Error Variance in Statistical Models

Questions and Answers

The variance in the independent variable that affects the dependent variable

The proportion of variance in the dependent variable that is explained by the independent variable(s)

The variance in the dependent variable that cannot be explained by the independent variable(s) (correct)

The correlation between the independent and dependent variables

σ² = Σ(ei) / (n + k - 1)

σ² = Σ(ei²) / (n - k - 1) (correct)

σ² = Σ(ei) / (n - k - 1)

σ² = Σ(ei²) / (n + k - 1)

The model is a good fit to the data (correct)

The model is overfitting the data

The independent variable(s) have a strong correlation with the dependent variable

The model is a poor fit to the data

A low error variance indicates a high R-squared value Signup and view all the answers

To evaluate the goodness of fit of the model Signup and view all the answers

The model is a poor fit to the data Signup and view all the answers

Study Notes

Error variance, also known as residual variance, is the variance in a dependent variable that cannot be explained by the independent variable(s) in a statistical model.

Error variance is calculated as the average of the squared differences between observed and predicted values of the dependent variable.
The formula for error variance is: σ² = Σ(ei²) / (n - k - 1), where:
- σ² is the error variance
- ei is the residual for each observation
- n is the total number of observations
- k is the number of independent variables

A small error variance indicates that the model is a good fit to the data, as most of the variance in the dependent variable can be explained by the independent variable(s).
A large error variance indicates that the model is a poor fit to the data, as most of the variance in the dependent variable remains unexplained.

Error variance is an important concept in statistical modeling, as it helps to evaluate the goodness of fit of a model and identify potential sources of error.
A low error variance is often desirable, as it indicates that the model is able to accurately predict the dependent variable.

Error variance is related to R-squared (R²), which is a measure of the proportion of variance in the dependent variable that is explained by the independent variable(s).
A high R² value indicates a low error variance, and vice versa.

Error variance, also known as residual variance, is the unexplained variance in a dependent variable.
It represents the variance that cannot be attributed to the independent variable(s) in a statistical model.

Error variance is calculated as the average of the squared differences between observed and predicted values of the dependent variable.
The formula for error variance is: σ² = Σ(ei²) / (n - k - 1), where:
- σ² is the error variance
- ei is the residual for each observation
- n is the total number of observations
- k is the number of independent variables

A small error variance indicates a good fit of the model to the data.
A large error variance indicates a poor fit of the model to the data.
Error variance helps to evaluate the goodness of fit of a model and identify potential sources of error.

Error variance is a crucial concept in statistical modeling.
A low error variance is desirable, as it indicates that the model accurately predicts the dependent variable.

Error variance is related to R-squared (R²), which measures the proportion of variance in the dependent variable explained by the independent variable(s).
A high R² value indicates a low error variance, and vice versa.