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Simple Regression: Key Terms
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Terms in this set (35)
Coefficient of Determination
R-Squared
Constant Elasticity Model
Elasticity of the DV, with respect to IV is constant; in multiple regression, both variables appear in logarithmic form
Control Variable
Explanatory variable
Covariate
Explanatory variable
Degrees of Freedom
the number of observations minus the number of estimated paramaters i.e. n-2 in a simple regression analysis
Dependent Variable
The variable to be explained in a multiple regression mode
Elasticity
The percentage change in one variable given a 1% ceteris paribus increase in another variable
Error Term (Disturbance)
The variable in a simple or multiple regression equation that contains unobserved factors that affect the DV. Error term may also include measurement errors in the observed dependent or independent variables
Error Variance
The variance of the error term in a multiple regression model
Explained Sum of Squares (SSE)
Total sample variation of the fitted value in a multiple regression model
Explained Variable
The variable that is used to explain variation in the dependent variable
F statistic
used to test multiple hypotheses about the parameters in a multiple regression model
First Order Conditions
Set of Linear equations used to solve for the OLS estimates
Fitted Value
the estimated values of the dependent variable when the values of the independent variable s for each observation are plugged into the OLS regression line
Gauss Markov assumptions
MLR1-MLR5
Heteroskedasticity
the variance of the error term, given the explanatory variables is not constant
Homoskedasticity
the errors in a regression model have constant variance conditional on the explanatory variables
Intercept Parameter
The parameter in a multiple linear regression model that gives the expected value of the dependent variable when all the independent variables equal zero
Mean Independent
The key requirement in multiple regression analysis that says the unobserved error has a mean that does not change across the subsets of the population defined by different values of the explanatory variables
OLS Regression Line
The equation relating the predicted value of the dependent variable to the independent variable, where the parameter estimates have been obtained by OLS
Ordinary Least Squares
A method for estimating the parameters of a multiple linear regression model. The ordinary least squares estimates are obtained by minimizing the sum of squared residuals
Population Regression Function
The expected or average value of one random variable, called the DV that depends on the values of one or more other variables, called the independent variable
Predicted Variable
Dependent Variable
Residual Sum of Squares (SSR)
Sum of Squared residuals
Response Variable
Dependent Variable
R-Squared
The proportion of the total sample variation in the dependent variable that is explained by the independent variable
Sample Regression Function
OLS regression Line
Semi-elasticity
the percentage change in the dependent variable given a one-unit increase in the independent variable
Simple Linear Regression Model
Model where the dv is a linear function of a single independent variable
Slope Parameter
the coefficient on an independent bariable in a multiple regression model
Standard Error of Beta 1 hat
Estimate of the standard deviation in the sampling distribution of Beta hat
Standard Error of the Regression
In multiple regression analysis, the estimate of the standard deviation of the population error, obtained as the square root o the sum of squared residuals over the degrees of freedom
Sum of Squared Residuals
sum of the squared OLS residuals across all observations
Total Sum of Squares
total sample variation in a dependent variable about its sample average
Zero Conditional Mean Assumption
given any values of the explanatory variables, the expected value of error equals zero
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