METRICS CONCEPTS

stochastic error term

element randomess we cant predict

Transformation error term

changing the variables will also affect the error term

Heterostedacity

occurs when the variance of the error term varies across observations, violating the assumption of constant variance in regression analysis.

Multiple regression anaylsis

A statistical technique that models the relationship between two or more independent variables and a dependent variable, allowing for the prediction of outcomes.

specification bias

occurs when a model is incorrectly specified, leading to biased estimates of the relationships between variables.

partial regression coefficient

represents the change in the dependent variable for a one-unit change in an independent variable, holding all other independent variables constant in a multiple regression model.

ols estimation

is a method used in regression analysis to estimate the parameters of a linear regression model by minimizing the sum of the squares of the differences between observed and predicted values.

Coefficient of determination

is a statistic that measures the proportion of variance in the dependent variable that can be explained by the independent variables in a regression model.

adjusted r²

is a modified version of the coefficient of determination that adjusts for the number of predictors in the model, providing a more accurate measure of model fit.

classical linear regression models

relationship between variables is linear

polynomial regression

is a form of regression analysis in which the relationship between the independent variable and the dependent variable is modeled as an nth degree polynomial. it models relationships that arent straight lines

normality assumptions

the errors in our model should follow a normal distribution

chow test

a statistical test used to determine whether the coefficients in two linear regression models on different datasets are equal. It is when data changes over time, determining if the relationship of what we are studying will change over time

Recursive Residual Test

scan through data and flag potential break post

Linear Restrictions

on the parameters of a regression model that impose constraints, allowing for hypothesis testing regarding the relationships between variables.

Restricted Least Square

incorportating restriciton directly in the model before estimating it

F test

compare residual sum of squares between restricted or unrestricted models