Statistical Sciences 2141A/B Lecture Notes - Lecture 29: Simple Linear Regression, Regression Analysis, Independent And Identically Distributed Random Variables

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Regression analysis is the part of statistics that investigates the relationship between two or more variables. Consider a data set consisting of the paired observations (x1, y1), (x2, y2), , (xn, yn) where xi represents the independent (or explanatory) variable and yi represents the dependent (or response) variable. The simplest mathematical relationship between two variables x and y is a linear relationship. However, since both x and y are rv"s, for each value of x there will be uncertainty of the value of y. In the simple linear regression model y = 0 + 1xi + i each yi is composed of a linear function of xi and an error term i. The error terms 1, 2, , n are generally assumed to be independent observations from a n(0, 2) distribution for some error variance 2. For a fixed value of x, it can be shown that. Therefore, the values y1, y2, , yn are observations of iid rv"s where.

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