STATS 380 Statistical Computing TERMS TEST SECOND SEMESTER, 2023
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STATS 380 Statistical Computing
TERMS TEST
SECOND SEMESTER, 2023
(Time allowed: 60 minutes + 15 extra minutes)
1. use : ）seq（））rep（）and some other commonly-used operators/functions）but def- initely not c（）or a loop）to create the following patterned sequences.
(a) 4 16 36 64 100 144 196 256 324 400
(b) 0 5 10 15 20 25 30 35 40 45 50 [3 marks]
(c) 1 2 4 8 16 32 64 128 256 512 1024 [3 marks]
(d) 100 101 102 103 104 200 201 202 203 204 300 301 302 303 304 [3 marks]
(e) 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 [3 marks]
[12 marks]
2. The object auckland is a data frame that comprises two numeric variables: year (year) and temp (the corresponding annual average temperature in Auckland). A few of its rows are shown below:
year temp
##
2012 15.41
2013 16.06
2014 15.61
2015 15.71
2016 16.32
##
with this data frame, write down some R code that inds and returns (only):
(a) The increase in the mean (average) temperature from the 1970s (1970-1979) to the 2010s (2010-2019). [4 marks]
(b) The ive hottest years, according to the annual average temperatures. [4 marks]
[8 marks]
3. write an R function that inds and returns, in a 2-column matrix, all of the pairs in a numeric sequence, at which the sequence changes signs from negative to positive (or 0). For example, passing the following sequence
> x = c（48, -62, -8, 0, 20, 7, 34, 2, -6, -58, 30, -27, -16, 51）
to your function as its argument, it should return
[,1] [,2]
[1,] -8 0
[2,] -58 30
[3,] -16 51
where each row stores a sign-changing pair as deined above.
[10 marks]
4. Many statistical methods require that data be standardised irst. write an R func- tion that standardises a given numeric matrix, in the sense that the values in each column will have mean 0 and the column vector length 1. For example, passing the following matrix
> x = cbind（0:2, c（0,0,10））
to your function as its argument, it should return
[,1] [,2]
[1,] -0.7071068 -0.4082483
[2,] 0.0000000 -0.4082483
[3,] 0.7071068 0.8164966
Note: The length of a vector a = (a1）. . . ）an ) is given by^Σ
ai(2) . Hence the vector 
ai(2) has length 1.
[10 marks]
5. The following graph mimics a face of Rubik,s cube. writesome R code to reproduce the grid and title as similarly as possible and randomly allocate 6 evenly spaced colours from the hcl function to the 9 squares. Make sure that no square is dis- torted, whenever the graph is produced. Make use of vectorised computation as much as you can.
A Face of Rubik，s cube
[10 marks]
2023-09-12