.3292994
Cincinnati 0.9527173 1.2451397 0.3967044 0.9095928 0.7145008 0.7818271
Cleveland 1.6165369 2.2955842 1.5157617 0.8458276 1.6831014 1.8519469
Columbus 0.7924629 1.1610661 0.4101208 0.8884034 0.6510902 0.7060108
Dallas 1.6498884 1.3357696 0.8364390 1.0663987 1.0059120 1.5673516
Denver 1.2474012 0.7197309 0.9786064 1.2065654 0.9876022 1.2597542
Des Moines 0.8520111 0.7763405 0.7692941 1.3866246 0.7693095 0.7889284
Detroit 2.1848709 2.3051874 1.6405866 1.0379333 1.7173059 2.2639502
Hartford 0.6274225 1.6796022 0.9653698 0.9774218 1.3306365 0.9015397
Houston 1.9687456 1.8753176 1.0864441 1.0979563 1.2593032 1.8707182
Indianapolis 1.0049935 1.2878842 0.4366325 0.6506949 0.7382036 1.0039774
Jacksonville 1.1830189 1.3591924 0.4579465 1.2481971 0.9009028 0.9028301
Kansas City 1.1180732 1.0034137 0.4411620 1.0460278 0.6392741 0.9981672
Little Rock 1.0196058 1.1180677 0.6602323 1.4913573 0.9919576 0.6899001
Louisville 0.8367893 1.2852808 0.2973461 0.7550477 0.8081651 0.7659849
Memphis 1.2990335 1.2832298 0.4058666 1.1178364 0.7702564 1.0791481
Miami 1.3027377 1.5147526 0.6136220 1.4440504 0.9646633 0.9549577
Milwaukee 1.3219121 1.2515211 0.7677655 0.9450964 0.5789316 1.3150195
Minneapolis 1.2735798 1.4527672 0.8910573 0.7215763 0.8203734 1.3532698
Nashville 0.9793926 1.1942983 0.2556195 1.0703143 0.7374728 0.7245691
New Orleans 1.2597165 1.3794896 0.5428978 1.3960122 0.9343037 0.9198058
Norfolk 0.6290894 1.2033965 0.5052352 1.1037597 0.8796800 0.5948162
Omaha 0.9794946 0.7416626 0.6832300 1.2865138 0.7002693 0.8973179
Philadelphia 3.1930675 3.5083195 2.7659190 1.9940651 2.9694238 3.3476470
Phoenix 1.6222617 0.6273029 1.3705831 1.6648557 1.5636345 1.5610562
Pittsburgh 0.7572591 1.7551255 1.0664364 0.7748561 1.3516107 1.0878015
Providence 1.3542025 2.4504145 1.8851790 1.5540474 2.2291843 1.7634307
Richmond 0.7023559 1.1157492 0.4024271 1.0957353 0.8690474 0.4832310
Salt Lake City 0.7825922 0.5770561 1.0295976 1.3883019 1.1372413 0.8809100
San Francisco 1.4350960 0.8577580 0.9241619 1.1671717 1.0625030 1.3918986
Seattle 0.8558651 1.4097885 0.5333362 0.8588437 0.5765558 0.7967752
St. Louis 1.2309669 1.8002873 1.0695388 0.4805645 1.4356224 1.4529429
Washington 1.0706818 1.3059179 0.4303261 0.5695704 0.8365661 1.0688477
Wichita 1.1916110 0.7458033 0.8841718 1.5120235 0.8596627 1.1061675
Wilmington 0.3842754 1.1754445 0.7453606 1.2618053 1.0729548 0.4133585
Chicago Cincinnati Cleveland Columbus Dallas Denver
Albuquerque
Atlanta
Baltimore
Buffalo
Charleston
Chicago
Cincinnati 5.7111565
Cleveland 4.6045880 1.4423932
Columbus 5.8011467 0.3423005 1.4852936
Dallas 5.4443167 0.9062132 1.7010357 0.9668230
Denver 5.7628406 0.8170377 1.7048090 0.8170683 0.8443119
Des Moines 6.2827229 0.8021059 1.9252490 0.6574325 1.1454978 0.8069040
Detroit 4.2795496 1.5774470 1.2220726 1.6170006 1.3067864 1.6321536
Hartford 5.6981827 0.9612822 1.1603119 0.9417247 1.6088790 1.3932890
Houston 5.1198750 1.1917120 1.7167742 1.2353958 0.6079947 1.3586933
Indianapolis 5.5457136 0.4877551 1.3465523 0.3256257 0.7849220 0.8377371
Jacksonville 6.0881644 0.7281028 1.9378293 0.6639855 1.0036905 1.2141869
Kansas City 5.8382323 0.4916564 1.6782878 0.4846781 0.6202654 0.6483884
Little Rock 6.4008157 0.7925687 2.0934183 0.7767318 1.2278139 1.1565672
Louisville 5.7064031 0.3845377 1.4206225 0.2348055 0.9487660 0.9361662
Memphis 5.8611661 0.6065601 1.8140108 0.6196274 0.6659557 0.9939046
Miami 6.2127224 0.8486140 2.0449749 0.8726147 1.1536538 1.3892042
Milwaukee 5.4954008 0.6932461 1.4472689 0.6725777 0.6159405 0.6681029
Minneapolis 5.2134520 0.7258237 1.0696259 0.7462033 0.8748857 0.7926094
Nashville 5.9475504 0.3764923 1.7085658 0.3859196 0.9058180 0.9440643
New Orleans 6.1955606 0.7626814 2.0365725 0.7892429 1.0592654 1.2615361
Norfolk 6.0876447 0.7077797 1.6738015 0.5189483 1.2046992 1.0955637
Omaha 6.1391577 0.7127621 1.8729456 0.5855288 0.9344647 0.6542093
Philadelphia 3.0114265 2.7333218 1.7465418 2.8039681 2.5244010 2.8473451
Phoenix 6.1014483 1.2952570 2.2745414 1.2795833 1.1718477 0.7414623
Pittsburgh 5.4544838 1.0444154 0.9622567 0.9285282 1.6063427 1.3985736
Providence 5.5867947 1.9220210 1.3973202 1.8428301 2.4387303 2.2172625
Richmond 6.0446952 0.4538711 1.6810407 0.3990625 1.1149521 0.9545456
Salt Lake City 6.1891631 0.9256564 1.8491634 0.8226259 1.3251638 0.6593786
San Francisco 5.6820672 0.8554960 1.7972720 0.8634830 0.5798657 0.3824823
Seattle 5.6761047 0.4220090 1.3112539 0.3212966 1.0787634 0.9913876
St. Louis 4.9850095 1.0397959 0.6246891 1.0847478 1.3054845 1.2714482
Washington 5.4583415 0.4916817 1.2970564 0.4245087 0.7046877 0.8223218
Wichita 6.3161194 0.9850014 2.0988774 0.8725436 1.0143558 0.8329903
Wilmington 6.2222250 0.8020874 1.7265893 0.6834780 1.4439914 1.1470613
Des Moines Detroit Hartford Houston Indianapolis
Albuquerque
Atlanta
Baltimore
Buffalo
Charleston
Chicago
Cincinnati
Cleveland
Columbus
Dallas
Denver
Des Moines
Detroit 2.0984393
Hartford 1.1853577 1.9421727
Houston 1.5976075 1.0543383 1.8544824
Indianapolis 0.8436174 1.3503539 1.0219662 0.9859325
Jacksonville 0.8451866 1.9375115 1.3167777 1.1923491 0.7386560
Kansas City 0.5749328 1.6361769 1.2121082 1.0570016 0.5023878
Little Rock 0.6033520 2.2574279 1.2510276 1.5913403 0.9782586
Louisville 0.7906048 1.5674199 0.8770470 1.1639793 0.2858565
Memphis 0.8336972 1.6793350 1.3609202 0.9153058 0.5995015
Miami 0.9700847 2.1194002 1.3955278 1.3418826 0.9826883
Milwaukee 0.9018408 1.2759027 1.3376536 0.9407396 0.5490795
Minneapolis 1.1315147 1.0657304 1.1708178 1.0893781 0.6096223
Nashville 0.6776339 1.7820568 1.0887482 1.1893820 0.5392416
New Orleans 0.8628569 2.0690650 1.3724967 1.2956543 0.9014517
Norfolk 0.5683577 1.9876912 0.8425527 1.5070888 0.6736572
Omaha 0.2278452 1.9307518 1.2484509 1.3998228 0.7191352
Philadelphia 3.3021382 1.3639247 2.7723507 2.2282108 2.5432496
Phoenix 1.1746968 2.0698843 1.8574681 1.6586312 1.3111774
Pittsburgh 1.3251163 1.6853019 0.5219248 1.7583630 0.9294636
Providence 2.0626020 2.4308259 1.0078089 2.6006293 1.8500070
Richmond 0.5896350 1.9245328 0.8822830 1.4432147 0.6332638
Salt Lake City 0.5729357 2.1051405 1.1397867 1.8144009 0.9982864
San Francisco 0.9275779 1.5234266 1.5375621 1.0922873 0.7935976
Seattle 0.8565831 1.5426220 0.8971304 1.2624972 0.4465436
St. Louis 1.4759918 1.2792352 0.7965881 1.4596166 0.9484356
Washington 0.9161919 1.2847178 1.0245078 0.9173853 0.1653802
Wichita 0.3704199 2.1249205 1.4660822 1.5040697 0.9677411
Wilmington 0.6262326 2.1829704 0.7144455 1.7985968 0.9065073
Jacksonville Kansas City Little Rock Louisville Memphis
Albuquerque
Atlanta
Baltimore
Buffalo
Charleston
Chicago
Cincinnati
Cleveland
Columbus
Dallas
Denver
Des Moines
Detroit
Hartford
Houston
Indianapolis
Jacksonville
Kansas City 0.6389826
Little Rock 0.5358469 0.6990741
Louisville 0.6043504 0.5438154 0.7959221
Memphis 0.3770857 0.3932089 0.6856173 0.5853732
Miami 0.3431683 0.8102372 0.5477120 0.8301535 0.5667628
Milwaukee 1.0407566 0.5207011 1.1860966 0.7672888 0.7572054
Minneapolis 1.2643090 0.8023304 1.4048482 0.8071967 1.0274482
Nashville 0.3706045 0.4158398 0.5012944 0.3744371 0.3656538
New Orleans 0.2661549 0.6794382 0.4260757 0.7533255 0.4406836
Norfolk 0.6246035 0.6874508 0.5943862 0.5009848 0.7684384
Omaha 0.7717798 0.3902246 0.6381258 0.7158075 0.6813096
Philadelphia 3.0956600 2.8609818 3.4080381 2.6996311 2.8831935
Phoenix 1.4293702 1.0915281 1.3476828 1.3414101 1.2899832
Pittsburgh 1.4036132 1.2932700 1.4832826 0.8704897 1.4321121
Providence 2.1956456 2.1372750 2.1749728 1.7565906 2.2745489
Richmond 0.5667359 0.5699330 0.4696073 0.3995623 0.6514444
Salt Lake City 1.2107358 0.8593086 0.9648167 0.9449702 1.1770594
San Francisco 1.0965402 0.5842246 1.1475603 0.9198689 0.8266978
Seattle 0.8272767 0.6815413 0.9750528 0.4146948 0.7827568
St. Louis 1.5017851 1.2283398 1.6097747 0.9837552 1.3840811
Washington 0.7694802 0.5150922 1.0125687 0.3315257 0.6029325
Wichita 0.8809829 0.5893874 0.7109279 0.9743055 0.8101452
Wilmington 0.9016490 0.8861139 0.6656869 0.7017645 1.0344450
Miami Milwaukee Minneapolis Nashville New Orleans Norfolk
Albuquerque
Atlanta
Baltimore
Buffalo
Charleston
Chicago
Cincinnati
Cleveland
Columbus
Dallas
Denver
Des Moines
Detroit
Hartford
Houston
Indianapolis
Jacksonville
Kansas City
Little Rock
Louisville
Memphis
Miami
Milwaukee 1.2048446
Minneapolis 1.4249061 0.4292596
Nashville 0.5417483 0.8213601 0.9910773
New Orleans 0.2087757 1.1181388 1.3558788 0.4249943
Norfolk 0.7689636 1.0191044 1.1332319 0.5303749 0.7257919
Omaha 0.9319709 0.7340582 1.0066451 0.5939666 0.8075204 0.6262011
Philadelphia 3.2433342 2.5561573 2.2725670 2.9524436 3.2171123 3.0857145
Phoenix 1.6186449 1.3004609 1.4600024 1.2799300 1.4755430 1.4418698
Pittsburgh 1.5597220 1.2886656 1.0492366 1.1987700 1.5407946 0.9721762
Providence 2.2949846 2.1828234 1.9371650 2.0338805 2.2956862 1.6911379
Richmond 0.7067128 0.9633579 1.0620243 0.3102307 0.6117859 0.3687304
Salt Lake City 1.3658356 1.0839700 1.1559989 0.9607798 1.2531989 0.8466683
San Francisco 1.3035243 0.6681669 0.8775790 0.8984838 1.1605095 1.1424571
Seattle 0.9596513 0.6947741 0.6690703 0.5794792 0.9317787 0.6669291
St. Louis 1.6379488 1.1478904 0.8507733 1.2640644 1.5966229 1.2227343
Washington 1.0000736 0.5766963 0.6050620 0.5679824 0.9190833 0.7350962
Wichita 0.9939478 0.9208096 1.2438721 0.8082171 0.8836727 0.7897026
Wilmington 0.9930940 1.2150549 1.2634996 0.7245900 0.9374859 0.3732735
Omaha Philadelphia Phoenix Pittsburgh Providence Richmond
Albuquerque
Atlanta
Baltimore
Buffalo
Charleston
Chicago
Cincinnati
Cleveland
Columbus
Dallas
Denver
Des Moines
Detroit
Hartford
Houston
Indianapolis
Jacksonville
Kansas City
Little Rock
Louisville
Memphis
Miami
Milwaukee
Minneapolis
Nashville
New Orleans
Norfolk
Omaha
Philadelphia 3.1615846
Phoenix 1.0399590 3.2273305
Pittsburgh 1.3450537 2.5215015 1.8667134
Providence 2.1401910 2.8681160 2.6063559 0.9890564
Richmond 0.5930259 3.0454209 1.2790155 1.0446066 1.8204081
Salt Lake City 0.6186288 3.2408445 0.9474151 1.2334765 1.9130662 0.7741503
San Francisco 0.7204541 2.7577774 0.6784343 1.5278359 2.3649219 0.9956354
Seattle 0.8103005 2.6990165 1.5388433 0.8489738 1.7810096 0.6103324
St. Louis 1.4173965 2.0406667 1.7618172 0.7126794 1.2972807 1.2056391
Washington 0.7786054 2.4544795 1.2703379 0.9477568 1.8445969 0.6671695
Wichita 0.3133027 3.3531565 1.0953678 1.5899266 2.3240163 0.8251839
Wilmington 0.7562163 3.2354719 1.4762021 0.9596305 1.5703335 0.4351713
Salt Lake City San Francisco Seattle St. Louis Washington
Albuquerque
Atlanta
Baltimore
Buffalo
Charleston
Chicago
Cincinnati
Cleveland
Columbus
Dallas
Denver
Des Moines
Detroit
Hartford
Houston
Indianapolis
Jacksonville
Kansas City
Little Rock
Louisville
Memphis
Miami
Milwaukee
Minneapolis
Nashville
New Orleans
Norfolk
Omaha
Philadelphia
Phoenix
Pittsburgh
Providence
Richmond
Salt Lake City
San Francisco 0.9118172
Seattle 1.0290434 1.0753560
St. Louis 1.3714667 1.3337634 1.0288568
Washington 1.0279631 0.7476788 0.5382130 0.8632244
Wichita 0.7909614 0.8558125 1.0767206 1.6368459 1.0138154
Wilmington 0.7234011 1.2757375 0.8174965 1.2659971 0.9558120
Wichita
Albuquerque
Atlanta
Baltimore
Buffalo
Charleston
Chicago
Cincinnati
Cleveland
Columbus
Dallas
Denver
Des Moines
Detroit
Hartford
Houston
Indianapolis
Jacksonville
Kansas City
Little Rock
Louisville
Memphis
Miami
Milwaukee
Minneapolis
Nashville
New Orleans
Norfolk
Omaha
Philadelphia
Phoenix
Pittsburgh
Providence
Richmond
Salt Lake City
San Francisco
Seattle
St. Louis
Washington
Wichita
Wilmington 0.9338633(distance_df_scaled <- pollution_dist
%>% as.matrix
%>% data.frame(check.names = FALSE) #handles the issue of replacing spaces with periods
%>% rownames_to_column('CityA')
%>% pivot_longer(cols = -CityA,
names_to = 'CityB',
values_to = 'Distance'
)
%>% filter(CityA != CityB) #remove the distances betwen a city and itself
#remove duplicate rows
%>% rowwise()
%>% mutate(City1 = min(CityA, CityB),
City2 = max(CityA, CityB))
%>% ungroup()
%>% distinct(City1, City2, .keep_all = TRUE)
%>% select(-c(CityA, CityB))
%>% arrange(desc(Distance))
)# A tibble: 820 × 3
Distance City1 City2
<dbl> <chr> <chr>
1 6.43 Albuquerque Chicago
2 6.40 Chicago Little Rock
3 6.33 Charleston Chicago
4 6.32 Chicago Wichita
5 6.28 Chicago Des Moines
6 6.22 Chicago Wilmington
7 6.21 Chicago Miami
8 6.20 Chicago New Orleans
9 6.19 Chicago Salt Lake City
10 6.15 Albany Chicago
# ℹ 810 more rows(most_dissimilar <- distance_df_scaled[1,])# A tibble: 1 × 3
Distance City1 City2
<dbl> <chr> <chr>
1 6.43 Albuquerque Chicago# Albuquerque and Chicago
(most_similar <- distance_df_scaled
%>% arrange(desc(-Distance))
)[1,]# A tibble: 1 × 3
Distance City1 City2
<dbl> <chr> <chr>
1 0.165 Indianapolis Washington# Indianapolis and WashingtonScaling accounts for the difference in variability, resulting in different answers for the most similar and dissimilar cities.
C)
Which city is Minneapolis most similar to? Most dissimilar to?
(scaled_pollution <- scale(USairpollution, center = FALSE, scale = TRUE)) SO2 temp manu popul wind precip
Albany 1.1971497 0.8363065 0.06002535 0.13718084 0.9102788 0.8544499
Albuquerque 0.2862749 0.9979456 0.06275377 0.28855281 0.9206229 0.1990131
Atlanta 0.6245998 1.0805220 0.50203016 0.58774895 0.9413110 1.2381327
Baltimore 1.2231747 0.9663205 0.85263275 1.07024709 0.9930314 1.0580733
Buffalo 0.2862749 0.8275218 0.53340705 0.54754078 1.2826656 0.9248857
Charleston 0.8067748 0.9698344 0.04774743 0.08396414 0.6723650 1.0437300
Chicago 2.8627493 0.8890149 4.56192625 3.98415740 1.0757840 0.8821120
Cincinnati 0.5985748 0.9487511 0.63026613 0.53571484 0.7344295 0.9999318
Cleveland 1.6916246 0.8732024 1.37376188 0.88812770 1.1275044 0.8961991
Columbus 0.6766498 0.9048274 0.36288050 0.63860047 0.8895907 0.9479374
Dallas 0.2342249 1.1630985 0.87446015 0.99810889 1.1275044 0.9205315
Denver 0.4424249 0.9118552 0.61935243 0.60903564 0.9309670 0.3316884
Des Moines 0.4424249 0.8609037 0.14187809 0.23770129 1.1585367 0.7901613
Detroit 0.9108748 0.8767163 1.45152199 1.78926392 1.0447518 0.7929787
Hartford 1.4573996 0.8626607 0.56205551 0.18684977 0.9309670 1.1108361
Houston 0.2602499 1.2105361 0.98359714 1.45813775 1.1171604 1.2342908
Indianapolis 0.7286998 0.9188830 0.49248068 0.88221473 1.0033755 0.9922479
Jacksonville 0.3643499 1.2017513 0.18553289 0.62559195 0.9102788 1.3951405
Kansas City 0.3643499 0.9575358 0.51976492 0.59957489 1.0344077 0.9476812
Little Rock 0.3383249 1.0717373 0.12414333 0.15610234 0.8482143 1.2427431
Louisville 0.7807498 0.9768622 0.39698581 0.70127793 0.8585584 1.1041767
Memphis 0.2602499 1.0822790 0.45973958 0.73793833 0.9516551 1.2575986
Miami 0.2602499 1.3264945 0.28239197 0.39616881 0.9309670 1.5316578
Milwaukee 0.4163999 0.8029245 0.77623685 0.84791952 1.2206011 0.7445701
Minneapolis 0.7547248 0.7642717 0.95358447 0.87984954 1.0964722 0.6644014
Nashville 0.4684499 1.0436262 0.37515841 0.52980187 0.8171821 1.1781983
New Orleans 0.2342249 1.1999944 0.27829933 0.42691624 0.8689025 1.4540504
Norfolk 0.8067748 1.0418692 0.13096439 0.36423879 1.0964722 1.1443891
Omaha 0.3643499 0.9048274 0.24692244 0.41035993 1.1275044 0.7730005
Philadelphia 1.7957245 0.9592927 2.30824737 2.30605727 0.9930314 1.0227274
Phoenix 0.2602499 1.2351333 0.29057724 0.68826940 0.6206446 0.1805717
Pittsburgh 1.5875246 0.8855010 0.47338170 0.61494860 0.9723433 0.9277031
Providence 2.4463494 0.8784732 0.46792485 0.21168423 1.0964722 1.0949560
Richmond 0.6766498 1.0155150 0.26874984 0.35359545 0.7861499 1.0908580
Salt Lake City 0.7286998 0.8960427 0.18689710 0.20813645 0.8999347 0.3885493
San Francisco 0.3122999 0.9961886 0.61798822 0.84673692 0.8999347 0.5291647
Seattle 0.7547248 0.8977996 0.51703650 0.62795713 0.9723433 0.9935285
St. Louis 1.4573996 0.9821330 1.05726461 0.73557314 0.9826873 0.9192508
Washington 0.7547248 1.0067303 0.59206818 0.89522326 0.9619992 0.9960898
Wichita 0.2081999 0.9944317 0.17052655 0.32757839 1.3136978 0.7832457
Wilmington 0.9368998 0.9487511 0.10913699 0.09460748 0.9309670 1.0309235
predays
Albany 1.1409297
Albuquerque 0.4901772
Atlanta 0.9719031
Baltimore 0.9380978
Buffalo 1.4029210
Charleston 1.2507970
Chicago 1.0310624
Cincinnati 1.1155757
Cleveland 1.3099563
Columbus 1.1324784
Dallas 0.6592038
Denver 0.7268145
Des Moines 0.8704871
Detroit 1.0902217
Hartford 1.0733191
Houston 0.8704871
Indianapolis 1.0226111
Jacksonville 0.9803544
Kansas City 0.8366818
Little Rock 0.8451331
Louisville 1.0395137
Memphis 0.8873898
Miami 1.0817704
Milwaukee 1.0395137
Minneapolis 1.1578324
Nashville 1.0057084
New Orleans 0.9550004
Norfolk 0.9803544
Omaha 0.8282305
Philadelphia 0.9719031
Phoenix 0.3042479
Pittsburgh 1.2423457
Providence 1.0564164
Richmond 0.9719031
Salt Lake City 0.7521685
San Francisco 0.5662392
Seattle 1.3860183
St. Louis 0.8873898
Washington 0.9380978
Wichita 0.6930092
Wilmington 0.9634518
attr(,"scaled:scale")
SO2 temp manu popul wind precip predays
38.424601 56.916933 733.023687 845.599122 9.667368 39.042663 118.324554 (pollution_dist <- dist(scaled_pollution, method = 'euclidean')) Albany Albuquerque Atlanta Baltimore Buffalo Charleston
Albuquerque 1.3160259
Atlanta 0.9811116 1.3099703
Baltimore 1.2672298 1.7485984 0.8736702
Buffalo 1.1977179 1.3448794 0.7625596 1.2608968
Charleston 0.5269780 1.2913223 0.8327770 1.4123771 1.0731608
Chicago 6.1549629 6.4291048 5.7630433 4.9990364 5.9045923 6.3292994
Cincinnati 0.9527173 1.2451397 0.3967044 0.9095928 0.7145008 0.7818271
Cleveland 1.6165369 2.2955842 1.5157617 0.8458276 1.6831014 1.8519469
Columbus 0.7924629 1.1610661 0.4101208 0.8884034 0.6510902 0.7060108
Dallas 1.6498884 1.3357696 0.8364390 1.0663987 1.0059120 1.5673516
Denver 1.2474012 0.7197309 0.9786064 1.2065654 0.9876022 1.2597542
Des Moines 0.8520111 0.7763405 0.7692941 1.3866246 0.7693095 0.7889284
Detroit 2.1848709 2.3051874 1.6405866 1.0379333 1.7173059 2.2639502
Hartford 0.6274225 1.6796022 0.9653698 0.9774218 1.3306365 0.9015397
Houston 1.9687456 1.8753176 1.0864441 1.0979563 1.2593032 1.8707182
Indianapolis 1.0049935 1.2878842 0.4366325 0.6506949 0.7382036 1.0039774
Jacksonville 1.1830189 1.3591924 0.4579465 1.2481971 0.9009028 0.9028301
Kansas City 1.1180732 1.0034137 0.4411620 1.0460278 0.6392741 0.9981672
Little Rock 1.0196058 1.1180677 0.6602323 1.4913573 0.9919576 0.6899001
Louisville 0.8367893 1.2852808 0.2973461 0.7550477 0.8081651 0.7659849
Memphis 1.2990335 1.2832298 0.4058666 1.1178364 0.7702564 1.0791481
Miami 1.3027377 1.5147526 0.6136220 1.4440504 0.9646633 0.9549577
Milwaukee 1.3219121 1.2515211 0.7677655 0.9450964 0.5789316 1.3150195
Minneapolis 1.2735798 1.4527672 0.8910573 0.7215763 0.8203734 1.3532698
Nashville 0.9793926 1.1942983 0.2556195 1.0703143 0.7374728 0.7245691
New Orleans 1.2597165 1.3794896 0.5428978 1.3960122 0.9343037 0.9198058
Norfolk 0.6290894 1.2033965 0.5052352 1.1037597 0.8796800 0.5948162
Omaha 0.9794946 0.7416626 0.6832300 1.2865138 0.7002693 0.8973179
Philadelphia 3.1930675 3.5083195 2.7659190 1.9940651 2.9694238 3.3476470
Phoenix 1.6222617 0.6273029 1.3705831 1.6648557 1.5636345 1.5610562
Pittsburgh 0.7572591 1.7551255 1.0664364 0.7748561 1.3516107 1.0878015
Providence 1.3542025 2.4504145 1.8851790 1.5540474 2.2291843 1.7634307
Richmond 0.7023559 1.1157492 0.4024271 1.0957353 0.8690474 0.4832310
Salt Lake City 0.7825922 0.5770561 1.0295976 1.3883019 1.1372413 0.8809100
San Francisco 1.4350960 0.8577580 0.9241619 1.1671717 1.0625030 1.3918986
Seattle 0.8558651 1.4097885 0.5333362 0.8588437 0.5765558 0.7967752
St. Louis 1.2309669 1.8002873 1.0695388 0.4805645 1.4356224 1.4529429
Washington 1.0706818 1.3059179 0.4303261 0.5695704 0.8365661 1.0688477
Wichita 1.1916110 0.7458033 0.8841718 1.5120235 0.8596627 1.1061675
Wilmington 0.3842754 1.1754445 0.7453606 1.2618053 1.0729548 0.4133585
Chicago Cincinnati Cleveland Columbus Dallas Denver
Albuquerque
Atlanta
Baltimore
Buffalo
Charleston
Chicago
Cincinnati 5.7111565
Cleveland 4.6045880 1.4423932
Columbus 5.8011467 0.3423005 1.4852936
Dallas 5.4443167 0.9062132 1.7010357 0.9668230
Denver 5.7628406 0.8170377 1.7048090 0.8170683 0.8443119
Des Moines 6.2827229 0.8021059 1.9252490 0.6574325 1.1454978 0.8069040
Detroit 4.2795496 1.5774470 1.2220726 1.6170006 1.3067864 1.6321536
Hartford 5.6981827 0.9612822 1.1603119 0.9417247 1.6088790 1.3932890
Houston 5.1198750 1.1917120 1.7167742 1.2353958 0.6079947 1.3586933
Indianapolis 5.5457136 0.4877551 1.3465523 0.3256257 0.7849220 0.8377371
Jacksonville 6.0881644 0.7281028 1.9378293 0.6639855 1.0036905 1.2141869
Kansas City 5.8382323 0.4916564 1.6782878 0.4846781 0.6202654 0.6483884
Little Rock 6.4008157 0.7925687 2.0934183 0.7767318 1.2278139 1.1565672
Louisville 5.7064031 0.3845377 1.4206225 0.2348055 0.9487660 0.9361662
Memphis 5.8611661 0.6065601 1.8140108 0.6196274 0.6659557 0.9939046
Miami 6.2127224 0.8486140 2.0449749 0.8726147 1.1536538 1.3892042
Milwaukee 5.4954008 0.6932461 1.4472689 0.6725777 0.6159405 0.6681029
Minneapolis 5.2134520 0.7258237 1.0696259 0.7462033 0.8748857 0.7926094
Nashville 5.9475504 0.3764923 1.7085658 0.3859196 0.9058180 0.9440643
New Orleans 6.1955606 0.7626814 2.0365725 0.7892429 1.0592654 1.2615361
Norfolk 6.0876447 0.7077797 1.6738015 0.5189483 1.2046992 1.0955637
Omaha 6.1391577 0.7127621 1.8729456 0.5855288 0.9344647 0.6542093
Philadelphia 3.0114265 2.7333218 1.7465418 2.8039681 2.5244010 2.8473451
Phoenix 6.1014483 1.2952570 2.2745414 1.2795833 1.1718477 0.7414623
Pittsburgh 5.4544838 1.0444154 0.9622567 0.9285282 1.6063427 1.3985736
Providence 5.5867947 1.9220210 1.3973202 1.8428301 2.4387303 2.2172625
Richmond 6.0446952 0.4538711 1.6810407 0.3990625 1.1149521 0.9545456
Salt Lake City 6.1891631 0.9256564 1.8491634 0.8226259 1.3251638 0.6593786
San Francisco 5.6820672 0.8554960 1.7972720 0.8634830 0.5798657 0.3824823
Seattle 5.6761047 0.4220090 1.3112539 0.3212966 1.0787634 0.9913876
St. Louis 4.9850095 1.0397959 0.6246891 1.0847478 1.3054845 1.2714482
Washington 5.4583415 0.4916817 1.2970564 0.4245087 0.7046877 0.8223218
Wichita 6.3161194 0.9850014 2.0988774 0.8725436 1.0143558 0.8329903
Wilmington 6.2222250 0.8020874 1.7265893 0.6834780 1.4439914 1.1470613
Des Moines Detroit Hartford Houston Indianapolis
Albuquerque
Atlanta
Baltimore
Buffalo
Charleston
Chicago
Cincinnati
Cleveland
Columbus
Dallas
Denver
Des Moines
Detroit 2.0984393
Hartford 1.1853577 1.9421727
Houston 1.5976075 1.0543383 1.8544824
Indianapolis 0.8436174 1.3503539 1.0219662 0.9859325
Jacksonville 0.8451866 1.9375115 1.3167777 1.1923491 0.7386560
Kansas City 0.5749328 1.6361769 1.2121082 1.0570016 0.5023878
Little Rock 0.6033520 2.2574279 1.2510276 1.5913403 0.9782586
Louisville 0.7906048 1.5674199 0.8770470 1.1639793 0.2858565
Memphis 0.8336972 1.6793350 1.3609202 0.9153058 0.5995015
Miami 0.9700847 2.1194002 1.3955278 1.3418826 0.9826883
Milwaukee 0.9018408 1.2759027 1.3376536 0.9407396 0.5490795
Minneapolis 1.1315147 1.0657304 1.1708178 1.0893781 0.6096223
Nashville 0.6776339 1.7820568 1.0887482 1.1893820 0.5392416
New Orleans 0.8628569 2.0690650 1.3724967 1.2956543 0.9014517
Norfolk 0.5683577 1.9876912 0.8425527 1.5070888 0.6736572
Omaha 0.2278452 1.9307518 1.2484509 1.3998228 0.7191352
Philadelphia 3.3021382 1.3639247 2.7723507 2.2282108 2.5432496
Phoenix 1.1746968 2.0698843 1.8574681 1.6586312 1.3111774
Pittsburgh 1.3251163 1.6853019 0.5219248 1.7583630 0.9294636
Providence 2.0626020 2.4308259 1.0078089 2.6006293 1.8500070
Richmond 0.5896350 1.9245328 0.8822830 1.4432147 0.6332638
Salt Lake City 0.5729357 2.1051405 1.1397867 1.8144009 0.9982864
San Francisco 0.9275779 1.5234266 1.5375621 1.0922873 0.7935976
Seattle 0.8565831 1.5426220 0.8971304 1.2624972 0.4465436
St. Louis 1.4759918 1.2792352 0.7965881 1.4596166 0.9484356
Washington 0.9161919 1.2847178 1.0245078 0.9173853 0.1653802
Wichita 0.3704199 2.1249205 1.4660822 1.5040697 0.9677411
Wilmington 0.6262326 2.1829704 0.7144455 1.7985968 0.9065073
Jacksonville Kansas City Little Rock Louisville Memphis
Albuquerque
Atlanta
Baltimore
Buffalo
Charleston
Chicago
Cincinnati
Cleveland
Columbus
Dallas
Denver
Des Moines
Detroit
Hartford
Houston
Indianapolis
Jacksonville
Kansas City 0.6389826
Little Rock 0.5358469 0.6990741
Louisville 0.6043504 0.5438154 0.7959221
Memphis 0.3770857 0.3932089 0.6856173 0.5853732
Miami 0.3431683 0.8102372 0.5477120 0.8301535 0.5667628
Milwaukee 1.0407566 0.5207011 1.1860966 0.7672888 0.7572054
Minneapolis 1.2643090 0.8023304 1.4048482 0.8071967 1.0274482
Nashville 0.3706045 0.4158398 0.5012944 0.3744371 0.3656538
New Orleans 0.2661549 0.6794382 0.4260757 0.7533255 0.4406836
Norfolk 0.6246035 0.6874508 0.5943862 0.5009848 0.7684384
Omaha 0.7717798 0.3902246 0.6381258 0.7158075 0.6813096
Philadelphia 3.0956600 2.8609818 3.4080381 2.6996311 2.8831935
Phoenix 1.4293702 1.0915281 1.3476828 1.3414101 1.2899832
Pittsburgh 1.4036132 1.2932700 1.4832826 0.8704897 1.4321121
Providence 2.1956456 2.1372750 2.1749728 1.7565906 2.2745489
Richmond 0.5667359 0.5699330 0.4696073 0.3995623 0.6514444
Salt Lake City 1.2107358 0.8593086 0.9648167 0.9449702 1.1770594
San Francisco 1.0965402 0.5842246 1.1475603 0.9198689 0.8266978
Seattle 0.8272767 0.6815413 0.9750528 0.4146948 0.7827568
St. Louis 1.5017851 1.2283398 1.6097747 0.9837552 1.3840811
Washington 0.7694802 0.5150922 1.0125687 0.3315257 0.6029325
Wichita 0.8809829 0.5893874 0.7109279 0.9743055 0.8101452
Wilmington 0.9016490 0.8861139 0.6656869 0.7017645 1.0344450
Miami Milwaukee Minneapolis Nashville New Orleans Norfolk
Albuquerque
Atlanta
Baltimore
Buffalo
Charleston
Chicago
Cincinnati
Cleveland
Columbus
Dallas
Denver
Des Moines
Detroit
Hartford
Houston
Indianapolis
Jacksonville
Kansas City
Little Rock
Louisville
Memphis
Miami
Milwaukee 1.2048446
Minneapolis 1.4249061 0.4292596
Nashville 0.5417483 0.8213601 0.9910773
New Orleans 0.2087757 1.1181388 1.3558788 0.4249943
Norfolk 0.7689636 1.0191044 1.1332319 0.5303749 0.7257919
Omaha 0.9319709 0.7340582 1.0066451 0.5939666 0.8075204 0.6262011
Philadelphia 3.2433342 2.5561573 2.2725670 2.9524436 3.2171123 3.0857145
Phoenix 1.6186449 1.3004609 1.4600024 1.2799300 1.4755430 1.4418698
Pittsburgh 1.5597220 1.2886656 1.0492366 1.1987700 1.5407946 0.9721762
Providence 2.2949846 2.1828234 1.9371650 2.0338805 2.2956862 1.6911379
Richmond 0.7067128 0.9633579 1.0620243 0.3102307 0.6117859 0.3687304
Salt Lake City 1.3658356 1.0839700 1.1559989 0.9607798 1.2531989 0.8466683
San Francisco 1.3035243 0.6681669 0.8775790 0.8984838 1.1605095 1.1424571
Seattle 0.9596513 0.6947741 0.6690703 0.5794792 0.9317787 0.6669291
St. Louis 1.6379488 1.1478904 0.8507733 1.2640644 1.5966229 1.2227343
Washington 1.0000736 0.5766963 0.6050620 0.5679824 0.9190833 0.7350962
Wichita 0.9939478 0.9208096 1.2438721 0.8082171 0.8836727 0.7897026
Wilmington 0.9930940 1.2150549 1.2634996 0.7245900 0.9374859 0.3732735
Omaha Philadelphia Phoenix Pittsburgh Providence Richmond
Albuquerque
Atlanta
Baltimore
Buffalo
Charleston
Chicago
Cincinnati
Cleveland
Columbus
Dallas
Denver
Des Moines
Detroit
Hartford
Houston
Indianapolis
Jacksonville
Kansas City
Little Rock
Louisville
Memphis
Miami
Milwaukee
Minneapolis
Nashville
New Orleans
Norfolk
Omaha
Philadelphia 3.1615846
Phoenix 1.0399590 3.2273305
Pittsburgh 1.3450537 2.5215015 1.8667134
Providence 2.1401910 2.8681160 2.6063559 0.9890564
Richmond 0.5930259 3.0454209 1.2790155 1.0446066 1.8204081
Salt Lake City 0.6186288 3.2408445 0.9474151 1.2334765 1.9130662 0.7741503
San Francisco 0.7204541 2.7577774 0.6784343 1.5278359 2.3649219 0.9956354
Seattle 0.8103005 2.6990165 1.5388433 0.8489738 1.7810096 0.6103324
St. Louis 1.4173965 2.0406667 1.7618172 0.7126794 1.2972807 1.2056391
Washington 0.7786054 2.4544795 1.2703379 0.9477568 1.8445969 0.6671695
Wichita 0.3133027 3.3531565 1.0953678 1.5899266 2.3240163 0.8251839
Wilmington 0.7562163 3.2354719 1.4762021 0.9596305 1.5703335 0.4351713
Salt Lake City San Francisco Seattle St. Louis Washington
Albuquerque
Atlanta
Baltimore
Buffalo
Charleston
Chicago
Cincinnati
Cleveland
Columbus
Dallas
Denver
Des Moines
Detroit
Hartford
Houston
Indianapolis
Jacksonville
Kansas City
Little Rock
Louisville
Memphis
Miami
Milwaukee
Minneapolis
Nashville
New Orleans
Norfolk
Omaha
Philadelphia
Phoenix
Pittsburgh
Providence
Richmond
Salt Lake City
San Francisco 0.9118172
Seattle 1.0290434 1.0753560
St. Louis 1.3714667 1.3337634 1.0288568
Washington 1.0279631 0.7476788 0.5382130 0.8632244
Wichita 0.7909614 0.8558125 1.0767206 1.6368459 1.0138154
Wilmington 0.7234011 1.2757375 0.8174965 1.2659971 0.9558120
Wichita
Albuquerque
Atlanta
Baltimore
Buffalo
Charleston
Chicago
Cincinnati
Cleveland
Columbus
Dallas
Denver
Des Moines
Detroit
Hartford
Houston
Indianapolis
Jacksonville
Kansas City
Little Rock
Louisville
Memphis
Miami
Milwaukee
Minneapolis
Nashville
New Orleans
Norfolk
Omaha
Philadelphia
Phoenix
Pittsburgh
Providence
Richmond
Salt Lake City
San Francisco
Seattle
St. Louis
Washington
Wichita
Wilmington 0.9338633(distance_df_mn <- pollution_dist
%>% as.matrix
%>% data.frame(check.names = FALSE) #handles the issue of replacing spaces with periods
%>% rownames_to_column('CityA')
%>% pivot_longer(cols = -CityA,
names_to = 'CityB',
values_to = 'Distance'
)
%>% filter(CityA == 'Minneapolis' & CityA != CityB) #filters to Minneapolis and removes duplicate entries
%>% arrange(desc(Distance))
)# A tibble: 40 × 3
CityA CityB Distance
<chr> <chr> <dbl>
1 Minneapolis Chicago 5.21
2 Minneapolis Philadelphia 2.27
3 Minneapolis Providence 1.94
4 Minneapolis Phoenix 1.46
5 Minneapolis Albuquerque 1.45
6 Minneapolis Miami 1.42
7 Minneapolis Little Rock 1.40
8 Minneapolis New Orleans 1.36
9 Minneapolis Charleston 1.35
10 Minneapolis Albany 1.27
# ℹ 30 more rows(most_dissimilar <- distance_df_mn[1,])# A tibble: 1 × 3
CityA CityB Distance
<chr> <chr> <dbl>
1 Minneapolis Chicago 5.21# Minneapolis is most dissimilar to Chicago
(most_similar <- distance_df_mn
%>% arrange(desc(-Distance))
)[1,]# A tibble: 1 × 3
CityA CityB Distance
<chr> <chr> <dbl>
1 Minneapolis Milwaukee 0.429# Minneapolis is most similar to Milwaukee