Estimating a regression model
Channel: Mikko Rönkkö
Date: 12/07/2019

The video dives into the concept of regression analysis, explaining how it uses data from dependent and independent variables to plot the best-fitting line, defined by regression coefficients known as betas. It discusses using Canadian census data – the 'Prestige' dataset, consisting of various factors like education, income, gender ratio, and prestige score of different occupations, to estimate these betas.

The video subsequently illustrates how the line is plotted by estimating beta0 and beta1, denoted with a caret or hat symbol (beta-hat-0 and beta-hat-1), which are calculated from a sample and serve as an estimate for the population's relationship. The line should pass through the middle of the observations, assuming that the observations are normally distributed around the line. To define this, a rule known as an estimator is used. This estimator should be consistent, unbiased, efficient, and should follow a known distribution when repeated estimates from repeated samples are made. The best rule for estimating the regression model is to use the residuals, minimizing the sum of these residuals raised to the second power, which is referred to as the ordinary least squares estimator.

Slides: https://osf.io/w23cq