C6780 Fyzikálně organická chemometrie

Faculty of Science
Spring 2003
Extent and Intensity
2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Miroslav Holík, CSc. (lecturer)
Guaranteed by
prof. RNDr. Miroslav Holík, CSc.
Chemistry Section – Faculty of Science
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Introduction to probability and statistics, random sampling, point and interval estimates, outlier detection, statistical hypotheses. Matrix calculations in chemistry, matrix decomposition by SVD, PCA, PLS methods. Correlation and regression, correlation coefficients (single, multiple, partial), multivariable regression, multicollinearity, non-linear regression (relaxation, derivative and simplex methods), weighted least squares, confluential analysis. Design and optimization of experiments, analysis of variance, Plackett-Burman plan. Cluster and discrimination analysis.
Syllabus
  • 1. Random sampling, point and interval estimate, tests. Sample and population quantities (mean-average, variance, standard deviation), large and small sets of data, probability distribution and density function (the normal and Student's distributions), degrees of freedom, tests for outliers, null hypothesis, errors of the 1st and 2nd kind. 2. Two random variables and the tests of their similarity. Testing the difference of the means (independent variables and paired, with equal and unequal variances, Euclidean distance, agreement factor, angle between vectors, coefficient of determination, correlation coefficient and its transformations. 3. Linear regression like a proportionality relation Standard deviation of variables and standard error of estimate, standard deviations of regressions parameters, tests for confidence intervals, standard error of prediction, 'hat' matrix and influential points, tests of linearity, analysis of residuals. 4. Analysis of variance - additivity and nonadditivity Single-way, two-ways, and two-ways with interaction variance, experiment planning. 5. Multivariable regression, multicollinearity Bias of estimate due to inproper model, parcial F test, stepwise regression, suppression of multicollinearity (ridge regression). 6. Nonlinear and weighted regression, confluential analysis. Linearization of nonlinear regression, use of weighted regression, orthogonal regression with errors in both variables, nonlinear regressions and conditionality tests. 7. Principal component analysis Pretreatment of data (normalization, standardization). SVD -singular value decomposition; principal component scores and loadings, number of significant principal conpoments, reproduction of data from reduced components and loadings. Factor analysis and other variant methods. 8. SVD in regression and correlation analysis Principal component regression (PCR), suppression of the multicollinearity, transformation matrices, target testing, missing data calculation, methods NIPALS and PLS. 9. Planning and optimization of experiments Multiparameter analysis of variance, metods with repetition and separation into groups, latin and graecolatin squares, faktorial designs, Box-Hunter scheme, Plackett-Burman method. 10. Optimization with simplex, relaxation and derivation methods. Modified and supermodified simplex, weighted and two-site simplex, testing criteria for end of optimization. Single dimension optimization, relaxation methods, derivation metods for optimizing of parameters of nonlinear equations.
Assessment methods (in Czech)
Ústní zkouška buď v angličtině nebo v češtině.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008.
  • Enrolment Statistics (Spring 2003, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2003/C6780