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# A95329 Statistics

Scuola di Economia e Management
Syllabus

 Docente Titolare Marta Nai Ruscone E-mail mnairuscone@liuc.it Office "Edificio 1" (in front of main tower), ground floor Phone 0331 572330

Learning Objectives

The course deals with concepts, methods and techniques for analyzing data, first from a data-descriptive perspective, and then from an inferential viewpoint. The course will also provide basic ideas of probability theory to evaluate uncertainty statements. The focus is on analyzing real data, using software tools.

Learning targets

1. Demonstrate the ability to apply fundamental concepts in exploratory data analysis.

2. Demonstrate an understanding of the basic concepts of probability and random variables.

3. Understand the concept of the sampling distribution of a statistic, and in particular describe the behaviour of the sample mean.

4. Understand the foundations for classical inference involving confidence intervals and hypothesis testing.

5. Apply inferential methods relating to the means of Normal distributions.

6. Apply and interpret basic summary and modelling techniques for bivariate data and use inferential methods in the context of simple linear models with Normally distributed errors.

7. Interpret and analyse data that may be displayed in a two—way table.

8. Apply and interpret simple and multiple linear regression model: explanatory power of the model, parameter estimation, forecasting.

Course Content

–    Describing data: frequency distributions, graphical representation, measures of location and spread.

–    Two-way frequency tables, scatterplots, and measures of dependence (covariance, correlation coefficient).

–    Probability: events, rules of probability, discrete and continuous random variables.

–    Sampling and sampling distributions: sampling mean, proportion and variance.

–    Inference: point estimation (statistic, main properties); confidence interval; hypothesis testing: single population and two-populations.

–    Simple and multiple linear regression model: explanatory power of the model, parameter estimation, forecasting.

Course Delivery

Course Evaluation

Syllabus

Session 0
Hours of lesson: 0
Instructor:

Topics:

Università Carlo Cattaneo - LIUC

School of Economics and Management

Statistics (8 CFU)

Detailed syllabus, textbooks and examination rules

Detailed syllabus

The course is structured as follows:

 LECTURE TOPICS REFERENCE Descriptive Statistics 1. (3h) Introduction to the course content, teaching materials and book’s website. Why statistics? Decision making under uncertainty. Population and sample. Descriptive and inferential statistics.  Kinds of variables and levels of measurement (qualitative and quantitative data). Frequency distribution. Ch. 1§1.1     Ch. 1§1.2 2. (3h) Graphs to describe categorical variables (bar chart, pie chart, Pareto diagram). Line chart to describe time series data. Frequency distribution and graphs to describe numerical variables: histograms with equal size and unequal class width. Frequency density. Cumulative distribution function for discrete and continuous variables. Ch. 1§1.3 Ch. 1§1.4 Ch. 1§1.5   Ch. 1§1.6 3. (3h) Measures of central tendency: mode, median, simple and weighted average. Quartiles and quantiles. Ch. 2§2.1, 2.3 4. (3h) Measure of variability: range, interquartile range, variance, standard deviation, coefficient of variation. Boxplot and shapes of distributions. Ch. 2§2.2 Appendix 1 of Ch. 4 5. (3h) Chebichev’s inequality. Measures of relationship between variables: covariance and linear correlation coefficient. Ch. 2§2.2 Ch. 2§2.4 Statistical Inference 6. (3h) Preliminary concepts on random variables.  The binomial distribution (and the Bernoulli distribution as a special case).  The normal distribution and standardization. The use of tables. Sum of Bernoulli and normal random variables. Ch. 4§4.1 Ch. 4§4.2, 4.3, 4.4 Appendix 4 of Ch. 4 Ch. 5§5.1, 5.2, 5.3, 7. (3h) Introduction to statistical inference: population, sample, statistics and parameters. Sampling distribution of the mean. Central Limit. Acceptance intervals. Ch. 6§6.1 Ch. 6§6.2 Ch. 5§5.4 8. (3h) Sampling distribution of the proportion. Sample variance. Estimators and estimates. Point estimators and their properties: unbiasedness and efficiency. Ch. 6§6.3 Ch. 6§6.4 Ch. 7§7.1 9. (3h) Interval estimator. Interpretation of confidence intervals. Confidence interval for the mean of a population with known and unknown variance. (Student’s t distribution) Ch. 7§7.2 Ch. 7§7.3 10. (3h) Large sample confidence interval.  Criteria for the determination of the sample size. (mean and population proportion) Ch. 7§7.4 Ch. 7§7.7 11. (3h) Sampling distribution of the sample variance. (Chi-square distribution). Confidence interval for the variance of a normal population. Ch. 6§6.4 Ch. 7§7.5 12. (3h) Confidence intervals for the difference between the means of two normal populations: case of dependent sample and independent samples with known variances and with unknown but equal variances. Ch. 8§8.1, 8.2 13. (3h) Hypotheses testing: basic concepts. Identification of the null hypothesis and of the alternative hypothesis. Ch. 9§9.1 14. (3h) Test for the mean of a normal population (known and unknown variance). p-value. Ch. 9§9.2, 9.3 15. (3h) Test for the proportion of a population (large samples). Calculation of the Type II error probability and the power of a test. Test for the differences between the means of two normal populations: dependent samples, independent samples (with known variance and with unknown but equal variances). Ch. 9§9.4 Ch. 9§9.5 Ch. 10§10.1 Ch. 10§10.2 16. (3h) Test for variance of normal population. Test for the equality of the variances between two normal populations. Ch. 9§9.6 Ch. 10§10.4 17. (3h) Final considerations on hypothesis testing. Ch. 10§10.5 18. (3h) Goodness of fit test: the case of completely specified probabilities. Ch. 14§14.1, 14.3 19. (3h) Contingency tables and test of statistical independence. Ch. 14§14.3 20. (3h) Correlation analysis and test for the absence of correlation. Ch. 11§11.7 Regression Analysis 21. (2h) Introduction to the linear regression model. Classical assumptions. The least squares estimator. Empirical examples. NCT,  Chapter 11, 11.1-11.3 22. (2h) Goodness of fit. Statistical inference: hypothesis testing and confidence intervals. Empirical examples. NCT, Chapter 11, 11.4-11.5 23. (2h) The multiple linear regression model. Estimation and interpretation of coefficients (marginal effects). Empirical examples. NCT, Chapter 12, 12.1-12.2 24. (2h) Hypothesis testing within the multiple linear regression model. Nonlinear transformations on dependent and explanatory variables. Empirical examples. NCT, Chapter 12, 12.4-12.5 25. (2h) Dummy variables for regression models. Empirical examples. NCT, Chapter 12, 12.7-12.8 26. (2h) Model misspecification. Empirical examples. NCT, Chapter 12, 12.9 27. (2h) Relaxation of classical assumptions: multicollinearity. Empirical examples. NCT, Chapter 13, 13.5 28. (2h) Relaxation of classical assumptions: heteroscedasticity. Models for heteroscedasticity and diagnostic tests Empirical examples. NCT, Chapter 13, 13.6 29. (2h) Relaxation of classical assumptions: autocorrelation. Models for autocorrelation and diagnostic tests. Empirical examples. NCT, Chapter 13, 13.7 30. (2h) Introduction to time series analysis. ARMA models. Empirical examples. NCT, Chapter 16, 16.1-16.2, 16.4

Textbooks

P. Newbold, W. L. Carlson, B. Thorne (NCT). Statistics for Business and Economics, and Student CD, Pearson (Eighth edition – Global edition, 2013).

Examination rules

The exam consists of a written general test, whose structure will be communicated in due course.

Students who systematically attend the course lectures are allowed to replace the general written test with three written partial tests.

After each exam session, a meeting will be held to allow students to see their exam papers. The date will be communicated together with the exam’s results.