1. Using a for loop, write a function to calculate the number of zeroes in a numeric vector. Before entering the loop, set up a counter variable counter <- 0. Inside the loop, add 1 to counter each time you have a zero in the vector. Finally, use return(counter) for the output.
library(ggplot2)

#setting counter to zero 
counter <- 0

#creating requested function
counting_zeroes <- function(vect) {
  counter <- 0
  
  for (num in vect) {
    if (num == 0) {
      counter <- counter + 1
    }
  }
  
  return(counter)
}

#testing 1 2 1 2 
exvector <- c(0,2,3,0,0,3,3)
ex2vector <-c(0,2,1,1,1,1,1)

counting_zeroes(exvector)
## [1] 3
counting_zeroes(ex2vector)
## [1] 1
#this confirms it is working

#2: Use subsetting instead of a loop to rewrite the function as a single line of code.

#resetting counter to 0 just to make sure 
counter <- 0
counting_zeroes_2 <-function(vec) {
  #this just tells the # of 0s in the vector using the sum function 
  sum(vec ==0)
  
}

#testing with same vectors as before
counting_zeroes_2(exvector)
## [1] 3
counting_zeroes_2(ex2vector)
## [1] 1

#3: Write a function that takes as input two integers representing the number of rows and columns in a matrix. The output is a matrix of these dimensions in which each element is the product of the row number x the column number.

#creating the function 
matrix_dimensions <-function(int1,int2){
  #below, I am creating sequences of numbers that are equal to the inputs of int1 and int2 respectively
  y <- 1:int1
  z<- 1:int2
  
  #This outer function essentially mulitplying the row # by column #, as ditinguished by the third argument
  matrix <- outer(y, z, "*")
  
  return(matrix)
  
}

#testing, seems like it works. 
matrix_dimensions(5,7)
##      [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,]    1    2    3    4    5    6    7
## [2,]    2    4    6    8   10   12   14
## [3,]    3    6    9   12   15   18   21
## [4,]    4    8   12   16   20   24   28
## [5,]    5   10   15   20   25   30   35
#testing again, and seems like it works again. 
matrix_dimensions(17,44)
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
##  [1,]    1    2    3    4    5    6    7    8    9    10    11    12    13
##  [2,]    2    4    6    8   10   12   14   16   18    20    22    24    26
##  [3,]    3    6    9   12   15   18   21   24   27    30    33    36    39
##  [4,]    4    8   12   16   20   24   28   32   36    40    44    48    52
##  [5,]    5   10   15   20   25   30   35   40   45    50    55    60    65
##  [6,]    6   12   18   24   30   36   42   48   54    60    66    72    78
##  [7,]    7   14   21   28   35   42   49   56   63    70    77    84    91
##  [8,]    8   16   24   32   40   48   56   64   72    80    88    96   104
##  [9,]    9   18   27   36   45   54   63   72   81    90    99   108   117
## [10,]   10   20   30   40   50   60   70   80   90   100   110   120   130
## [11,]   11   22   33   44   55   66   77   88   99   110   121   132   143
## [12,]   12   24   36   48   60   72   84   96  108   120   132   144   156
## [13,]   13   26   39   52   65   78   91  104  117   130   143   156   169
## [14,]   14   28   42   56   70   84   98  112  126   140   154   168   182
## [15,]   15   30   45   60   75   90  105  120  135   150   165   180   195
## [16,]   16   32   48   64   80   96  112  128  144   160   176   192   208
## [17,]   17   34   51   68   85  102  119  136  153   170   187   204   221
##       [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25]
##  [1,]    14    15    16    17    18    19    20    21    22    23    24    25
##  [2,]    28    30    32    34    36    38    40    42    44    46    48    50
##  [3,]    42    45    48    51    54    57    60    63    66    69    72    75
##  [4,]    56    60    64    68    72    76    80    84    88    92    96   100
##  [5,]    70    75    80    85    90    95   100   105   110   115   120   125
##  [6,]    84    90    96   102   108   114   120   126   132   138   144   150
##  [7,]    98   105   112   119   126   133   140   147   154   161   168   175
##  [8,]   112   120   128   136   144   152   160   168   176   184   192   200
##  [9,]   126   135   144   153   162   171   180   189   198   207   216   225
## [10,]   140   150   160   170   180   190   200   210   220   230   240   250
## [11,]   154   165   176   187   198   209   220   231   242   253   264   275
## [12,]   168   180   192   204   216   228   240   252   264   276   288   300
## [13,]   182   195   208   221   234   247   260   273   286   299   312   325
## [14,]   196   210   224   238   252   266   280   294   308   322   336   350
## [15,]   210   225   240   255   270   285   300   315   330   345   360   375
## [16,]   224   240   256   272   288   304   320   336   352   368   384   400
## [17,]   238   255   272   289   306   323   340   357   374   391   408   425
##       [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37]
##  [1,]    26    27    28    29    30    31    32    33    34    35    36    37
##  [2,]    52    54    56    58    60    62    64    66    68    70    72    74
##  [3,]    78    81    84    87    90    93    96    99   102   105   108   111
##  [4,]   104   108   112   116   120   124   128   132   136   140   144   148
##  [5,]   130   135   140   145   150   155   160   165   170   175   180   185
##  [6,]   156   162   168   174   180   186   192   198   204   210   216   222
##  [7,]   182   189   196   203   210   217   224   231   238   245   252   259
##  [8,]   208   216   224   232   240   248   256   264   272   280   288   296
##  [9,]   234   243   252   261   270   279   288   297   306   315   324   333
## [10,]   260   270   280   290   300   310   320   330   340   350   360   370
## [11,]   286   297   308   319   330   341   352   363   374   385   396   407
## [12,]   312   324   336   348   360   372   384   396   408   420   432   444
## [13,]   338   351   364   377   390   403   416   429   442   455   468   481
## [14,]   364   378   392   406   420   434   448   462   476   490   504   518
## [15,]   390   405   420   435   450   465   480   495   510   525   540   555
## [16,]   416   432   448   464   480   496   512   528   544   560   576   592
## [17,]   442   459   476   493   510   527   544   561   578   595   612   629
##       [,38] [,39] [,40] [,41] [,42] [,43] [,44]
##  [1,]    38    39    40    41    42    43    44
##  [2,]    76    78    80    82    84    86    88
##  [3,]   114   117   120   123   126   129   132
##  [4,]   152   156   160   164   168   172   176
##  [5,]   190   195   200   205   210   215   220
##  [6,]   228   234   240   246   252   258   264
##  [7,]   266   273   280   287   294   301   308
##  [8,]   304   312   320   328   336   344   352
##  [9,]   342   351   360   369   378   387   396
## [10,]   380   390   400   410   420   430   440
## [11,]   418   429   440   451   462   473   484
## [12,]   456   468   480   492   504   516   528
## [13,]   494   507   520   533   546   559   572
## [14,]   532   546   560   574   588   602   616
## [15,]   570   585   600   615   630   645   660
## [16,]   608   624   640   656   672   688   704
## [17,]   646   663   680   697   714   731   748
#now realizing you may have wanted a forloop. I will email you. 

#4a: Simulate a dataset with 3 groups of data, each group drawn from a distribution with a different mean. The final data frame should have 1 column for group and 1 column for the response variable.

#setting seed for reproducibility
set.seed(487)

#setting the size for each
size <- 1000
#creating the means for each group
means <- c(147, 465, 765)

#creating the groups, each with 1000 observations
groups <- rep(1:3, each = size)

#creating the distributions around each mean using rnorm
cell_count <- c(rnorm(size, means[1], 3),
               rnorm(size, means[2], 3),
               rnorm(size, means[3], 3)
               )

#creating the actual dataframe 
z <- data.frame(Group = groups, Cell_Count = cell_count)

#let's see
print(z)
##      Group Cell_Count
## 1        1   147.9520
## 2        1   149.2385
## 3        1   143.4585
## 4        1   151.8173
## 5        1   144.0203
## 6        1   147.3182
## 7        1   147.4601
## 8        1   151.3212
## 9        1   146.2643
## 10       1   148.1393
## 11       1   144.6566
## 12       1   149.4381
## 13       1   147.0516
## 14       1   142.2583
## 15       1   146.6764
## 16       1   149.7816
## 17       1   139.9553
## 18       1   146.9587
## 19       1   149.4394
## 20       1   144.6255
## 21       1   148.1561
## 22       1   150.9236
## 23       1   149.4836
## 24       1   139.4259
## 25       1   143.4339
## 26       1   146.8229
## 27       1   150.3677
## 28       1   146.5538
## 29       1   151.6160
## 30       1   149.8578
## 31       1   151.5846
## 32       1   142.5675
## 33       1   146.1937
## 34       1   148.1734
## 35       1   141.5909
## 36       1   152.3183
## 37       1   141.3950
## 38       1   149.5178
## 39       1   148.9442
## 40       1   146.3608
## 41       1   146.8692
## 42       1   145.0417
## 43       1   146.9748
## 44       1   148.3269
## 45       1   145.7795
## 46       1   148.4403
## 47       1   148.0260
## 48       1   144.8543
## 49       1   143.4784
## 50       1   144.5636
## 51       1   145.8103
## 52       1   148.2592
## 53       1   149.0375
## 54       1   148.0327
## 55       1   152.6881
## 56       1   141.2943
## 57       1   146.3652
## 58       1   140.6077
## 59       1   150.8787
## 60       1   148.2476
## 61       1   149.6346
## 62       1   147.0994
## 63       1   143.5555
## 64       1   147.2957
## 65       1   151.5087
## 66       1   146.3384
## 67       1   146.0121
## 68       1   147.9927
## 69       1   152.2752
## 70       1   145.7988
## 71       1   145.1723
## 72       1   145.5752
## 73       1   141.7815
## 74       1   144.9038
## 75       1   148.6396
## 76       1   146.6282
## 77       1   148.2362
## 78       1   141.9688
## 79       1   145.3292
## 80       1   143.5371
## 81       1   148.7871
## 82       1   147.3245
## 83       1   145.6699
## 84       1   146.6599
## 85       1   140.0229
## 86       1   146.7838
## 87       1   144.5478
## 88       1   146.8516
## 89       1   145.0140
## 90       1   144.2426
## 91       1   148.0028
## 92       1   143.7419
## 93       1   144.0112
## 94       1   147.5165
## 95       1   149.1176
## 96       1   147.7769
## 97       1   153.9695
## 98       1   149.1003
## 99       1   149.5198
## 100      1   142.9510
## 101      1   147.6543
## 102      1   147.0584
## 103      1   148.3296
## 104      1   145.6190
## 105      1   151.0340
## 106      1   145.3024
## 107      1   151.3738
## 108      1   149.3315
## 109      1   148.4672
## 110      1   149.6360
## 111      1   150.7754
## 112      1   145.6371
## 113      1   152.9905
## 114      1   145.8886
## 115      1   148.2548
## 116      1   147.5689
## 117      1   142.9527
## 118      1   148.6690
## 119      1   149.6421
## 120      1   146.4552
## 121      1   149.8167
## 122      1   144.5927
## 123      1   148.6829
## 124      1   148.5609
## 125      1   148.0905
## 126      1   147.5798
## 127      1   148.4374
## 128      1   150.1404
## 129      1   148.8060
## 130      1   149.5370
## 131      1   147.4547
## 132      1   143.6386
## 133      1   148.3645
## 134      1   146.8698
## 135      1   145.7917
## 136      1   150.0816
## 137      1   145.2574
## 138      1   139.5068
## 139      1   147.6718
## 140      1   149.1039
## 141      1   154.5831
## 142      1   150.6302
## 143      1   147.0895
## 144      1   144.6646
## 145      1   144.3944
## 146      1   145.7282
## 147      1   148.4125
## 148      1   147.2970
## 149      1   145.4419
## 150      1   146.7921
## 151      1   149.3057
## 152      1   144.5657
## 153      1   146.8230
## 154      1   148.6717
## 155      1   146.7799
## 156      1   144.7498
## 157      1   149.8842
## 158      1   143.4784
## 159      1   149.6316
## 160      1   146.3967
## 161      1   144.4438
## 162      1   143.4110
## 163      1   147.8785
## 164      1   150.6738
## 165      1   139.6396
## 166      1   149.7568
## 167      1   140.5594
## 168      1   145.6185
## 169      1   155.5272
## 170      1   147.5802
## 171      1   145.5420
## 172      1   149.7834
## 173      1   146.2837
## 174      1   146.3779
## 175      1   147.9546
## 176      1   147.1937
## 177      1   152.3727
## 178      1   147.1001
## 179      1   148.6258
## 180      1   145.7340
## 181      1   146.4508
## 182      1   148.3992
## 183      1   143.6699
## 184      1   147.1525
## 185      1   143.7123
## 186      1   146.1897
## 187      1   147.1052
## 188      1   150.1839
## 189      1   149.4669
## 190      1   141.7576
## 191      1   151.9274
## 192      1   146.2960
## 193      1   141.9046
## 194      1   147.0781
## 195      1   153.2019
## 196      1   142.8850
## 197      1   146.5506
## 198      1   142.3572
## 199      1   145.6122
## 200      1   147.5235
## 201      1   149.0658
## 202      1   148.4667
## 203      1   139.6748
## 204      1   153.4796
## 205      1   146.7828
## 206      1   148.9593
## 207      1   150.0671
## 208      1   147.2529
## 209      1   151.4985
## 210      1   144.8870
## 211      1   147.9550
## 212      1   143.8163
## 213      1   146.0115
## 214      1   141.7876
## 215      1   145.1762
## 216      1   149.8850
## 217      1   148.5274
## 218      1   146.5094
## 219      1   150.6780
## 220      1   147.8215
## 221      1   147.3515
## 222      1   143.7092
## 223      1   143.0384
## 224      1   144.9672
## 225      1   142.9036
## 226      1   147.1561
## 227      1   149.7565
## 228      1   144.9958
## 229      1   146.5921
## 230      1   144.4928
## 231      1   154.3869
## 232      1   148.3483
## 233      1   151.0437
## 234      1   148.3962
## 235      1   145.5307
## 236      1   142.9429
## 237      1   147.9228
## 238      1   146.0758
## 239      1   147.8974
## 240      1   148.8553
## 241      1   143.8086
## 242      1   144.2201
## 243      1   146.1491
## 244      1   143.7053
## 245      1   148.7877
## 246      1   150.7936
## 247      1   147.0109
## 248      1   144.8703
## 249      1   142.5335
## 250      1   145.5548
## 251      1   146.7045
## 252      1   148.3907
## 253      1   150.4102
## 254      1   140.6979
## 255      1   146.3201
## 256      1   145.8644
## 257      1   146.7653
## 258      1   150.2382
## 259      1   150.9061
## 260      1   147.6521
## 261      1   150.6088
## 262      1   146.3593
## 263      1   140.8390
## 264      1   148.7236
## 265      1   142.5797
## 266      1   149.4772
## 267      1   154.7931
## 268      1   153.2182
## 269      1   147.7541
## 270      1   145.8801
## 271      1   149.2848
## 272      1   150.7197
## 273      1   145.6605
## 274      1   143.3028
## 275      1   147.3666
## 276      1   148.4120
## 277      1   144.0809
## 278      1   143.4851
## 279      1   148.1413
## 280      1   144.8034
## 281      1   142.7912
## 282      1   145.6499
## 283      1   147.5062
## 284      1   145.6027
## 285      1   145.0784
## 286      1   149.7036
## 287      1   142.4010
## 288      1   151.4620
## 289      1   144.5456
## 290      1   144.7910
## 291      1   153.2156
## 292      1   148.5563
## 293      1   146.1794
## 294      1   145.1455
## 295      1   150.9458
## 296      1   148.5486
## 297      1   149.8199
## 298      1   146.1884
## 299      1   148.1961
## 300      1   142.4724
## 301      1   150.3148
## 302      1   141.2328
## 303      1   144.8060
## 304      1   147.0690
## 305      1   152.1671
## 306      1   149.2539
## 307      1   148.6845
## 308      1   147.6940
## 309      1   146.2059
## 310      1   153.5225
## 311      1   144.5108
## 312      1   144.5310
## 313      1   143.8855
## 314      1   148.4445
## 315      1   144.3092
## 316      1   147.6726
## 317      1   143.2699
## 318      1   146.3929
## 319      1   146.2615
## 320      1   147.7387
## 321      1   144.8587
## 322      1   149.3735
## 323      1   151.1545
## 324      1   149.9008
## 325      1   139.1884
## 326      1   143.4346
## 327      1   147.9128
## 328      1   148.6518
## 329      1   142.7872
## 330      1   144.0357
## 331      1   147.2879
## 332      1   153.4365
## 333      1   151.1495
## 334      1   150.9076
## 335      1   149.1011
## 336      1   144.4353
## 337      1   144.6012
## 338      1   150.0236
## 339      1   148.4448
## 340      1   145.1928
## 341      1   144.6690
## 342      1   147.2634
## 343      1   146.8621
## 344      1   149.9165
## 345      1   149.9311
## 346      1   147.0826
## 347      1   144.6150
## 348      1   147.5166
## 349      1   147.0404
## 350      1   143.8261
## 351      1   150.4565
## 352      1   149.9458
## 353      1   148.4808
## 354      1   147.8481
## 355      1   149.7095
## 356      1   146.6543
## 357      1   149.3303
## 358      1   151.4792
## 359      1   142.3966
## 360      1   142.8496
## 361      1   142.8682
## 362      1   145.1431
## 363      1   146.0012
## 364      1   147.7451
## 365      1   150.1506
## 366      1   152.9871
## 367      1   152.4609
## 368      1   144.7300
## 369      1   145.5793
## 370      1   145.5690
## 371      1   145.1203
## 372      1   148.2109
## 373      1   145.2317
## 374      1   146.0693
## 375      1   145.8542
## 376      1   151.1971
## 377      1   149.6704
## 378      1   147.7490
## 379      1   144.3854
## 380      1   147.7910
## 381      1   143.6877
## 382      1   151.2997
## 383      1   154.4853
## 384      1   145.4649
## 385      1   142.7753
## 386      1   148.4794
## 387      1   149.7794
## 388      1   148.8866
## 389      1   154.3028
## 390      1   150.4439
## 391      1   148.4315
## 392      1   141.3974
## 393      1   149.3981
## 394      1   148.8554
## 395      1   151.6148
## 396      1   146.0989
## 397      1   150.1650
## 398      1   145.7339
## 399      1   144.2768
## 400      1   147.0215
## 401      1   147.2075
## 402      1   145.8685
## 403      1   148.7870
## 404      1   140.3743
## 405      1   143.2270
## 406      1   150.9084
## 407      1   149.0114
## 408      1   146.0071
## 409      1   142.7322
## 410      1   148.0297
## 411      1   140.0817
## 412      1   142.5577
## 413      1   140.2881
## 414      1   150.1634
## 415      1   146.2592
## 416      1   148.6875
## 417      1   148.6150
## 418      1   151.1662
## 419      1   148.2996
## 420      1   147.3425
## 421      1   148.7984
## 422      1   145.0124
## 423      1   150.5285
## 424      1   145.7741
## 425      1   145.1765
## 426      1   139.3806
## 427      1   149.0765
## 428      1   144.4653
## 429      1   145.7778
## 430      1   150.8543
## 431      1   142.9770
## 432      1   151.3836
## 433      1   140.9419
## 434      1   150.2476
## 435      1   145.2386
## 436      1   142.9107
## 437      1   147.6680
## 438      1   148.1862
## 439      1   147.4566
## 440      1   146.5490
## 441      1   144.2026
## 442      1   146.4554
## 443      1   150.0078
## 444      1   144.6752
## 445      1   143.3746
## 446      1   147.2398
## 447      1   145.6287
## 448      1   144.8921
## 449      1   144.3311
## 450      1   140.1696
## 451      1   152.4061
## 452      1   145.3601
## 453      1   148.4516
## 454      1   145.6456
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## 1938     2   470.2753
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## 1947     2   462.4156
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## 1949     2   464.7288
## 1950     2   466.4742
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## 1953     2   462.2508
## 1954     2   471.6146
## 1955     2   460.9371
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## 1957     2   464.8891
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## 1960     2   464.6923
## 1961     2   466.0384
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## 1965     2   464.4000
## 1966     2   465.4107
## 1967     2   465.7025
## 1968     2   462.2522
## 1969     2   465.1298
## 1970     2   456.6719
## 1971     2   465.9013
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## 1973     2   466.6482
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## 1976     2   463.7900
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## 1978     2   468.3368
## 1979     2   465.2748
## 1980     2   463.7680
## 1981     2   465.6238
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## 1983     2   461.8294
## 1984     2   466.9636
## 1985     2   464.0651
## 1986     2   464.0473
## 1987     2   466.2247
## 1988     2   464.4789
## 1989     2   464.9941
## 1990     2   463.0984
## 1991     2   459.0029
## 1992     2   462.5756
## 1993     2   464.3731
## 1994     2   459.8763
## 1995     2   469.8989
## 1996     2   467.1581
## 1997     2   465.0576
## 1998     2   464.1378
## 1999     2   466.7824
## 2000     2   465.6726
## 2001     3   762.0833
## 2002     3   762.3926
## 2003     3   766.4863
## 2004     3   768.6027
## 2005     3   769.5177
## 2006     3   766.1345
## 2007     3   764.7022
## 2008     3   767.1707
## 2009     3   762.4581
## 2010     3   762.9146
## 2011     3   763.5968
## 2012     3   760.6826
## 2013     3   767.1826
## 2014     3   760.3304
## 2015     3   762.7092
## 2016     3   768.8417
## 2017     3   769.2471
## 2018     3   762.4926
## 2019     3   765.0489
## 2020     3   767.6881
## 2021     3   764.1479
## 2022     3   764.4173
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## 2500     3   766.0446
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## 2502     3   764.4371
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## 2504     3   764.7514
## 2505     3   768.2065
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## 2507     3   763.3426
## 2508     3   766.0393
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## 2510     3   761.2409
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## 2512     3   768.1443
## 2513     3   766.9359
## 2514     3   763.6533
## 2515     3   765.6670
## 2516     3   769.1251
## 2517     3   767.2264
## 2518     3   766.5740
## 2519     3   757.5039
## 2520     3   764.5924
## 2521     3   763.8368
## 2522     3   765.3962
## 2523     3   766.4718
## 2524     3   761.9739
## 2525     3   764.0644
## 2526     3   763.3065
## 2527     3   765.6668
## 2528     3   765.6352
## 2529     3   766.8952
## 2530     3   767.8857
## 2531     3   763.6148
## 2532     3   765.8404
## 2533     3   768.2903
## 2534     3   767.0901
## 2535     3   770.1869
## 2536     3   762.1118
## 2537     3   767.1569
## 2538     3   767.0889
## 2539     3   760.2067
## 2540     3   765.8400
## 2541     3   762.5516
## 2542     3   763.0839
## 2543     3   771.7888
## 2544     3   765.7101
## 2545     3   763.7855
## 2546     3   762.3536
## 2547     3   767.2302
## 2548     3   767.8192
## 2549     3   763.9397
## 2550     3   761.3798
## 2551     3   767.3926
## 2552     3   758.5815
## 2553     3   767.4125
## 2554     3   765.6291
## 2555     3   763.7670
## 2556     3   761.8477
## 2557     3   764.8009
## 2558     3   762.1203
## 2559     3   763.5431
## 2560     3   760.7326
## 2561     3   766.0577
## 2562     3   767.4889
## 2563     3   762.1207
## 2564     3   766.9917
## 2565     3   763.7237
## 2566     3   764.2669
## 2567     3   768.8846
## 2568     3   760.8297
## 2569     3   762.7875
## 2570     3   765.8119
## 2571     3   760.7700
## 2572     3   766.8615
## 2573     3   767.7490
## 2574     3   763.4355
## 2575     3   765.8821
## 2576     3   761.4648
## 2577     3   766.7858
## 2578     3   770.4850
## 2579     3   766.5842
## 2580     3   770.1797
## 2581     3   762.1452
## 2582     3   761.8864
## 2583     3   766.3931
## 2584     3   762.7030
## 2585     3   769.1648
## 2586     3   762.4795
## 2587     3   764.1208
## 2588     3   762.2060
## 2589     3   769.9524
## 2590     3   767.0188
## 2591     3   769.1186
## 2592     3   765.2936
## 2593     3   761.3132
## 2594     3   767.1500
## 2595     3   767.7158
## 2596     3   762.6543
## 2597     3   766.6435
## 2598     3   768.5041
## 2599     3   765.5846
## 2600     3   763.2438
## 2601     3   762.0740
## 2602     3   768.2946
## 2603     3   765.6239
## 2604     3   761.4512
## 2605     3   762.0922
## 2606     3   765.1806
## 2607     3   769.7422
## 2608     3   764.2534
## 2609     3   768.6971
## 2610     3   764.2459
## 2611     3   766.6929
## 2612     3   769.1230
## 2613     3   759.4569
## 2614     3   766.2203
## 2615     3   760.8774
## 2616     3   766.3588
## 2617     3   768.0166
## 2618     3   764.2664
## 2619     3   760.9496
## 2620     3   760.3951
## 2621     3   768.1604
## 2622     3   766.8495
## 2623     3   762.8144
## 2624     3   761.7129
## 2625     3   760.5537
## 2626     3   766.6621
## 2627     3   760.5654
## 2628     3   760.0089
## 2629     3   759.6421
## 2630     3   770.0404
## 2631     3   764.1969
## 2632     3   769.7693
## 2633     3   766.3982
## 2634     3   767.6345
## 2635     3   763.5503
## 2636     3   765.7372
## 2637     3   762.0750
## 2638     3   763.6223
## 2639     3   767.8935
## 2640     3   765.2882
## 2641     3   769.3420
## 2642     3   764.6910
## 2643     3   770.2352
## 2644     3   763.4673
## 2645     3   764.4796
## 2646     3   766.3579
## 2647     3   764.2001
## 2648     3   763.5240
## 2649     3   765.5523
## 2650     3   771.6931
## 2651     3   765.2359
## 2652     3   768.1402
## 2653     3   765.9078
## 2654     3   766.9695
## 2655     3   764.5028
## 2656     3   763.1872
## 2657     3   765.3760
## 2658     3   767.0863
## 2659     3   763.1754
## 2660     3   767.4724
## 2661     3   760.6735
## 2662     3   771.4199
## 2663     3   763.8631
## 2664     3   767.1489
## 2665     3   766.0123
## 2666     3   763.5164
## 2667     3   764.3483
## 2668     3   764.7311
## 2669     3   760.6999
## 2670     3   763.5929
## 2671     3   766.3677
## 2672     3   764.7213
## 2673     3   763.0205
## 2674     3   764.7586
## 2675     3   765.4229
## 2676     3   765.7872
## 2677     3   765.0423
## 2678     3   766.2277
## 2679     3   766.7004
## 2680     3   763.8224
## 2681     3   765.2141
## 2682     3   765.6422
## 2683     3   763.0227
## 2684     3   764.8332
## 2685     3   769.3202
## 2686     3   768.5357
## 2687     3   764.8517
## 2688     3   768.4182
## 2689     3   768.0922
## 2690     3   766.1439
## 2691     3   763.6706
## 2692     3   767.1224
## 2693     3   764.8448
## 2694     3   766.9278
## 2695     3   763.8827
## 2696     3   763.8843
## 2697     3   766.2813
## 2698     3   773.3666
## 2699     3   761.0853
## 2700     3   763.1387
## 2701     3   766.8654
## 2702     3   766.0842
## 2703     3   763.7671
## 2704     3   761.8109
## 2705     3   765.1082
## 2706     3   764.0727
## 2707     3   761.6032
## 2708     3   764.4165
## 2709     3   767.3168
## 2710     3   766.5567
## 2711     3   762.2923
## 2712     3   767.5451
## 2713     3   763.0271
## 2714     3   763.6432
## 2715     3   766.7602
## 2716     3   767.8139
## 2717     3   768.7993
## 2718     3   765.0843
## 2719     3   764.1493
## 2720     3   757.0766
## 2721     3   766.2887
## 2722     3   764.3749
## 2723     3   760.1465
## 2724     3   764.2846
## 2725     3   763.8013
## 2726     3   767.4278
## 2727     3   763.3902
## 2728     3   767.1095
## 2729     3   765.4229
## 2730     3   767.7883
## 2731     3   768.6442
## 2732     3   764.8417
## 2733     3   764.0715
## 2734     3   768.0499
## 2735     3   763.4443
## 2736     3   766.5411
## 2737     3   768.6610
## 2738     3   760.4279
## 2739     3   763.9868
## 2740     3   766.8062
## 2741     3   761.1036
## 2742     3   765.8620
## 2743     3   767.6544
## 2744     3   762.2467
## 2745     3   766.7205
## 2746     3   762.7902
## 2747     3   770.1165
## 2748     3   764.1825
## 2749     3   763.1779
## 2750     3   763.5866
## 2751     3   767.8810
## 2752     3   767.1452
## 2753     3   763.4331
## 2754     3   760.2596
## 2755     3   760.9420
## 2756     3   763.7716
## 2757     3   761.0614
## 2758     3   761.4713
## 2759     3   764.6692
## 2760     3   763.0159
## 2761     3   758.7079
## 2762     3   761.2773
## 2763     3   770.4225
## 2764     3   763.1903
## 2765     3   761.8481
## 2766     3   766.3939
## 2767     3   765.7723
## 2768     3   763.3251
## 2769     3   769.1579
## 2770     3   769.1266
## 2771     3   768.5700
## 2772     3   762.3453
## 2773     3   764.0251
## 2774     3   768.8988
## 2775     3   761.4426
## 2776     3   768.2637
## 2777     3   763.7835
## 2778     3   763.4133
## 2779     3   767.5956
## 2780     3   763.8422
## 2781     3   768.8273
## 2782     3   767.2873
## 2783     3   767.3403
## 2784     3   763.8626
## 2785     3   764.9051
## 2786     3   771.8267
## 2787     3   768.6141
## 2788     3   766.8374
## 2789     3   763.4763
## 2790     3   768.5909
## 2791     3   766.0108
## 2792     3   761.3996
## 2793     3   766.9903
## 2794     3   765.1746
## 2795     3   769.0191
## 2796     3   758.0089
## 2797     3   769.1097
## 2798     3   764.6848
## 2799     3   769.1128
## 2800     3   766.8090
## 2801     3   762.5232
## 2802     3   767.1044
## 2803     3   762.6464
## 2804     3   767.7172
## 2805     3   766.2472
## 2806     3   763.1386
## 2807     3   761.8859
## 2808     3   766.1708
## 2809     3   766.2576
## 2810     3   762.3787
## 2811     3   764.8806
## 2812     3   765.9596
## 2813     3   766.0641
## 2814     3   767.7325
## 2815     3   767.6585
## 2816     3   763.8986
## 2817     3   769.7457
## 2818     3   759.5455
## 2819     3   766.2162
## 2820     3   764.1378
## 2821     3   764.9788
## 2822     3   766.1075
## 2823     3   765.1265
## 2824     3   769.7669
## 2825     3   764.4152
## 2826     3   761.9106
## 2827     3   766.7688
## 2828     3   766.2231
## 2829     3   763.8593
## 2830     3   762.9066
## 2831     3   763.4384
## 2832     3   773.6734
## 2833     3   770.7054
## 2834     3   765.6884
## 2835     3   763.1889
## 2836     3   768.5511
## 2837     3   764.8946
## 2838     3   765.9642
## 2839     3   764.7172
## 2840     3   767.8489
## 2841     3   764.0045
## 2842     3   767.8530
## 2843     3   767.4558
## 2844     3   762.3160
## 2845     3   762.9321
## 2846     3   763.5595
## 2847     3   763.3322
## 2848     3   760.3127
## 2849     3   767.0176
## 2850     3   768.5588
## 2851     3   768.8835
## 2852     3   770.5509
## 2853     3   760.4031
## 2854     3   765.6859
## 2855     3   768.7678
## 2856     3   762.8271
## 2857     3   762.6591
## 2858     3   765.3791
## 2859     3   767.0419
## 2860     3   763.7716
## 2861     3   766.8597
## 2862     3   764.5267
## 2863     3   762.4993
## 2864     3   765.0462
## 2865     3   763.9647
## 2866     3   763.6916
## 2867     3   767.1373
## 2868     3   762.0179
## 2869     3   768.1681
## 2870     3   766.0194
## 2871     3   770.5914
## 2872     3   761.1931
## 2873     3   767.9375
## 2874     3   763.1568
## 2875     3   761.5186
## 2876     3   768.3226
## 2877     3   764.5955
## 2878     3   761.4954
## 2879     3   763.0197
## 2880     3   764.4625
## 2881     3   763.0764
## 2882     3   766.1856
## 2883     3   767.1877
## 2884     3   765.7384
## 2885     3   761.7142
## 2886     3   763.2814
## 2887     3   766.8808
## 2888     3   766.4048
## 2889     3   760.2413
## 2890     3   763.4221
## 2891     3   766.5273
## 2892     3   768.0486
## 2893     3   764.9998
## 2894     3   768.3498
## 2895     3   760.6214
## 2896     3   762.1020
## 2897     3   763.0883
## 2898     3   770.0957
## 2899     3   762.1785
## 2900     3   769.3935
## 2901     3   762.6235
## 2902     3   764.0961
## 2903     3   765.2654
## 2904     3   758.7952
## 2905     3   760.5021
## 2906     3   763.7335
## 2907     3   764.8395
## 2908     3   765.6529
## 2909     3   769.8619
## 2910     3   765.6727
## 2911     3   761.7289
## 2912     3   765.8039
## 2913     3   764.4392
## 2914     3   760.0745
## 2915     3   766.5072
## 2916     3   765.4782
## 2917     3   766.4731
## 2918     3   767.8348
## 2919     3   764.1612
## 2920     3   765.2467
## 2921     3   766.2356
## 2922     3   765.6532
## 2923     3   762.3810
## 2924     3   767.5025
## 2925     3   766.2197
## 2926     3   763.1537
## 2927     3   761.4775
## 2928     3   768.5550
## 2929     3   763.7304
## 2930     3   768.0310
## 2931     3   764.5495
## 2932     3   770.7115
## 2933     3   768.4708
## 2934     3   768.4160
## 2935     3   770.5140
## 2936     3   766.6833
## 2937     3   762.7080
## 2938     3   762.8216
## 2939     3   764.3857
## 2940     3   764.5382
## 2941     3   762.2117
## 2942     3   765.1801
## 2943     3   766.3524
## 2944     3   762.8311
## 2945     3   765.3999
## 2946     3   768.3865
## 2947     3   768.5357
## 2948     3   766.4720
## 2949     3   761.2200
## 2950     3   761.6885
## 2951     3   762.5184
## 2952     3   767.8821
## 2953     3   764.6366
## 2954     3   765.4426
## 2955     3   764.7034
## 2956     3   762.4161
## 2957     3   765.3029
## 2958     3   764.8255
## 2959     3   766.8925
## 2960     3   765.6009
## 2961     3   764.7938
## 2962     3   764.0780
## 2963     3   764.3587
## 2964     3   762.5612
## 2965     3   763.3279
## 2966     3   764.0852
## 2967     3   768.7663
## 2968     3   767.5262
## 2969     3   768.0432
## 2970     3   761.7769
## 2971     3   764.6468
## 2972     3   762.8251
## 2973     3   761.8090
## 2974     3   757.9429
## 2975     3   761.7091
## 2976     3   768.1533
## 2977     3   769.6051
## 2978     3   767.9433
## 2979     3   767.8520
## 2980     3   764.5871
## 2981     3   764.2638
## 2982     3   761.0909
## 2983     3   762.5112
## 2984     3   762.6924
## 2985     3   762.8887
## 2986     3   766.9049
## 2987     3   766.1125
## 2988     3   759.9287
## 2989     3   761.7593
## 2990     3   759.7064
## 2991     3   764.6671
## 2992     3   763.4769
## 2993     3   766.9564
## 2994     3   761.7897
## 2995     3   765.1579
## 2996     3   768.6095
## 2997     3   764.9816
## 2998     3   764.3172
## 2999     3   765.5532
## 3000     3   767.3819
#everything seems to be working

#4b: Write a custom function that 1) reshuffles the response variable, and 2) calculates the mean of each group in the reshuffled data. Store the means in a vector of length 3.

#creating custom function "reshuffle"

reshuffle <- function(dataframe){
  
  reshuffled_cell_counts <- sample(dataframe$Cell_Count)
  
  #this is dual purposed,to initially create and then adjust for the new means
  reshuffled_means <- 3
  
  #a for loop to iterate through the creation of the means 
  for (i in 1:3){
    
    reshuffled_means[i] <- mean(reshuffled_cell_counts[dataframe$Group == i])
    
  }
  #this needs to be outside of the second nest or it will only return the first group. 
  return(reshuffled_means)
}

zreshuffled <- reshuffle(z)

print(zreshuffled)
## [1] 455.8343 457.8905 463.5304

#4c: Use a for loop to repeat the function in b 100 times. Store the results in a data frame that has 1 column indicating the replicate number and 1 column for each new group mean, for a total of 4 columns.

#first creating an empty df 

hundred_replicates <- data.frame(Replicate = 1:100, 
                                 Group1 = 100,
                                 Group2 = 100,
                                 Group3 = 100)

#this is the for loop to create all of the additional replicates
for (i in 1:100){
  
  #using reshuffle function during iteration
  additional_means <- reshuffle(z)
  
  #updates each column 2:4 during iteration
  hundred_replicates[i, 2:4] <- additional_means
}

print(hundred_replicates)
##     Replicate   Group1   Group2   Group3
## 1           1 450.7707 460.7572 465.7273
## 2           2 454.3532 455.7325 467.1695
## 3           3 458.8935 460.4801 457.8815
## 4           4 461.9083 460.5924 454.7545
## 5           5 465.6724 460.7907 450.7921
## 6           6 459.1980 453.5768 464.4804
## 7           7 466.3592 463.6931 447.2029
## 8           8 463.3662 463.7625 450.1265
## 9           9 466.7351 449.2371 461.2831
## 10         10 449.6354 470.5569 457.0628
## 11         11 467.5708 464.8188 444.8656
## 12         12 455.0292 455.3351 466.8909
## 13         13 460.7638 462.7972 453.6942
## 14         14 467.5484 450.7534 458.9534
## 15         15 464.2756 452.9221 460.0575
## 16         16 456.6316 456.3636 464.2599
## 17         17 457.9606 463.4468 455.8479
## 18         18 453.7259 463.6921 459.8372
## 19         19 456.4504 451.9394 468.8654
## 20         20 461.1933 448.6675 467.3944
## 21         21 450.8398 463.6092 462.8062
## 22         22 462.3393 456.0704 458.8455
## 23         23 473.4277 452.0531 451.7744
## 24         24 460.8693 453.2374 463.1485
## 25         25 463.1010 462.3196 451.8346
## 26         26 455.0308 462.2735 459.9509
## 27         27 447.8983 464.3239 465.0330
## 28         28 449.9679 463.5370 463.7503
## 29         29 454.5544 465.4337 457.2671
## 30         30 465.1228 455.0706 457.0618
## 31         31 460.1822 457.8412 459.2317
## 32         32 462.9539 449.3632 464.9381
## 33         33 464.8250 454.6871 457.7431
## 34         34 459.9126 455.4127 461.9300
## 35         35 457.4573 454.1004 465.6975
## 36         36 460.9528 457.6030 458.6993
## 37         37 464.2862 457.9278 455.0412
## 38         38 455.7979 457.7642 463.6932
## 39         39 466.2583 462.2077 448.7892
## 40         40 463.8137 452.7709 460.6706
## 41         41 458.0243 455.2461 463.9848
## 42         42 454.1666 456.0754 467.0132
## 43         43 458.2711 465.4264 453.5578
## 44         44 474.5161 450.5973 452.1418
## 45         45 455.7991 463.1384 458.3178
## 46         46 464.9486 455.3602 456.9464
## 47         47 462.6386 457.2351 457.3815
## 48         48 470.2557 456.5232 450.4763
## 49         49 460.7563 464.9563 451.5426
## 50         50 446.2491 465.5316 465.4745
## 51         51 464.7088 463.6064 448.9400
## 52         52 454.2040 463.3572 459.6939
## 53         53 450.7324 463.1167 463.4061
## 54         54 451.5066 460.9489 464.7998
## 55         55 462.7263 461.3241 453.2048
## 56         56 460.0563 460.4229 456.7760
## 57         57 457.6163 460.6570 458.9819
## 58         58 461.2211 466.6071 449.4269
## 59         59 453.1826 468.0695 456.0032
## 60         60 449.0856 460.8894 467.2802
## 61         61 466.7949 456.2401 454.2201
## 62         62 455.9698 458.9384 462.3470
## 63         63 458.7242 458.4270 460.1041
## 64         64 463.8329 464.3102 449.1122
## 65         65 459.2486 458.8944 459.1122
## 66         66 457.3674 467.7459 452.1419
## 67         67 453.5335 459.3490 464.3726
## 68         68 455.6286 455.1236 466.5031
## 69         69 452.9175 454.2998 470.0379
## 70         70 457.2769 470.6496 449.3287
## 71         71 476.4561 452.3947 448.4043
## 72         72 449.0217 457.6383 470.5952
## 73         73 467.8073 472.2416 437.2063
## 74         74 448.3248 464.9260 464.0043
## 75         75 457.1973 464.6798 455.3781
## 76         76 467.2232 453.0054 457.0266
## 77         77 458.2800 453.4171 465.5581
## 78         78 461.5982 465.8406 449.8164
## 79         79 437.7116 467.8455 471.6981
## 80         80 451.8104 453.4095 472.0353
## 81         81 461.8661 454.2103 461.1788
## 82         82 446.5000 473.3350 457.4202
## 83         83 462.6478 453.0255 461.5820
## 84         84 461.3395 457.7956 458.1201
## 85         85 452.8812 461.1477 463.2263
## 86         86 454.4720 454.0943 468.6888
## 87         87 461.5548 454.4315 461.2689
## 88         88 462.8849 459.7752 454.5951
## 89         89 457.6076 459.5045 460.1431
## 90         90 469.3216 448.8108 459.1228
## 91         91 462.9314 466.4680 447.8558
## 92         92 458.1505 462.6030 456.5017
## 93         93 462.3619 458.5365 456.3568
## 94         94 464.5930 477.9356 434.7266
## 95         95 465.6830 453.7130 457.8592
## 96         96 445.3910 466.7413 465.1229
## 97         97 461.2680 450.1208 465.8665
## 98         98 468.5460 458.4571 450.2521
## 99         99 461.2990 456.6931 459.2631
## 100       100 466.2562 457.0272 453.9718

#4d: Use qplot() to create a histogram of the means for each reshuffled group. Or, if you want a challenge, use ggplot() to overlay all 3 histograms in the same figure. How do the distributions of reshuffled means compare to the original means?

#for whatever reason I cannot figure out how to get the outline done on this for the boxes
qplot(data = hundred_replicates, x = Group1, fill = "Group1", geom = "histogram", bins = 20) +
  labs(x = "Mean", y = "Frequency", title = "Histogram of Reshuffled Means (Group 1)")
## Warning: `qplot()` was deprecated in ggplot2 3.4.0.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

qplot(data = hundred_replicates, x = Group2, fill = "Group2", geom = "histogram", bins = 20) +
  labs(x = "Mean", y = "Frequency", title = "Histogram of Reshuffled Means (Group 2)")

qplot(data = hundred_replicates, x = Group3, fill = "Group3", geom = "histogram", bins = 20) +
  labs(x = "Mean", y = "Frequency", title = "Histogram of Reshuffled Means (Group 3)")