Learning objectives
To have a general view of the main concepts of descriptive and inferential statistics
Prerequisites
Calculus, linear algebra
Course unit content
Part one
Introduction
• Collecting data, review of available statistical sources
• the data matrix; Graphic representations.
Summary of a phenomenon
• Frequency distributions and double entry tables
• averages (analytical mean and other indexes of position)
• Absolute and relative variability indices, concentration
• the shape of a distributions.
Time series
• Simple mobile and fixed base index numbers
• Time series concatenation with different bases; The average annual rate of variation
• compound price index numbers and deflated values at current prices
Relationships between two variables
• covariance and linear correlation coefficient
• the covariance matrix and correlation matrix
• linear regression: the ordinary least squares method; The interpretation of the parameters; model's goodness of fit;
• linear interpolation of time series
Part II
Introduction to probability and sampling
- Outlook of probability theories
- random variables: general aspects and applications
- theorems
- Sample distribution of statistical indexes
Estimating problems
- Average punctual estimate and relative frequency
- Estimate by average interval in case of large and small samples
- Estimate by relative frequency in case of large samples
Problems of hypothesis verification
- Introduction to statistical tests; Observed significance level (P-value)
- Tests in case of large and small samples - Tests on relative frequency in case of large samples
- Tests on two universes in the case of large samples
Univariate linear regression model
-Deriving the model of linear regression
- Estimation of model parameters and hypothesis testing
- Model checking. The meaning of ANOVA table.
Full programme
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Bibliography
M.A. Milioli, M. Riani S. Zani, Introduzione all’analisi dei dati statistici, (terza edizione ampliata) Pitagora, Bologna, 2014.
http://www.riani.it/MRZ
Cerioli, M.A. Milioli, Introduzione all’inferenza statistica senza (troppo) sforzo, 2a edizione, Uni.nova, Parma, 2004.
A. Cerioli, M. A. Milioli, M. Riani, "Esercizi di statistica", uni.nova, Parma, 2016. http://www.riani.it/CMR
Teaching methods
Knowledge acquisition: frontal lessons
Acquisition of the ability of applying what has been studied: written tests
Acquisition of judgment: during the course students will be encouraged to detect strengths and weaknesses of the methods and of the basic statistic indices.
Acquisition of learning skills: for each topic we will start from the illustration of the problems which have to be solved and we will analyze critically the adopted solutions.
Acquisition of technical language. While teaching, the meaning of the terms commonly used in statistics will be described.
Assessment methods and criteria
The Assessment is via a written test, using the same questions for all the students. The exam has a maximum duration of 90 minutes. The test generally consists of 4 exercises. To each is given a score. The different exercises are in turn divided into subgroups. The first exercise generally concern the topic of descriptive statistics. The last three, on the other hand, refer to probability and inferential statistics. The questions deal with some important points of the theory and practice of statistics and are intended to assess the ability of understanding, independence of judgment and the ability to communicate with appropriate statistical language.
The broad articulation of the questions in the different topics should enable to assess both the learning capacity and the ability to apply the knowledge which has been studied.
Other information
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2030 agenda goals for sustainable development
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