Sumários

Lecture 6B

14 Outubro 2026, 11:00 • Yiu Lim LUI

We continued the discussion of linear regression.  We finished Exercise 4.1 and 4.2.

Lecture 6 Summary

13 Outubro 2026, 09:30 • Yiu Lim LUI

 

·  Core Purpose: The lecture focuses on analyzing the relationship between two quantitative variables X and Y using scatterplots as a preliminary visual tool.

·  Association Metrics: Covariance measures the direction of a linear relationship, while the correlation coefficient (r, ranging from -1 to +1) quantifies both the direction and strength of that linear association.

·  Regression and OLS: Simple linear regression models y as a function of x, employing the Ordinary Least Squares (OLS) method to estimate parameters by minimizing squared errors.

·  Properties and Geometry: OLS guarantees that estimation errors have a zero mean and are uncorrelated with , mathematically equivalent to minimizing the n-dimensional Euclidean distance between the observed data vector and the predicted vector.

·  Model Quality: Fit quality is evaluated using residual variance and the coefficient of determination R^2, where R^2 represents the proportion of total variation in y explained by the model and equals r^2 in simple linear regression.

Lecture 5 b (Theory and Practice)

7 Outubro 2026, 11:00 • Yiu Lim LUI

  • Definition and Importance: Skewness measures the asymmetry of a probability distribution. Identifying it is essential because relying solely on the average for heavily skewed data distorts typical observations, and unaccounted skewness can invalidate statistical tests that assume a normal distribution.

  • Visual and Basic Identification: Skewness can be spotted visually using histograms, bar charts, and boxplots, or by analyzing the relative positions of the most frequent value, the median, and the average.

  • Pearson's Coefficient: This measure calculates how far the average is pulled away from the most frequent value, standardized by the standard deviation, with positive or negative values indicating the direction of the tail.

  • Bowley's Coefficient: This method compares the spread of the upper half of the data against the lower half using quartiles. It is particularly useful because it is robust and less affected by extreme values or outliers.

  • Moment Coefficient: This theoretical approach relies on central deviations to capture the net imbalance of the distribution's tails, heavily weighting values that lie far from the center.

    • Lecture 5 a (Theory and Practice)

    6 Outubro 2026, 09:30 • Yiu Lim LUI

    We finished exercise 3.2 to 3.6. And breiftly discuss the concept of skewness.

    Lecture 4 (Practice)

    30 Setembro 2026, 11:00 • Yiu Lim LUI

    We reviewed the core concepts and completed exercises 2.2 to 2.6,  3.1 and 3.3.