FIT3152 Data Analytics Assignment

1. Using the data sets provided as csv files and the lecture notes, try and reproduce all of the statistics and graphics from Lecture 1.
Files are: {InvestA, InvestB, Toothbrush, Workers, Food Retail 2014-2020 time series}.csv

2. The following data records the length of rivers in the South Island of New Zealand. The lengths are given in kilometres. Data is grouped depending on where it flows into. Source: http://www.statsci.org/data/oz/nzrivers.html
Pacific Ocean:
209, 48, 169, 138, 64, 97, 161, 95, 145, 90, 121, 80, 56, 64, 209, 64, 72, 288, 322.
Tasman Sea:
76, 64, 68, 64, 37, 32, 32, 51, 56, 40, 64, 56, 80, 121, 177, 56, 80, 35, 72, 72, 108, 48.

(a) Calculate the summary stats for each group of rivers. Draw a boxplot.
(b) Test the hypothesis that rivers flowing into the Tasman Sea are shorter on average than those flowing into the Pacific Ocean. Use a significance of 1%

3. When anthropologists analyze human skeletal remains, an important piece of information is living stature. Since skeletons are commonly based on statistical methods that utilize measurements on small bones, the following data was presented in a paper in the American Journal of Physical Anthropology to validate one such method. Variables are: MetaCarp- Metacarpal bone length in cm, Stature (Height of skeleton) in cm. Source:http://www.statsci.org/data/general/stature.html

Draw a scatterplot of the data with Stature as the vertical axis. Calculate the regression equation predicting Stature from MetaCarp. Comment on the accuracy of the model. Superimpose the line of best fit on your scatterplot.

4. The ocean swell produces spectacular eruptions of water through a hole in the cliff at Kiama, about 120km south of Sydney, known as the Blowhole. The times at which 65 successive eruptions occurred from 1340 hours on 12 July 1998 were observed using a digital watch. Source: http://www.statsci.org/data/oz/kiama.html

Challenge: download the data into R. directly from: http://www.statsci.org/data/oz/kiama.txt (See ATHR page 18) or alternatively use the file: Data: kiama.txt

Read these data into R, creating a vector named 'kiama'. Calculate the mean, standard deviation. Draw the default histogram. Using help, try and draw an improved histogram of your own design by changing range, class intervals and colour etc.

5. The timber data are for specimens of 50 varieties of timber, for modulus of rigidity, modulus of elasticity and air dried density, arranged in increasing order of magnitude of the density. Source: http://www.statsci.org/data/oz/timber.html
Read these data into R., creating a data frame named 'timber. You can use the data file: timber.txt or load directly from: http://www.statsci.org/data/oz/timber.txt

(a) which variable: elasticity or density is a better predictor of rigidity?
(b) using your choice of variable calculate the regression equation predicting rigidity, draw a scatterplot of the data, showing the fitted model.
(c) challenge: calculate the regression equation predicting rigidity as a function of both elasticity and density. Comment on the quality of your model vs the single predictor in (b).

6. Challenge: Using the data: InvestA.csv draw a boxplot. You will need to use the help file to work out the syntax-try ?boxplot as a starting point...
Using the data: InvestA.csv, now use the 'aggregate' function to calculate the mean of each group. This is similar to the 'tapply' function but returns a data frame. Use help to work out the syntax...

If you are having trouble finding out how to group data inside the boxplot, have a closer look at the "formula" argument of boxplot function. Also, it is possible to use formula argument in aggregate function. in the same way with boxplot function.

7. Analyse Victorian Retail Tumover: for Food retailing: Household goods retailing; Clothing, footwear and personal accessory retailing; Department stores; Other retailing; Cafes, restaurants and takeaway food service for the period Jan 2010-Dec 2020 using Australian Bureau of Statistics data. You will need to copy the data from the Excel file: 8501.0 Retail Trade, Australia.xls.

Draw a time series plot of the data and plot the time series decomposition. Comment on the main elements in the time series.

Can you see any COVID-19 effects during 2020?

Additional Statistic Notes:

Q2) Hypothesis Testing and p-value

In a statistical hypothesis test, a hypothesis about a certain population parameter is tested using sample data usually consisting of one or two groups.
The hypothesis is evaluated against a null hypothesis that assumes equality or no difference between the group(s) and the value being tested.
p-values evaluate how well the used sample data support the argument of the null hypothesis.
High p-values indicate that the sample data is likely with a true null hypothesis, while a low p-value indicates that the data is unlikely with a true null.
Therefore, a low p-value indicates that there is more evidence to conclude that the tested hypothesis is true against the null hypothesis.
Compare p-value against the desired significance to determine the likelihood that the hypothesis is true.

Q3)Regression

Provides a model for the relationship between different variables with the primary aim of prediction.Simple linear regression models the relationship between one dependent variable and an associated independent variable.
Can plot expected value of dependent variable for all possible values of the independent variable using the derived formula.Minimize sum of squared error (squared residuals) to come up with best fit.

Q4) Histogram

A histogram graphically displays the shape and spread of data.Groups data into a number of class intervals and counts the frequency in each.

Q5) Correlation and Prediction

Correlation indicates the degree of association between two variables. Usually quantifies the strength of the linear relationship between the variables (from -1 to +1). Positive correlation - value of one variable increases with the increase in the second variable. Negative Correlation - value of one variable decreases with the increase in the second variable Higher association between two variables (positive or negative correlation) indicates a better predictive capability.

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