AIMS AND SCOPE
The aim of the course is introduce the knowledge of the R language for statistical data analysis with special focus on descriptive statistics, probability distributions and statistical inference.
Lectures and practical activities and data analysis in R.
Basics of linear algebra and statistics.
Use of the statistical software in R regarding:
Descriptive Statistics. Simple Statistical Distributions. Data tables. Frequency distributions. Main summary statistics: arithmetic mean, geometric mean, harmonic mean. Median and percentiles. Variance, standard deviation, relative variation. Graphical representations. Multiple Statistical Distributions. Contingency Tables. Joint distributions, marginal and conditional distributions. Covariance and correlation.
Probability. Random number generation and data modeling according to different probability distributions: uniform, binomial, Poisson, Gaussian.
Statistical inference. Sample distributions: Student-t, chi-square. Confidence estimation. Confidence level. Confidence bounds for means, variances, proportions. Hypothesis testing. Null hypotheses and alternative hypotheses. P-values. Statistical tests for means, variances, proportions, comparison of means, comparison of proportions.
Statistical models. The simple regression model. Goodness of fit. Residual analysis. Inference on the parameters of a linear regression model.
Documents available on the web page of The R Project for Statistical Computing: https://www.r-project.org and other resources available on the web.
|1||Introduction to R, Basic Commands in R, Indexing Data, Matrices and Lists, Loading Data||Lecture Notes|
|2||Graphs, Data Types and Structures, Conditional Statements and Loops, Graphs and Data Visualization||Lecture Notes|
|3||Mean, Median, Variance, standard deviation, quantiles, percentiles, interquartile distance, boxplot, outlier detection||Lecture Notes|
|4||Functions in R, data filtering||Lecture Notes|
|5||Bivariate analysis, statistical inference, contingency table, joint probability, marginal probability, chi-squared test, t-test, linear regression.||Lecture Notes|
Practical activity and data analyis with R
Perform a univariate analysis considering the attribute X
Report the correlation matrix among the attributes considering 2 digits precision
Perform a Linear Regression analysis of the relationship between the two features X and Y with the variable Z. Report below the output of the summary() function applied on the linear regression model obtained using lm(). Then, comment the results.
Is the dataset balanced with respect to the attribute X?
Visualize the scatter plot considering the variables X and Y. Report below the code used to create the plot.