MindMap Gallery Univariate linear regression model
Chapter 2 of Econometrics, Univariate Regression Model, briefly summarizes the knowledge of parameter estimation, goodness-of-fit test and estimator distribution, interval estimation and significance test of variables of linear regression~.
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Univariate linear regression model
Interval estimation and significance testing of variables
The idea and concept of interval estimation
confidence interval
Basic idea
source of problem
Inspection purpose
Test basics
hypothetical test
Significance test of variables
The first step is to formulate a hypothesis
Step 2: Define the test statistic
The third step is to calculate the value of the test statistic based on the sample and the null hypothesis.
Step 4: Determine the Denied Domain
The fifth step is t* judgment/p value judgment
Goodness of fit test and estimator distribution
The concept of goodness of fit
Decomposition of total variation
Total sum of squared deviations
regression sum of squares
residual sum of squares
coefficient of determination
definition
Features
Ranges
2·
3·
effect
Distribution of Least Squares Estimators
Estimate of the variance of the random disturbance term
Perform normalized transformation on βk tips
Parameter estimates of ~
~Basic assumptions
Model and variable assumptions
Assumption of random disturbance term u
1. Zero mean assumption
2. Homoskedasticity assumption
3·No autocorrelation assumption
4. No endogeneity assumption
5·Normality assumption
Assumptions about the explained variable Y
ordinary least squares
The basic idea of OLS
OLS estimate
OLS estimator
least squares estimator
Least squares estimator in dispersion form
OLS estimation formula
Properties of OLS regression lines
Statistical properties of parameter estimators
impartiality
effectiveness
consistency
other
Linear Characteristics of OLS Estimators
Unbiasedness of OLS estimator
Variance of OLS estimator
Gauss Markov theorem
Regression analysis overview
Econometric concepts
Interrelationships between Economic Variables
deterministic functional relationship
Uncertainty Statistical Correlation
Statistical correlation model
Description of statistical correlations (scatter plot)
Measure of statistical correlation
Overall linear correlation coefficient between X and Y
Sample linear correlation coefficient of X and Y
(one-way) causal relationship
It doesn't matter
regression analysis
Purpose
main content
regression line
regression function
Overall regression function and model
overall regression function
Premise: overall regression line
Expression form of overall regression function
Expression form of conditional mean
individual value representation
Two interpretations of the "linearity" of a linear regression model
As far as parameters are concerned
In terms of variables
Overall regression model
Random disturbance term and residual term
concept
nature
importance
Sample regression function and model
sample regression function
sample regression line
sample regression model