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Concept
Residuals are the differences between observed values and the values predicted by a model, serving as a diagnostic tool to assess the model's accuracy. Analyzing residuals helps identify patterns or biases in the model, indicating areas where the model may be improved or where assumptions may be violated.
Random error refers to the unpredictable and unavoidable fluctuations in measurement results that arise from uncontrollable variables, which can obscure the true value being measured. Unlike systematic errors, Random errors do not have a consistent direction or magnitude, and their effects can often be mitigated by increasing the sample size or averaging multiple observations.
Systematic error refers to consistent, predictable errors that occur in data collection or analysis, leading to results that are consistently biased in the same direction. Unlike random errors, Systematic errors can often be identified and corrected through calibration or improved experimental design.
Heteroscedasticity refers to the circumstance in which the variability of a variable is unequal across the range of values of a second variable that predicts it, often violating the assumptions of homoscedasticity in regression analysis. It can lead to inefficient estimates and invalid inference in statistical models, necessitating the use of robust standard errors or transformation techniques to address the issue.
Homoscedasticity refers to the assumption that the variance of errors or disturbances in a regression model is constant across all levels of the independent variable(s). It is crucial for ensuring the validity of statistical tests and confidence intervals in linear regression analysis, as heteroscedasticity can lead to inefficient estimates and biased inference.
The normal distribution, also known as the Gaussian distribution, is a continuous probability distribution characterized by its symmetrical bell-shaped curve, where the mean, median, and mode are all equal. It is fundamental in statistics because many natural phenomena and measurement errors are approximately normally distributed, making it a cornerstone for statistical inference and hypothesis testing.
Concept
Variance is a statistical measure that quantifies the dispersion of a set of data points around their mean, providing insight into the degree of spread in the dataset. A higher variance indicates that the data points are more spread out from the mean, while a lower variance suggests they are closer to the mean.
Concept
Bias refers to a systematic error or deviation from the truth in data collection, analysis, interpretation, or review that can lead to incorrect conclusions. It can manifest in various forms such as cognitive, statistical, or social biases, influencing both individual perceptions and scientific outcomes.
Concept
Noise refers to any unwanted or disruptive sound that interferes with normal auditory processing, communication, or comfort. It can originate from various sources such as industrial activities, transportation systems, and urban environments, impacting both mental and physical health.
Model specification involves selecting the appropriate independent variables, functional forms, and distributional assumptions to accurately represent the underlying data-generating process. A well-specified model leads to unbiased, consistent, and efficient estimators, while a poorly specified model can result in misleading inferences and predictions.
Multiple Linear Regression is a statistical technique used to model the relationship between one dependent variable and two or more independent variables by fitting a linear equation to observed data. It is widely used for prediction and forecasting, allowing for the assessment of the relative influence of each independent variable on the dependent variable.
Hansen's J-test is a statistical test used to assess the validity of instrumental variables in econometric models, specifically testing the overidentifying restrictions. It evaluates whether the instruments are uncorrelated with the error term, ensuring that they are valid and exogenous for reliable parameter estimation.
Overidentifying restrictions occur in econometric models when there are more instruments than endogenous variables to be estimated, allowing for a test of the model's validity. This situation enables the use of statistical tests, such as the Sargan or Hansen test, to evaluate whether the instruments used are appropriate and uncorrelated with the error term, thereby ensuring the model's reliability.
The Hansen Test, also known as the J-test, is a statistical method used to assess the validity of instruments in econometric models, particularly in the context of instrumental variable regression. It helps determine whether the instruments are uncorrelated with the error term, ensuring that the model is correctly specified and the instruments are valid.
The Spatial Error Model is used in spatial econometrics to account for spatial autocorrelation in the error terms of a regression model, which can lead to inefficient and biased estimates if ignored. It extends traditional regression models by incorporating a spatially lagged error term, allowing for more accurate inferences in the presence of spatial dependence.
Unexplained variance, also known as error variance, refers to the portion of variability in a dataset that is not accounted for by the statistical model being used. It represents the discrepancies between observed data and the values predicted by the model, highlighting areas where the model may need improvement or where other factors may be influencing the data.
Endogeneity refers to a situation in statistical models where an explanatory variable is correlated with the error term, leading to biased and inconsistent parameter estimates. This issue often arises due to omitted variable bias, measurement error, or simultaneous causality, and can be addressed using methods like instrumental variables or fixed effects models.
Homoskedasticity refers to the assumption in regression analysis that the variance of the errors is constant across all levels of the independent variable(s). It is a crucial assumption for the validity of ordinary least squares (OLS) estimations, as violations can lead to inefficient estimates and affect hypothesis testing results.
An overidentification test is used in econometrics to assess the validity of instruments in an instrumental variable (IV) regression model. It tests whether the instruments are uncorrelated with the error term, ensuring that the model is correctly specified and the instruments are valid.
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