STATISTICAL MODELS

The course aim at introducing basic concepts of statistical inference and statistical modeling for data analysis.

Simple Statistical Distribution. Data tables. Numerical and categorical data. Frequency distributions. Frequency density. Contingency Tables. Joint distributions, marginal and conditional distributions. Means and variance of marginal and conditional distributions. Association between statistical variables. Covariance and correlation.

Probability. Probability spaces. Random Variable. Probability models for count data: uniform, binomial, Poisson. Gaussian probability model. Central Limit Theorem

Statistical inference. Sample distributions: Student-t, chi-square, F-Snedecor. Point estimation. Properties of estimators. Methods of estimation: substitution principles, method of least squares, maximum likelihood estimates.

Confidence estimation. Confidence level. Confidence bounds for means, variances, proportions.

Hypothesis testing. Null hypotheses and alternative hypotheses. Test rules. Significance level. Power of a test. Statistical tests for means, variances, proportions; comparison of means, variances, proportions.

Statistical models. The simple regression model. Goodness of fit. Residual analysis. Testing on the parameters of a regression model. Multiple regression analysis.

Lecture notes