Itech7407 Real Time Analytic Engineers Assessment Answers

Answer:

Introduction

The study of variability in the various factors is very important in understanding the nature and trends involved in the variability. The variability pattern exists in the rainfall is responsible for the proportion of the rainfall in the different regions or areas. We know that the proportion of the rainfall is not same for different regions. There is low proportion of rainfall in some areas, high proportion of rainfall in some areas, however there is tremendous rainfall for particular areas. The amount of rainfall is measured in millimeter. There are so many factors responsible for the variability in the rainfall in different areas. Some possible factors may be climatic change, temperature, velocity of wind, etc. Actually, prediction of rainfall is very hard due to involvement of several factors or variables which are responsible for rainfall. Now a day, scientists make more advanced regression model for the purpose of rainfall prediction.  Many factors are taken into account for prediction of rainfall. Prediction models are improved due to use of technology. Rainfall is very important for farming, drinking water, industries, etc. Water is called as life! So, importance of rainfall in human life and entire bio-diversity is very high. Life on the earth is not possible without water. Rainfall consists of all forms of the water particles and it may be in state of liquid or solid. For example, rainfall may be in state of rain, drizzle, hail or snow. The rainfall falls form the clouds in any form and it reaches to ground. Each country keeps the records of the rainfall. Most of the countries have their own independent departments for weather prediction and meteorological activities. In most of the countries in the world, the measurement of the rainfall is observed at the 9 am daily according to the local time. For the measurement of the rainfall, a standard instrument is used and this instrument is called as rain gauge. The precipitation is most commonly known as the rain and it is recorded with the amount of precipitation. The data for the rainfall is collected from different stations and data is collected at the Bureau for further analysis.

Data Collection

For checking different research questions or hypotheses established for the research study, the first step in any research study is to collect the data and check the hypotheses by using proper statistical methods. For this research study, the data is collected from the authorized website for the rainfall data records. The rainfall data is collected at 9 am of the local time at each day. The rainfall data is nothing but the record of previous 24 hours. For this research study, the data is collected from the sixth month of the year 2004 up to second month of the year 2017. Data is collected for the Ballarat Hopetown Rd station number 89111. Data is collected for the monthly precipitation total in millimetres. Also, the quality of the rain is recorded. The collected climate data pass through a number of stages in quality control over the specific period of time. Also, there would be problem of gaps and missing data as every station does not have a complete unbroken record of the rainfall and climate information. Sometimes the stations have automatic system for the data collection and there would be possibility of failing the automatic system which may produce the biased observations. These types of errors or mistakes during data collection are responsible for the wrong prediction of the rainfall. Also, this type of data is not useful for the further use or statistical analysis.

Research Methodology

In this topic, we have to see the methodology used for the given research study of rainfall data. It is important to use the proper research methodology for getting the unbiased results. For this research study we have to study the variability and trends in the rainfall data for the Australian station. The data collection method in detail is described in above topic. The observations of daily rainfall are normally made at the 9 am of the local time and it is record of the previous 24 hours. The rainfall includes all forms of the precipitation that reach the ground such as rain, drizzle, hail and snow. For this research study, the data is collected from the sixth month of the year 2004 up to second month of the year 2017. Data is collected for the Ballarat Hopetown Rd station number 89111. Data is collected for the monthly precipitation total in millimetres. Also, the quality of the rain is recorded. After collection of data, we have to use this data for statistical analysis. We have to perform the statistical analysis by using the time series tools and techniques. We have to study the trend analysis and time series analysis for the given data for rainfall for the particular station in the Australia.

Statistical Analysis

For the statistical analysis of the rainfall data, we have to use the different tools and techniques of statistical analysis. We have to use the descriptive statistics, graphical analysis, and inferential statistics for this research study. We have to use the results from the IBM Watson and other computational software’s. Let us see this statistical analysis in detail.

First we have to see the descriptive statistics for the monthly precipitation total in millimetres for the given data. The required descriptive statistics are summarised as below:

The average monthly precipitation total is given as 54.4 with the standard deviation of 31.1. The minimum monthly precipitation total is recorded as the 1 millimetre while the maximum monthly precipitation is recorded as the 209.60 millimetres. The data is collected for the 152 observations or months.

Now, we have to see the box plot for the data for monthly precipitation total. The required box plot is given as below:

The above box plot shows that there is existence of outliers and data is skewed at right.

The histogram for the rainfall data is given as below:

Above histogram shows the right skewed nature of the rainfall data.

Now, we have to see the sequence plot or time series analysis for the monthly precipitation total.  

The sequence plot is given as below:

From the above diagram, it is observed that there is a presence of the trends. Also, continuously up and down movement of the rainfall based on the years is observed for the rainfall data.

It is observed that the data for the monthly precipitation total in millimetres have the seasonal variations and trends as per different months.

The IBM Watson screenshot for the trend analysis of monthly precipitation total is given as below:

The above trend line shows the variation in the values of precipitation and there is no any specific pattern found with this trend line.

The area under curve for the trend line is given as below:

The comparison for the each year for the monthly precipitation total is summarised as below:

The above bar graph shows that there is no any specific distribution is followed by the precipitation values.

The study of autocorrelation is very useful in the prediction of rainfall. The autocorrelations between the time series data points with different lags are summarized in the following autocorrelation model.

From the given autocorrelations with different lag points it is observed that about all autocorrelations are statistically significant at 5% level of significance as the corresponding p-values are less than alpha value 0.05.

Conclusions

1. The mean monthly precipitation total is given as 54.4 with the standard deviation of 31.1. The minimum monthly precipitation total is recorded as the 1 millimetre while the maximum monthly precipitation is recorded as the 209.60 millimetres. The data is collected for the 152 observations or months.
2. From the given box plot, it is observed that the collected contains the outliers and data for monthly precipitation is negatively skewed.
3. From the given histogram for the data for monthly precipitation total in millimetres, it is observed that the data is negatively skewed.
4. From the frequency distribution for the variable quality of the rainfall, it is observed that about 147 data observations have the required quality assumptions while five data points missed the quality characteristics for the rainfall data.
5. From the sequence plot for the yearly Precipitation total in millimetres, it is observed that there is a presence of the trends. There is a continuously up and down movement of the rainfall based on the years.
6. It is observed that the data for the monthly precipitation total in millimetres have the seasonal variations and trends as per different months. The continuous up and down nature of the curve shows the continuous variation according to the monthly data.

References

Antony, J. (2003). Design of Experiments for Engineers and Scientists. Butterworth Limited.

Babbie, E. R. (2009). The Practice of Social Research. Wadsworth.

Beran, R. (2000). React scatterplot smoothers: Superefficiency through basis economy. Journal of the American Statistical Association.

Bickel, P. J. and Doksum, K. A. (2000). Mathematical Statistics: Basic Ideas and Selected Topics, Vol I. Prentice Hall.

Casella, G. and Berger, R. L. (2002). Statistical Inference. Duxbury Press.

Cox, D. R. and Hinkley, D. V. (2000). Theoretical Statistics. Chapman and Hall Ltd.

Degroot, M. and Schervish, M. (2002). Probability and Statistics. Addison - Wesley.

Dobson, A. J. (2001). An introduction to generalized linear models. Chapman and Hall Ltd.

Evans, M. (2004). Probability and Statistics: The Science of Uncertainty. Freeman and Company.

Hastle, T., Tibshirani, R. and Friedman, J. H. (2001). The elements of statistical learning: data mining, inference, and prediction: with 200 full-color illustrations. Springer - Verlag Inc.

Hogg, R., Craig, A., and McKean, J. (2004).  An Introduction to Mathematical Statistics. Prentice Hall.

Liese, F. and Miescke, K. (2008). Statistical Decision Theory: Estimation, Testing, and Selection. Springer.

Pearl, J. (2000). Casuality: models, reasoning, and inference. Cambridge University Press.

Ross, S. (2014). Introduction to Probability and Statistics for Engineers and Scientists. London: Academic Press.

Todd, G. (2007). Descriptive Statistics. Topics in Biostatistics. New York: Springer.

Huck, S.W. (2007) Reading statistics and research. 5th ed., Allyn & Bacon: Boston, MA

Pallant, J. (2007) SPSS survival manual, 3rd ed., Allen & Unwin.

De Vaus, D. (2002) Analyzing social science data. SAGE Publications: London.

Wild, C.J., & Seber, G.A.F. (2000) Chance encounters: a first course in data analysis and inference. John Wiley & Sons: New York