Submit both the .Rmd and .html files for grading. You may remove the instructions and example problem above, but do not remove the YAML metadata block or the first, “setup” code chunk. Address the steps that appear below and answer all the questions. Be sure to address each question with code and comments as needed. You may use either base R functions or ggplot2 for the visualizations.

The following code chunk will:

  1. load the “ggplot2”, “gridExtra” and “knitr” packages, assuming each has been installed on your machine,
  2. read-in the abalones dataset, defining a new data frame, “mydata,”
  3. return the structure of that data frame, and
  4. calculate new variables, VOLUME and RATIO.

Do not include package installation code in this document. Packages should be installed via the Console or ‘Packages’ tab. You will also need to download the abalones.csv from the course site to a known location on your machine. Unless a file.path() is specified, R will look to directory where this .Rmd is stored when knitting.

## 'data.frame':    1036 obs. of  8 variables:
##  $ SEX   : Factor w/ 3 levels "F","I","M": 2 2 2 2 2 2 2 2 2 2 ...
##  $ LENGTH: num  5.57 3.67 10.08 4.09 6.93 ...
##  $ DIAM  : num  4.09 2.62 7.35 3.15 4.83 ...
##  $ HEIGHT: num  1.26 0.84 2.205 0.945 1.785 ...
##  $ WHOLE : num  11.5 3.5 79.38 4.69 21.19 ...
##  $ SHUCK : num  4.31 1.19 44 2.25 9.88 ...
##  $ RINGS : int  6 4 6 3 6 6 5 6 5 6 ...
##  $ CLASS : Factor w/ 5 levels "A1","A2","A3",..: 1 1 1 1 1 1 1 1 1 1 ...

Test Items starts from here - There are 6 sections - Total 50 points

##### Section 1: (6 points) Summarizing the data.

(1)(a) (1 point) Use summary() to obtain and present descriptive statistics from mydata. Use table() to present a frequency table using CLASS and RINGS. There should be 115 cells in the table you present.

##  SEX         LENGTH           DIAM            HEIGHT          WHOLE        
##  F:326   Min.   : 2.73   Min.   : 1.995   Min.   :0.525   Min.   :  1.625  
##  I:329   1st Qu.: 9.45   1st Qu.: 7.350   1st Qu.:2.415   1st Qu.: 56.484  
##  M:381   Median :11.45   Median : 8.925   Median :2.940   Median :101.344  
##          Mean   :11.08   Mean   : 8.622   Mean   :2.947   Mean   :105.832  
##          3rd Qu.:13.02   3rd Qu.:10.185   3rd Qu.:3.570   3rd Qu.:150.319  
##          Max.   :16.80   Max.   :13.230   Max.   :4.935   Max.   :315.750  
##      SHUCK              RINGS        CLASS        VOLUME       
##  Min.   :  0.5625   Min.   : 3.000   A1:108   Min.   :  3.612  
##  1st Qu.: 23.3006   1st Qu.: 8.000   A2:236   1st Qu.:163.545  
##  Median : 42.5700   Median : 9.000   A3:329   Median :307.363  
##  Mean   : 45.4396   Mean   : 9.993   A4:188   Mean   :326.804  
##  3rd Qu.: 64.2897   3rd Qu.:11.000   A5:175   3rd Qu.:463.264  
##  Max.   :157.0800   Max.   :25.000            Max.   :995.673  
##      RATIO        
##  Min.   :0.06734  
##  1st Qu.:0.12241  
##  Median :0.13914  
##  Mean   :0.14205  
##  3rd Qu.:0.15911  
##  Max.   :0.31176
##     
##        3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20
##   A1   9   8  24  67   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   A2   0   0   0   0  91 145   0   0   0   0   0   0   0   0   0   0   0   0
##   A3   0   0   0   0   0   0 182 147   0   0   0   0   0   0   0   0   0   0
##   A4   0   0   0   0   0   0   0   0 125  63   0   0   0   0   0   0   0   0
##   A5   0   0   0   0   0   0   0   0   0   0  48  35  27  15  13   8   8   6
##     
##       21  22  23  24  25
##   A1   0   0   0   0   0
##   A2   0   0   0   0   0
##   A3   0   0   0   0   0
##   A4   0   0   0   0   0
##   A5   4   1   7   2   1

Question (1 point): Briefly discuss the variable types and distributional implications such as potential skewness and outliers.

Answer: (Enter your answer here.)

There are a total of 10 variable types within the table. Sex and Class are categorical, while the remaining are numeric, or quantitative. Given the summary, we can tell that length, diameter, and height are left skewed, while whole, shuck, rings, volume, and ratio are right skewed. Of the categories, rings looks like there are some extreme outliers, while there are some in every category as well given that the minimum and maximum values are so far away from the median.

(1)(b) (1 point) Generate a table of counts using SEX and CLASS. Add margins to this table (Hint: There should be 15 cells in this table plus the marginal totals. Apply table() first, then pass the table object to addmargins() (Kabacoff Section 7.2 pages 144-147)). Lastly, present a barplot of these data; ignoring the marginal totals.

##      
##          F    I    M  Sum
##   A1     5   91   12  108
##   A2    41  133   62  236
##   A3   121   65  143  329
##   A4    82   21   85  188
##   A5    77   19   79  175
##   Sum  326  329  381 1036
##      
##         A1   A2   A3   A4   A5  Sum
##   F      5   41  121   82   77  326
##   I     91  133   65   21   19  329
##   M     12   62  143   85   79  381
##   Sum  108  236  329  188  175 1036

Essay Question (2 points): Discuss the sex distribution of abalones. What stands out about the distribution of abalones by CLASS?

Answer: (Enter your answer here.) What stands out about them in total is that while there are more males on average, the real outliers revolve around how there are significantly more infants in A2 than in A1. They begin to taper off in groups A3-A5, but it does seem a little weird that there are still infants in there groups. I would prefer to not make assumptions within the data, but given that there are more males listed throughout the groups in total, I would make an educated guess that of the infants, more would be female in order to even out the population.

(1)(c) (1 point) Select a simple random sample of 200 observations from “mydata” and identify this sample as “work.” Use set.seed(123) prior to drawing this sample. Do not change the number 123. Note that sample() “takes a sample of the specified size from the elements of x.” We cannot sample directly from “mydata.” Instead, we need to sample from the integers, 1 to 1036, representing the rows of “mydata.” Then, select those rows from the data frame (Kabacoff Section 4.10.5 page 87).

Using “work”, construct a scatterplot matrix of variables 2-6 with plot(work[, 2:6]) (these are the continuous variables excluding VOLUME and RATIO). The sample “work” will not be used in the remainder of the assignment.

##### Section 2: (5 points) Summarizing the data using graphics.

(2)(a) (1 point) Use “mydata” to plot WHOLE versus VOLUME. Color code data points by CLASS.

(2)(b) (2 points) Use “mydata” to plot SHUCK versus WHOLE with WHOLE on the horizontal axis. Color code data points by CLASS. As an aid to interpretation, determine the maximum value of the ratio of SHUCK to WHOLE. Add to the chart a straight line with zero intercept using this maximum value as the slope of the line. If you are using the ‘base R’ plot() function, you may use abline() to add this line to the plot. Use help(abline) in R to determine the coding for the slope and intercept arguments in the functions. If you are using ggplot2 for visualizations, geom_abline() should be used.

Essay Question (2 points): How does the variability in this plot differ from the plot in (a)? Compare the two displays. Keep in mind that SHUCK is a part of WHOLE. Consider the location of the different age classes.

Answer: (Enter your answer here.) There is less variance in plot b compared to plot a. The reason for this is that plot b is comparing shuck weight to whole weight, while in plot a the comparison is weight to volume. —–

### Section 3: (8 points) Getting insights about the data using graphs.

(3)(a) (2 points) Use “mydata” to create a multi-figured plot with histograms, boxplots and Q-Q plots of RATIO differentiated by sex. This can be done using par(mfrow = c(3,3)) and base R or grid.arrange() and ggplot2. The first row would show the histograms, the second row the boxplots and the third row the Q-Q plots. Be sure these displays are legible.

Essay Question (2 points): Compare the displays. How do the distributions compare to normality? Take into account the criteria discussed in the sync sessions to evaluate non-normality.

Answer: (Enter your answer here.) The plots show that the data is skewed right, with right tails on the histograms, box plots, and Q-Q plots as well. From what we can see, the data is not normally distributed, which presents an issue.

(3)(b) (2 points) The boxplots in (3)(a) indicate that there are outlying RATIOs for each sex. boxplot.stats() can be used to identify outlying values of a vector. Present the abalones with these outlying RATIO values along with their associated variables in “mydata”. Display the observations by passing a data frame to the kable() function. Basically, we want to output those rows of “mydata” with an outlying RATIO, but we want to determine outliers looking separately at infants, females and males.

SEX LENGTH DIAM HEIGHT WHOLE SHUCK RINGS CLASS VOLUME RATIO
3 I 10.080 7.350 2.205 79.37500 44.00000 6 A1 163.364040 0.2693371
37 I 4.305 3.255 0.945 6.18750 2.93750 3 A1 13.242072 0.2218308
42 I 2.835 2.730 0.840 3.62500 1.56250 4 A1 6.501222 0.2403394
58 I 6.720 4.305 1.680 22.62500 11.00000 5 A1 48.601728 0.2263294
67 I 5.040 3.675 0.945 9.65625 3.93750 5 A1 17.503290 0.2249577
89 I 3.360 2.310 0.525 2.43750 0.93750 4 A1 4.074840 0.2300704
105 I 6.930 4.725 1.575 23.37500 11.81250 7 A2 51.572194 0.2290478
200 I 9.135 6.300 2.520 74.56250 32.37500 8 A2 145.027260 0.2232339
350 F 7.980 6.720 2.415 80.93750 40.37500 7 A2 129.505824 0.3117620
379 F 15.330 11.970 3.465 252.06250 134.89812 10 A3 635.827846 0.2121614
420 F 11.550 7.980 3.465 150.62500 68.55375 10 A3 319.365585 0.2146560
421 F 13.125 10.290 2.310 142.00000 66.47062 9 A3 311.979938 0.2130606
458 F 11.445 8.085 3.150 139.81250 68.49062 9 A3 291.478399 0.2349767
586 F 12.180 9.450 4.935 133.87500 38.25000 14 A5 568.023435 0.0673388
746 M 13.440 10.815 1.680 130.25000 63.73125 10 A3 244.194048 0.2609861
754 M 10.500 7.770 3.150 132.68750 61.13250 9 A3 256.992750 0.2378764
803 M 10.710 8.610 3.255 160.31250 70.41375 9 A3 300.153640 0.2345924
810 M 12.285 9.870 3.465 176.12500 99.00000 10 A3 420.141472 0.2356349
852 M 11.550 8.820 3.360 167.56250 78.27187 10 A3 342.286560 0.2286735

Essay Question (2 points): What are your observations regarding the results in (3)(b)?

Answer: (Enter your answer here.) The largest ratio comes from females, making them the most extreme of the three classes, followed by the infants. However, there are outliers within all of the 3 classes.
—–

### Section 4: (8 points) Getting insights about possible predictors.

(4)(a) (3 points) With “mydata,” display side-by-side boxplots for VOLUME and WHOLE, each differentiated by CLASS There should be five boxes for VOLUME and five for WHOLE. Also, display side-by-side scatterplots: VOLUME and WHOLE versus RINGS. Present these four figures in one graphic: the boxplots in one row and the scatterplots in a second row. Base R or ggplot2 may be used.

Essay Question (5 points) How well do you think these variables would perform as predictors of age? Explain.

Answer: (Enter your answer here.) Volume nor weight act as great predictors of age which can be noticed from the scatter plots next to each other. —–

### Section 5: (12 points) Getting insights regarding different groups in the data.

(5)(a) (2 points) Use aggregate() with “mydata” to compute the mean values of VOLUME, SHUCK and RATIO for each combination of SEX and CLASS. Then, using matrix(), create matrices of the mean values. Using the “dimnames” argument within matrix() or the rownames() and colnames() functions on the matrices, label the rows by SEX and columns by CLASS. Present the three matrices (Kabacoff Section 5.6.2, p. 110-111). The kable() function is useful for this purpose. You do not need to be concerned with the number of digits presented.

Volume
A1 A2 A3 A4 A5
F 255.29938 276.8573 412.6079 498.0489 486.1525
I 66.51618 160.3200 270.7406 316.4129 318.6930
M 103.72320 245.3857 358.1181 442.6155 440.2074
Shuck
A1 A2 A3 A4 A5
F 38.90000 42.50305 59.69121 69.05161 59.17076
I 10.11332 23.41024 37.17969 39.85369 36.47047
M 16.39583 38.33855 52.96933 61.42726 55.02762
Ratio
A1 A2 A3 A4 A5
F 0.1546644 0.1554605 0.1450304 0.1379609 0.1233605
I 0.1569554 0.1475600 0.1372256 0.1244413 0.1167649
M 0.1512698 0.1564017 0.1462123 0.1364881 0.1262089

(5)(b) (3 points) Present three graphs. Each graph should include three lines, one for each sex. The first should show mean RATIO versus CLASS; the second, mean VOLUME versus CLASS; the third, mean SHUCK versus CLASS. This may be done with the ‘base R’ interaction.plot() function or with ggplot2 using grid.arrange().

Essay Question (2 points): What questions do these plots raise? Consider aging and sex differences.

Answer: (Enter your answer here.) As age increases, mean ratio decreases in terms of sex, particularly after A2. Both volume and shuck weight also increase as they get older, however volume plateaus between class A4 and A5, while shuck weight decreases after A4.

5(c) (3 points) Present four boxplots using par(mfrow = c(2, 2) or grid.arrange(). The first line should show VOLUME by RINGS for the infants and, separately, for the adult; factor levels “M” and “F,” combined. The second line should show WHOLE by RINGS for the infants and, separately, for the adults. Since the data are sparse beyond 15 rings, limit the displays to less than 16 rings. One way to accomplish this is to generate a new data set using subset() to select RINGS < 16. Use ylim = c(0, 1100) for VOLUME and ylim = c(0, 400) for WHOLE. If you wish to reorder the displays for presentation purposes or use ggplot2 go ahead.

Essay Question (2 points): What do these displays suggest about abalone growth? Also, compare the infant and adult displays. What differences stand out?

Answer: (Enter your answer here.) In total, as age increases, volume and whole weight increases. Adults are larger in volume and weight, which makes sense in comparison to infants. However, the deviation in sizes varies significantly within adults in comparison to infants. Both infant and adult volume and whole weight tend to peak between 11 and 12 years old, and then typically shrink. —–

### Section 6: (11 points) Conclusions from the Exploratory Data Analysis (EDA).

Conclusions

Essay Question 1) (5 points) Based solely on these data, what are plausible statistical reasons that explain the failure of the original study? Consider to what extent physical measurements may be used for age prediction.

Answer: (Enter your answer here.) From what I can see, the amount of outliers along with right skewing of some of the data limited normality, which made it difficult to set fair parameters and standard deviation. In addition, there may have been other variables which could have been useful that weren’t mentioned that play a factor in growth and weight, like climate temperature and food sources. The most confusing thing about the data was how larger, older infants could not be identified.

Essay Question 2) (3 points) Do not refer to the abalone data or study. If you were presented with an overall histogram and summary statistics from a sample of some population or phenomenon and no other information, what questions might you ask before accepting them as representative of the sampled population or phenomenon?

Answer: (Enter your answer here.) The questions I would ask would include what is the sample size, what is the standard deviation of the sample distribution, are there any previous studies of the area which can provide additional information, and is there a significant amount of skewing which might cause us to either discount information after it is collected.

Essay Question 3) (3 points) Do not refer to the abalone data or study. What do you see as difficulties analyzing data derived from observational studies? Can causality be determined? What might be learned from such studies?

Answer: (Enter your answer here.)

There are numerous difficulties analyzing data which is derived from observational studies. The collection and recording of data can either be manipulated or logged incorrectly, the possibility of biases can be a factor as well. I think causality would be very difficult to determine given the possibility of both bias and skewing in order to steer narratives. If there as a limited amount or no controls, it would be even more difficult, if not impossible, to glean relevant, valuable information. I think the biggest thing we can learn from observational studies is that they actually provide the basis for creative hypothesis or the inspiration for further, more in depth studies.