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MSE-213: Probability and statistics for materials science

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Lectures in this course (35)

Linear Regression: Basics and Principle of Least Squares Log in to Mediaspace to watch this video

Covers linear regression basics, focusing on minimizing error using the principle of least squares and includes an ANOVA table and practical example in R.

Linear Regression: Fundamentals and Goodness of Fit Log in to Mediaspace to watch this video

Explores linear regression fundamentals, non-linear regression issues, and R-squared goodness of fit, with examples like Anscombe's quartet and the Datasaurus dataset.

Multi-linear regression Log in to Mediaspace to watch this video

Covers the concept of multi-linear regression and the least squares method for model fitting.

Measures of central tendency Log in to Mediaspace to watch this video

Covers mean, median, mode, box plots, and histograms in datasets.

Model Selection Log in to Mediaspace to watch this video

Covers model selection, emphasizing the tradeoff between complexity and error in data analysis.

Confidence Bounds: Key Concepts and Variance Analysis Log in to Mediaspace to watch this video

Covers key assumptions, variance analysis, and confidence intervals in linear regression.

Linear Regression: Confidence Bounds Log in to Mediaspace to watch this video

Covers linear regression coefficients, confidence intervals, and R's calculation methods.

How to Lie with Statistics Log in to Mediaspace to watch this video

Explores scientific misconduct, p-value optimization, and spotting issues with conclusions using real-world examples.

Z-Test: Hypothesis Testing Log in to Mediaspace to watch this video

Introduces hypothesis testing, focusing on the Z-test and critical regions.

Measures of dispersion: Mean Square Error Log in to Mediaspace to watch this video

Explains data dispersion, central tendency, variance, standard deviation, and Mean Square Error.

Random Variables: Deterministic vs. Random Log in to Mediaspace to watch this video

Explores random variables, their variability, realization of random processes, and the scientific method in material science.

Elementary probability: Theory and calculations Log in to Mediaspace to watch this video

Introduces elementary probability theory, set theory operations, and probability calculations with practical examples.

Probability Density Function: Basics Log in to Mediaspace to watch this video

Covers the basics of Probability Density Function (PDF) in probability theory.

Expectation Values: Understanding Probability Distribution Functions Log in to Mediaspace to watch this video

Explains how to calculate expectation values for random variables using examples like a dice game.

Variance of Random Variables Log in to Mediaspace to watch this video

Covers the concept of variance for random variables and introduces calculation rules.

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