Emprical Methods Uzh Solution

EMPIRICAL METHODS INTRODUCTION TO NOTATION

Notation

To simplify derivations throughout the course we will alternately use two different (although equivalent) notations for our models.

This is either the Vector Notation or the Matrix Notation.

Notation – Vector Notation

Derivation

In the general multiple regression model, a dependent variable y is related to a number of explanatory variables x1  ,  x2  ,  ...,  xK through a linear equation by

Notation – Vector Notation

Derivation

In the general multiple regression model, a dependent variable y is related to a number of explanatory variables x1  ,  x2  ,  ...,  xK through a linear equation by

Notation – Vector Notation

Derivation

In the general multiple regression model, a dependent variable y is related to a number of explanatory variables x1  ,  x2  ,  ...,  xK through a linear equation by

Notation – Vector Notation

Derivation

In the general multiple regression model, a dependent variable y is related to a number of explanatory variables x1  ,  x2  ,  ...,  xK through a linear equation by

Notation – Vector Notation

VN-Usage

Using vector notation we therefore write more concisely

Notation – Vector Notation

VN-Usage

Using vector notation we therefore write more concisely

while,

Notation – Vector Notation

VN-Usage

Using vector notation we therefore write more concisely

and thus,

Notation – Matrix Notation

Derivation

In a general multiple regression model, a dependent variable y is related to a number of explanatory variables x1  ,  x2  ,  ...,  xK through a linear equation by

Notation – Matrix Notation

Derivation

In a general multiple regression model, a dependent variable y is related to a number of explanatory variables x1  ,  x2  ,  ...,  xK through a linear equation by

which...