ECON10005 Lecture Notes - Lecture 17: Regression Analysis, Covariance, Linear Regression
27 Jul 2018
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Document Summary
Give information about the linear releationship between two variables. The covariance of two random variables, x and y, is given by: If x and y are discrete random variances: An unbiased and consistent estimator for is the sample covariance: Mean and variance describe shape of marginal density function. Covariance and correlation coefficient describe shape of joint density function. Another way to think about correlation and covariance. Weight sum of all possible realisations of x, using the conditional density function as the weights. Conditional mean of y, given a value of x, is: Positively covary conditional means will be increasing functions of the conditioning variable (e. g. ) mean of x will be higher, the greater the value of the conditioning variable y. Slice of the joint density function, along the value of the conditioning variable. Model of the conditional mean of y, given x. Models the conditional mean of y as a a linear function of x with parametres and.
