Flashcards in Quantitative Analysis Deck (27):
Used to refer to 1) correlation between two variables that reflects chance relationships in a particular data set, 2) correlation induced by a calculation that mixes each of two variables with a third, and 3) correlation between two variables arising not from a direct relation between them but from their relation to a third variable.
Also known as linear least squares, computes a line that best fits the observations; it chooses values for intercept b0 and b1 that minimize the sum of the squared vertical distances between the observations and the regression line.
Standard Error of Estimate (SEE)
Measures uncertainty; is similar to the standard deviation for a single variable, except that it measures the standard deviation of the residual term in the regression. An indicator of the strength of the relationship between the dependent and independent variables. The SEE will be low if the relationship is strong and high if it is weak.
Coefficient of Determination (R^2)
The fraction of the total variation that is explained by the regression.
Type 1 Error
Rejecting the null when it is true.
Type 2 Error
Failing to reject the null when it is in fact false.
Analysis of Variance (ANOVA)
A statistical procedure for dividing the total variability into components that can be attributed to different sources. Used to determine usefulness of the independent variable or variables in explaining variation in the dependent variable.
Is the correlation of the two variables, which is also the square root of the R^2 for one variable equations.
Explained Variation/degrees of freedom
Multiple Linear Regression
Allows you to determine the effect of more than one independent variable on a particular dependent variable.
The variance of the errors differs across observations.
Occurs when Heteroskedasticity of the error variance is not correlated with the independent variables in the multiple regression.
Heteroskedasticity in the error variance that is correlated with (conditional on) the values of the independent variables in the regression.
When regression errors are correlated across observations. Also known as, autocorrelated.
Positive Serial Correlation
Serial correlation in which a positive error for one observation increases the chance of a positive error for another observation. It also means that a negative error for one observation increases the chance of a negative error for another observation. The residual terms are correlated with one another, leading to coefficient error terms that are too small.
Occurs when two or more independent variables (or combinations of independent variables) are highly (but not perfectly) correlated with each other.
A variable's properties, such as mean and variance, are not constant through time.
P-Value of Regression
The smallest level of significance at which we can reject a null hypothesis that the population value of the coefficient is 0, in a two-sided test.
Multiple R-Squared to Multiple Regression
The percentage of the variation in the dependent variable that is explained by the model.
Autoregressive Model (AR)
A time series regressed on its own past values.
A time series' properties, such as the mean and the variance do not change over time. Assume in an autoregressive model to conduct a valid statistical reference.
A time series in which the value of the time series in one period is the value of the series in the previous period plus an unpredictable random error.
If a long-term financial or economic relationship exists between two time-series, such that they do not diverge from each other without bound in the long run.
Out of Sample Error Forecasts
Refers to the difference between the realized value and the forecasted value for the dates beyond the estimation period.
Calculating RMSE for Out of Sample Forecast Errors
1) Take the difference between the actual and the forecast errors
2) Square the error
3) Sum the squared errors
4) Divide by the number of forecasts
5) take the square root of the average
The Hansen Procedure
Used to solve issues with Heteroskedasticity and serial correlation.