Data Analysis Assignment #1 (50 points total)

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.

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.

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: (Sex and Class are qualitative variables.The remaining variables are quantitative. The Height variable has the closest mean and median, with a skewness of -.225262. Length has a skewness of -.67 and Diameter with a skewness of -.62, which indicates the presence of low outliers. The skewness of Whole (.047), Shuck (.64), Rings (1.24), Volume (.44), and Ratio (.71), are positive which is an indicator of high outliers.)

(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.

##      
##         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.)

(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.

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

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: (The first plot seems to contain more variable than the sceond plot. Such results are an indicator of a strong correlation between the two varying weights, such as the Shuck and Whole Weights in grams, more so than the correlation between volume and weight. There is a stronger consistency in the first plot, whereas the second plot, indicates that the older the abalone, the greater variable appears on the data plot. This could be a direct correlation that the older the abalone is, the heavier its shell will become as well as its inner meat, that is usually shucked, becomes more and more sparse. )

### 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: (Reviewing the QQ Plots of Ratios, it is noticed that the Theoretical Quantities versus teh Sample Quantities, seem to be non-normally distributed since they are skewed to the right. Looking at all three graphs, both the Female and Infant data results contain a higher positive skew then the Male data results. The female distribution has the most extreme outliers. The infant has the greatest quantity of outliers.)

(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: (The infant classification contains the most shuck to volume ratio outliers compared to the female and male classifications. The highest outlier is A3, followed by A1, then A2. A5 is the extreme outlier which was found in the female classification. A3 was the only outlier found in the male classification, whereas, the infant and female had outliers ranging from A1-A5.It seems that the infant classification could also be the reason why it is difficult to bring about a correlation for the data output of the physical measurements and age identification.)

### 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: (None of these variable combinations, such as volume or whole weight versus rings, are great indicators of the abalones’ age. The volume and whole weight to ring ratios both have positive correlations such that, the higher the volume and whole weight, the higher count of rings will be available. The same can be stated with the correlation between volume and weight versus class. For instance the volume of the abalone can be 750 and whole weight about 230, the ring count would be between 10-24 for classes A3-A5. These results are for too broad and need to be specified further for greater age accuracy.)

### 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: (Upon reviewing the Mean Ratio, it is indicated that there is a steady decline amongst all sex classes and age classes. On the other hand, the Mean Volume and Mean Shuck are increasing for all sex and age classes. There is one slight variation between the Mean Volume and Mean Shuck graphs; the Mean Shuck Graphs begins to decline when reaching A4 and continuing to A5. The Mean Volume steadies after a minimal dip, among all sex classes between A4 and A5. There are a few questions that are being raised, why is it with the Mean Ratio, both female and male classes very closely resemble each other? Why do the Mean Volume and Mean Shuck indicated that the female class is larger and heavier than the male class, which contradicts the Mean Ratio output? Why is there an indirect correlation between the Mean Ratio versus both the Mean Volume and Mean Shuck, especially with each older class?)

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: (These graphs indicate that the abalones’ growth begins from ring 1 until ring 11, which is its infancy. The infant class also has a drastic increase in volume and whole weight during their growth period. When the Infant class abalone reaches its 12th ring, its volume and whole weight begin to decrease. There is a similar pattern to be found in the Adult class, from rings 1 to 11, there is an increase in volume and whole weight and then slightly declines after the 11th ring. There is a contrast between the Infant class and Adult class when approaching their 14th ring. The 14th ring for the Infant class showcases a decline in both volume and whole weight. The Adult class did the opposite at the 14th ring. Finally, it is important to note that the Infant class has a lower IQR and standard deviation compared to the Adult class.)

### 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: (Due to inaccuracies of the infant classifications, the original study was not successful. An abalone that has not fully developed cannot have their sex properly identified. There needs to be further classifications to better identify a non-fully developed abalone versus a small adult abalone. The lack of proper sex classification for the abalones can also make it harder to predict their age. For instance, how can we know the abalone’s age; by its larger size brought about by aging or because it is of the female sex? )

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: (Why specifically this sample population/phenomenon? What are the outliers or influential factors involved that led to these data results being presented in the histogram? What conclusions and/or solutions are you trying to develop based off of the provided histogram? What type of sampling method was used, such as simple random samples or non-random sampling? When was the sample taken, as we cannot work off of outdated information. How large was the sample size and what were their parameters? For example, if I wanted to do a demographic study of an impoverished community located within a developing country, I would need to know why the populace is living in poverty. Is it a war-torn country? Is there lack of government funds and why? If there is no accessibility to healthcare, education, food, water, and/or electricity; is there a means to create jobs for the impoverished in which they can earn a living wage in order to provide for themselves and their families?)

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: (Observational studies are incomplete as they do not indicate the correlation of the causality. They are basically presumptions, even erroneous, based off of one point-of-view which can start from the construction of the study, data collection, and its result analysis. Observational studies can help lead to different variables of interest but cannot be the determining factor. Data analysis needs to know the exact outlying factors that led to the end-result. )

Data Analysis Assignment #1 (50 points total)

Dukum, Dian

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