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You may (in fact, are encouraged to) use the Internet to search up any information to help you with this assignment, though you must cite any external (i.e. non-course related) websites that you use. Similarly, after attempting this assignment by yourself, you may collaborate with other students in the course, but you must each write your own code and acknowledge all students with whom you collaborated for each problem (you don’t need to cite by subpart). However, you may not post on Internet forums (e.g. Stack Exchange) for help with this assignment; doing so is considered an Honor Code violation. You also may not copy verbatim any code from the Internet, even with citation.

Please provide your responses to each problem in this .Rmd file in the R code chunks directly below each subpart, inserting additional R code chunks if needed. For text responses, please place them between <p> tags (this places your text in a grey-background textbox, to make them easier to grade). Please see the sample after Problem 1(a).

On Gradescope, you need only submit the .html file created by knitting the document with your responses. Problem 0 will provide guidance on how to do this.

Each problem subpart is graded on a 0-1-2 scale, and counts equally within this assignment. Credit is given based on the approach and code, not necessarily the final answer.

Problem 0

Read Sections 2.2-2.6 of “R Markdown: The Definitive Guide”. It will introduce you to using R markdown. You may skip subsection 2.5.3 if you are not familiar with LaTeX. It is not needed for this class.

Problem 1

  1. Load the nycflights13 package.
library(nycflights13)

Insert any text responses between <p> HTML tags, with class=“comment”. This is an example of how to do this; you may want to copy this line of text and the tags in the line above and the line below, and then paste at every point in the document where you want to insert text. Finally, replace this text with the words you want to write.

  1. Consider the airports tibble (data frame). How many observations and variables does it have?
nrow(airports)
## [1] 1458
ncol(airports)
## [1] 8

Recalling that each row in a tibble corresponds to an observation and each column to a variable, we conclude that airports has 1,458 observations and 8 variables.

  1. What is the mean altitude of all the airports in the tibble? Give the units.

We start by looking at the help page for the tibble airports:

?airports

This shows us that the column alt refers to altitude in feet. We want to take the mean value of all numbers in this column. We can extract this column via indexing, and then use the built-in mean() function from Lecture 2:

mean(airports$alt)
## [1] 1001.416

The mean altitude is 1001.416 feet.

  1. How many different time zones are represented among the airports in the tibble? Hint: look at the help page for unique().

The help page for unique() tells us that this function gives us the unique values in a vector. From the help page for the airports tibble we know the time zones are given in the column labeled tzone. Thus the following code stores the unique time zones in the tibble:

unique_tzones <- unique(airports$tzone)

To get the number of unique time zones, we could print out our variable unique_tzones, and count the number of entries. Alternatively (better), we could do this programatically using the length() function:

length(unique_tzones)
## [1] 10
  1. Select the name, lat, lon, and alt of the 3rd and 5th airports in the tibble. The result should be just one 2 x 4 tibble.
airports[c(3,5), c("name", "lat", "lon", "alt")]
## # A tibble: 2 × 4
##   name                    lat   lon   alt
##   <chr>                 <dbl> <dbl> <dbl>
## 1 Schaumburg Regional    42.0 -88.1   801
## 2 Jekyll Island Airport  31.1 -81.4    11

Problem 2

  1. Write a function called percent_decrease that takes in two arguments — num and percent — and returns the value when num is decreased by percent percent. For instance, if num is 10 and percent is 20, your function should return 8.
percent_decrease <- function(num, percent){
  return(num*(1-percent/100))
}
  1. Use your function from (a) to calculate the cost of an item of clothing which originally sold for $39.95, but is on sale for 40% off. Use round() to print out the price to the nearest cent.

The help menu for round() tells us that the second argument specifies how many digits after the decimal point to round to. A cent has two decimal places, so our second argument needs to be 2:

round(percent_decrease(num=39.95, percent=40), 2)
## [1] 23.97
  1. Define a vector evens containing all even integers between 0 and 2022, inclusive. Hint: look at the help menu for the seq() function!
evens <- seq(from=0, to=2022, by=2)
  1. Run the following code:
decreased_evens <- percent_decrease(num=evens, percent=50)

Note that evens is a numeric vector, even though you designed your function percent_decrease() to take in a single number as its first argument. Explain how R makes sense of this. Hint: This is loosely related to the concepts of “broadcasting” and “vectorization”.

We look at what’s inside decreased_evens:

decreased_evens
##    [1]    0    1    2    3    4    5    6    7    8    9   10   11   12   13
##   [15]   14   15   16   17   18   19   20   21   22   23   24   25   26   27
##   [29]   28   29   30   31   32   33   34   35   36   37   38   39   40   41
##   [43]   42   43   44   45   46   47   48   49   50   51   52   53   54   55
##   [57]   56   57   58   59   60   61   62   63   64   65   66   67   68   69
##   [71]   70   71   72   73   74   75   76   77   78   79   80   81   82   83
##   [85]   84   85   86   87   88   89   90   91   92   93   94   95   96   97
##   [99]   98   99  100  101  102  103  104  105  106  107  108  109  110  111
##  [113]  112  113  114  115  116  117  118  119  120  121  122  123  124  125
##  [127]  126  127  128  129  130  131  132  133  134  135  136  137  138  139
##  [141]  140  141  142  143  144  145  146  147  148  149  150  151  152  153
##  [155]  154  155  156  157  158  159  160  161  162  163  164  165  166  167
##  [169]  168  169  170  171  172  173  174  175  176  177  178  179  180  181
##  [183]  182  183  184  185  186  187  188  189  190  191  192  193  194  195
##  [197]  196  197  198  199  200  201  202  203  204  205  206  207  208  209
##  [211]  210  211  212  213  214  215  216  217  218  219  220  221  222  223
##  [225]  224  225  226  227  228  229  230  231  232  233  234  235  236  237
##  [239]  238  239  240  241  242  243  244  245  246  247  248  249  250  251
##  [253]  252  253  254  255  256  257  258  259  260  261  262  263  264  265
##  [267]  266  267  268  269  270  271  272  273  274  275  276  277  278  279
##  [281]  280  281  282  283  284  285  286  287  288  289  290  291  292  293
##  [295]  294  295  296  297  298  299  300  301  302  303  304  305  306  307
##  [309]  308  309  310  311  312  313  314  315  316  317  318  319  320  321
##  [323]  322  323  324  325  326  327  328  329  330  331  332  333  334  335
##  [337]  336  337  338  339  340  341  342  343  344  345  346  347  348  349
##  [351]  350  351  352  353  354  355  356  357  358  359  360  361  362  363
##  [365]  364  365  366  367  368  369  370  371  372  373  374  375  376  377
##  [379]  378  379  380  381  382  383  384  385  386  387  388  389  390  391
##  [393]  392  393  394  395  396  397  398  399  400  401  402  403  404  405
##  [407]  406  407  408  409  410  411  412  413  414  415  416  417  418  419
##  [421]  420  421  422  423  424  425  426  427  428  429  430  431  432  433
##  [435]  434  435  436  437  438  439  440  441  442  443  444  445  446  447
##  [449]  448  449  450  451  452  453  454  455  456  457  458  459  460  461
##  [463]  462  463  464  465  466  467  468  469  470  471  472  473  474  475
##  [477]  476  477  478  479  480  481  482  483  484  485  486  487  488  489
##  [491]  490  491  492  493  494  495  496  497  498  499  500  501  502  503
##  [505]  504  505  506  507  508  509  510  511  512  513  514  515  516  517
##  [519]  518  519  520  521  522  523  524  525  526  527  528  529  530  531
##  [533]  532  533  534  535  536  537  538  539  540  541  542  543  544  545
##  [547]  546  547  548  549  550  551  552  553  554  555  556  557  558  559
##  [561]  560  561  562  563  564  565  566  567  568  569  570  571  572  573
##  [575]  574  575  576  577  578  579  580  581  582  583  584  585  586  587
##  [589]  588  589  590  591  592  593  594  595  596  597  598  599  600  601
##  [603]  602  603  604  605  606  607  608  609  610  611  612  613  614  615
##  [617]  616  617  618  619  620  621  622  623  624  625  626  627  628  629
##  [631]  630  631  632  633  634  635  636  637  638  639  640  641  642  643
##  [645]  644  645  646  647  648  649  650  651  652  653  654  655  656  657
##  [659]  658  659  660  661  662  663  664  665  666  667  668  669  670  671
##  [673]  672  673  674  675  676  677  678  679  680  681  682  683  684  685
##  [687]  686  687  688  689  690  691  692  693  694  695  696  697  698  699
##  [701]  700  701  702  703  704  705  706  707  708  709  710  711  712  713
##  [715]  714  715  716  717  718  719  720  721  722  723  724  725  726  727
##  [729]  728  729  730  731  732  733  734  735  736  737  738  739  740  741
##  [743]  742  743  744  745  746  747  748  749  750  751  752  753  754  755
##  [757]  756  757  758  759  760  761  762  763  764  765  766  767  768  769
##  [771]  770  771  772  773  774  775  776  777  778  779  780  781  782  783
##  [785]  784  785  786  787  788  789  790  791  792  793  794  795  796  797
##  [799]  798  799  800  801  802  803  804  805  806  807  808  809  810  811
##  [813]  812  813  814  815  816  817  818  819  820  821  822  823  824  825
##  [827]  826  827  828  829  830  831  832  833  834  835  836  837  838  839
##  [841]  840  841  842  843  844  845  846  847  848  849  850  851  852  853
##  [855]  854  855  856  857  858  859  860  861  862  863  864  865  866  867
##  [869]  868  869  870  871  872  873  874  875  876  877  878  879  880  881
##  [883]  882  883  884  885  886  887  888  889  890  891  892  893  894  895
##  [897]  896  897  898  899  900  901  902  903  904  905  906  907  908  909
##  [911]  910  911  912  913  914  915  916  917  918  919  920  921  922  923
##  [925]  924  925  926  927  928  929  930  931  932  933  934  935  936  937
##  [939]  938  939  940  941  942  943  944  945  946  947  948  949  950  951
##  [953]  952  953  954  955  956  957  958  959  960  961  962  963  964  965
##  [967]  966  967  968  969  970  971  972  973  974  975  976  977  978  979
##  [981]  980  981  982  983  984  985  986  987  988  989  990  991  992  993
##  [995]  994  995  996  997  998  999 1000 1001 1002 1003 1004 1005 1006 1007
## [1009] 1008 1009 1010 1011
str(decreased_evens)
##  num [1:1012] 0 1 2 3 4 5 6 7 8 9 ...

We observe that decreased_evens is a vector with the same length as evens; R has decreased each entry in evens by 50%.

  1. Finally, try this:
decreased_evens_2 <- percent_decrease(num=evens, percent=c(50,100))

Explain what’s going on now.

We look at the values again:

decreased_evens_2
##    [1]    0    0    2    0    4    0    6    0    8    0   10    0   12    0
##   [15]   14    0   16    0   18    0   20    0   22    0   24    0   26    0
##   [29]   28    0   30    0   32    0   34    0   36    0   38    0   40    0
##   [43]   42    0   44    0   46    0   48    0   50    0   52    0   54    0
##   [57]   56    0   58    0   60    0   62    0   64    0   66    0   68    0
##   [71]   70    0   72    0   74    0   76    0   78    0   80    0   82    0
##   [85]   84    0   86    0   88    0   90    0   92    0   94    0   96    0
##   [99]   98    0  100    0  102    0  104    0  106    0  108    0  110    0
##  [113]  112    0  114    0  116    0  118    0  120    0  122    0  124    0
##  [127]  126    0  128    0  130    0  132    0  134    0  136    0  138    0
##  [141]  140    0  142    0  144    0  146    0  148    0  150    0  152    0
##  [155]  154    0  156    0  158    0  160    0  162    0  164    0  166    0
##  [169]  168    0  170    0  172    0  174    0  176    0  178    0  180    0
##  [183]  182    0  184    0  186    0  188    0  190    0  192    0  194    0
##  [197]  196    0  198    0  200    0  202    0  204    0  206    0  208    0
##  [211]  210    0  212    0  214    0  216    0  218    0  220    0  222    0
##  [225]  224    0  226    0  228    0  230    0  232    0  234    0  236    0
##  [239]  238    0  240    0  242    0  244    0  246    0  248    0  250    0
##  [253]  252    0  254    0  256    0  258    0  260    0  262    0  264    0
##  [267]  266    0  268    0  270    0  272    0  274    0  276    0  278    0
##  [281]  280    0  282    0  284    0  286    0  288    0  290    0  292    0
##  [295]  294    0  296    0  298    0  300    0  302    0  304    0  306    0
##  [309]  308    0  310    0  312    0  314    0  316    0  318    0  320    0
##  [323]  322    0  324    0  326    0  328    0  330    0  332    0  334    0
##  [337]  336    0  338    0  340    0  342    0  344    0  346    0  348    0
##  [351]  350    0  352    0  354    0  356    0  358    0  360    0  362    0
##  [365]  364    0  366    0  368    0  370    0  372    0  374    0  376    0
##  [379]  378    0  380    0  382    0  384    0  386    0  388    0  390    0
##  [393]  392    0  394    0  396    0  398    0  400    0  402    0  404    0
##  [407]  406    0  408    0  410    0  412    0  414    0  416    0  418    0
##  [421]  420    0  422    0  424    0  426    0  428    0  430    0  432    0
##  [435]  434    0  436    0  438    0  440    0  442    0  444    0  446    0
##  [449]  448    0  450    0  452    0  454    0  456    0  458    0  460    0
##  [463]  462    0  464    0  466    0  468    0  470    0  472    0  474    0
##  [477]  476    0  478    0  480    0  482    0  484    0  486    0  488    0
##  [491]  490    0  492    0  494    0  496    0  498    0  500    0  502    0
##  [505]  504    0  506    0  508    0  510    0  512    0  514    0  516    0
##  [519]  518    0  520    0  522    0  524    0  526    0  528    0  530    0
##  [533]  532    0  534    0  536    0  538    0  540    0  542    0  544    0
##  [547]  546    0  548    0  550    0  552    0  554    0  556    0  558    0
##  [561]  560    0  562    0  564    0  566    0  568    0  570    0  572    0
##  [575]  574    0  576    0  578    0  580    0  582    0  584    0  586    0
##  [589]  588    0  590    0  592    0  594    0  596    0  598    0  600    0
##  [603]  602    0  604    0  606    0  608    0  610    0  612    0  614    0
##  [617]  616    0  618    0  620    0  622    0  624    0  626    0  628    0
##  [631]  630    0  632    0  634    0  636    0  638    0  640    0  642    0
##  [645]  644    0  646    0  648    0  650    0  652    0  654    0  656    0
##  [659]  658    0  660    0  662    0  664    0  666    0  668    0  670    0
##  [673]  672    0  674    0  676    0  678    0  680    0  682    0  684    0
##  [687]  686    0  688    0  690    0  692    0  694    0  696    0  698    0
##  [701]  700    0  702    0  704    0  706    0  708    0  710    0  712    0
##  [715]  714    0  716    0  718    0  720    0  722    0  724    0  726    0
##  [729]  728    0  730    0  732    0  734    0  736    0  738    0  740    0
##  [743]  742    0  744    0  746    0  748    0  750    0  752    0  754    0
##  [757]  756    0  758    0  760    0  762    0  764    0  766    0  768    0
##  [771]  770    0  772    0  774    0  776    0  778    0  780    0  782    0
##  [785]  784    0  786    0  788    0  790    0  792    0  794    0  796    0
##  [799]  798    0  800    0  802    0  804    0  806    0  808    0  810    0
##  [813]  812    0  814    0  816    0  818    0  820    0  822    0  824    0
##  [827]  826    0  828    0  830    0  832    0  834    0  836    0  838    0
##  [841]  840    0  842    0  844    0  846    0  848    0  850    0  852    0
##  [855]  854    0  856    0  858    0  860    0  862    0  864    0  866    0
##  [869]  868    0  870    0  872    0  874    0  876    0  878    0  880    0
##  [883]  882    0  884    0  886    0  888    0  890    0  892    0  894    0
##  [897]  896    0  898    0  900    0  902    0  904    0  906    0  908    0
##  [911]  910    0  912    0  914    0  916    0  918    0  920    0  922    0
##  [925]  924    0  926    0  928    0  930    0  932    0  934    0  936    0
##  [939]  938    0  940    0  942    0  944    0  946    0  948    0  950    0
##  [953]  952    0  954    0  956    0  958    0  960    0  962    0  964    0
##  [967]  966    0  968    0  970    0  972    0  974    0  976    0  978    0
##  [981]  980    0  982    0  984    0  986    0  988    0  990    0  992    0
##  [995]  994    0  996    0  998    0 1000    0 1002    0 1004    0 1006    0
## [1009] 1008    0 1010    0
str(decreased_evens_2)
##  num [1:1012] 0 0 2 0 4 0 6 0 8 0 ...

The first entry of evens was decreased by 50%. The second entry was decreased by 100% (i.e. set to 0). Then the third entry was decreased by 50%, the fourth by 100%, etc.

Problem 3

Karen needs to buy cookies for her daughter’s 6th birthday party. She only shops at Costco, which sells cookies in batches of 12. There will be 21 cookie-eating guests at the party.

  1. Suppose Karen wants to give every cookie-eating guest the same number of cookies, but is very concerned about having as few left over as possible, since she personally hates cookies. Karen is very indecisive and considers buying anywhere from 2 to 10 batches, inclusive. Create a length 9 vector called leftovers specifying how many left over cookies she will have for each number of batches from 2 to 10. Hint: the seq() function from problem 2 may come in handy, as well as the modulo operator.
leftovers <- (12*seq(from=2, to=10, by=1)) %% 21
  1. Convert leftovers to a named list with character names “2”,…,“10”, corresponding to the number of batches.
leftovers <- as.list(leftovers)
names(leftovers) <- as.character(seq(from=2, to=10, by=1))
  1. Run the following two lines of code. Explain what kind of data structure and data type(s) each line returns, and describe (in words) the contents of what they are returning.
leftovers < 4
##     2     3     4     5     6     7     8     9    10 
##  TRUE FALSE FALSE FALSE FALSE  TRUE FALSE  TRUE FALSE
leftovers[leftovers < 4]
## $`2`
## [1] 3
## 
## $`7`
## [1] 0
## 
## $`9`
## [1] 3

We use str() to figure out the structure of the output of each line of code.

str(leftovers < 4)
##  Named logi [1:9] TRUE FALSE FALSE FALSE FALSE TRUE ...
##  - attr(*, "names")= chr [1:9] "2" "3" "4" "5" ...
str(leftovers[leftovers < 4])
## List of 3
##  $ 2: num 3
##  $ 7: num 0
##  $ 9: num 3

The first line returns a logical vector of length 9. Each entry of this logical vector is TRUE if the corresponding entry of leftovers is less than 4, and FALSE otherwise. The second line returns a (named) list consisting of all entries in leftovers that are less than 4.

  1. Use names() and part (c) to return all numbers of batches Karen can purchase to have less than 4 cookies left over.
names(leftovers[leftovers<4])
## [1] "2" "7" "9"
  1. What does the following line do? What kind of data structure does it return? What are its dimensions?
leftovers[-2]
## $`2`
## [1] 3
## 
## $`4`
## [1] 6
## 
## $`5`
## [1] 18
## 
## $`6`
## [1] 9
## 
## $`7`
## [1] 0
## 
## $`8`
## [1] 12
## 
## $`9`
## [1] 3
## 
## $`10`
## [1] 15
str(leftovers[-2])
## List of 8
##  $ 2 : num 3
##  $ 4 : num 6
##  $ 5 : num 18
##  $ 6 : num 9
##  $ 7 : num 0
##  $ 8 : num 12
##  $ 9 : num 3
##  $ 10: num 15

We observe this code extracts all but the 2nd entry of leftovers. The result is a (named) list of length 8.