Statistics for Data Science

Course Title: Statistics for Data Science

Course No: BDS104

Nature of the Course: Theory + Lab

Semester: 1

Full Marks: 45 + 30

Pass Marks: 18 + 12

Credit Hours: 3

Course Description

This course covers descriptive statistics, exploratory data analysis, correlation and regression, index numbers, time series analysis, forecasting, probability, and Bayes' theorem for Data Science.

Course Objectives

Students will understand descriptive statistics, correlation and regression, index numbers, time series analysis, forecasting, probability, and Bayes' theorem, with applications in Data Science.

Course Contents

1. Introduction

2 hrs

1.1. Definition, scope and importance of Statistics

1.2. Population and sample data

1.3. Variable and its types: discrete and continuous

1.4. Qualitative and quantitative Sources of data: primary and secondary

1.5. Types of data: cross-sectional, temporal and panel

1.6. Scale of measurement of data: nominal, ordinal, interval and ratio

1.7. Application of Statistics in Data Science

2. Data summarization

10 hrs

2.1. Definition and need of data summarization

2.2. Methods of data summarization: tabular and graphical methods, frequency tables, cross-tabulations, bar diagrams, pie chart, histogram, frequency curve, ogives, frequency polygon

2.3. Measures of central tendency, partition values, dispersion, asymmetry (skewness) and kurtosis and their computational methods

2.4. Moments: raw and central moments, relation between raw and central moments, properties of moments

2.5. Exploratory data analysis: stem-and-leaf display, five number summary, box-plot

2.6. Solving problems relevant to Data Science

3. Correlation and regression analysis

12 hrs

3.1. Correlation and its types, assumptions, scatterplot, Karl Pearson's correlation coefficient: definition, computation, properties

3.2. Spearman's and Kendall's rank correlation coefficients

3.3. Simple and multiple linear regression, model assumptions, regression lines, ordinary least squares, interpretation of intercept and slope, correlation and regression parameters, goodness of fit, coefficient of determination, and residual analysis

3.4. Solving problems relevant to Data Science

4. Index numbers

8 hrs

4.1. Introduction, simple and weighted index numbers, methods of construction of price, quantity and value indices using unweighted and weighted aggregate methods: Laspeyers, Paasche, Fisher, fixed-weight aggregate methods, average of relative method

4.2. Consumer price index, purchasing power of money, real wages, base shifting, inflation and deflation

4.3. Time reversal and factor reversal tests

4.4. Issues in constructing and uses of index numbers

4.5. Applications of different index number techniques in monetary and finance related data

5. Time series analysis and forecasting

10 hrs

5.1. Introduction, components of a time series- secular trend, cyclic variation, seasonal variation, irregular variation

5.2. Time series analysis for forecasting using trend projection method, moving average method, curvilinear methods

5.3. Seasonal variation, determining the seasonal index, de-seasonalizing data

5.4. Test for autocorrelation

5.5. Forecasting methods- naive methods, linear methods, moving average methods, and simple exponential smoothing method

5.6. Measuring accuracy of forecasting models using mean square error (MSE), mean absolute deviation (MAD) and mean absolute percentage error (MAPE)

5.7. Solving problems relevant to Data Science

6. Probability

6 hrs

6.1. Review of fundamental concepts of probability, counting rules, types of probability, laws of probability, conditional probability, pair-wise and mutually independence

6.2. Bayes' theorem and its application, prior and posterior probability

6.3. Solving problems relevant to Data Science

Laboratory Works

The laboratory work includes using any statistical software such as Microsoft Excel, SPSS, R etc. Practical Problems

1.Mean, median, mode, partition values, measures of dispersion and coefficient of variation.
2.Measure of skewness and kurtosis, five number summary and Box and whisker plot.
3.Scatter diagram, Karl Pearson's correlation coefficient and Spearman's Rank correlation coefficient (ungrouped data) and interpretation. Compute manually and check with computer output.
4.Fitting of simple regression model, calculation of error term, standard error of the estimate, coefficient of determination and interpretation. Residuals plot
5.Fitting of multiple regression model, calculation of residuals, standard error of the estimate, coefficient of determination and interpretation.
6.Computation of probability in different conditions and Bayes' theorem.
7.Calculation of unweighted and weighted index number.
8.Linear and quadratic models, percent of trend, relative cyclical residual and interpretation of results.
9.Forecasting models

Reference Books

1.Bruce Peter and Bruce Andrew (2017). Practical Statistics for Data Scientists, O'Reilly Media, Inc., 1005 Gravenstein Highway North, Sebastopol, CA 95472, U.S.A.
2.Sheldon M. Ross (2010). Introductory Statistics, Elsevier Publication, U.S.A.
3.Neil Weiss (2010): Introductory Statistics, 5th edition: Pearson Publishers
4.Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers and Keying YE, Probability and Statistics for Engineers and Scientists, Pearson, 2012.
5.Anderson David R., Williams Thomas A., Cochran James J., Sweeney Dennis, Camm Jeffrey D., Ohlmann Jeffrey W. Statistics for Business & Economics, 14th Edition, Cengage Learning Inc., U.S.A.

Notes:

This syllabus follows the official BDS curriculum of Tribhuvan University. In case of any doubt or revision, the university's published syllabus shall be considered authoritative.

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