Lecturer: Ing. Martina Hanová, PhD.

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Presentation transcript:

Lecturer: Ing. Martina Hanová, PhD. econometrics Lecturer: Ing. Martina Hanová, PhD.

Assumption of Ordinary Least Squares Linearity: The true relationship between the mean of the response variable E(Y) and the explanatory variables X1, ... Xn is a straight line. the mean of the response is not a linear function of the predictors/ transforming the response and/or predictor variables unequal error variances/ transforming the response and/or predictor variables or use "weighted least squares regression.„

DATA TRANSFORMATION To introduce basic ideas behind data transformations we first consider a simple linear regression model in which: We transform the predictor (x) values only. We transform the response (y) values only. We transform both the predictor (x) values and response (y) values.

Examples of logarithmic transformations Simple regression equation: Y = a + b*X Meaning: A unit increase in X is associated with an average of b units increase in Y. Equation: Y = a*ebX log(Y) = c + b*X Meaning: A unit increase in X is associated with an average of 100*b% increase in Y. Equation: Y = a*Xb log(Y) = c + b*log(X) Meaning: A 1% increase in X is associated with a b% increase in Y. Equation: Y = a + b*log(X) Meaning: A 1% increase in X is associated with an average b/100 units increase in Y.

The log-log transformation From taking the log of both sides of the equation: Cobb–Douglas production function Y = total production (the monetary value of all goods produced in a year) L = labor input K = capital input A = total factor productivity α and β – output elasticities

Log – log model The coefficients in a log-log model represent the elasticity of Y variable with respect to Xi variables. The coefficient is the estimated percent change in Y for a percent change in your Xi.

Log-transforming Only the Response Log-lin model ln Y = β0 + β1 * X + ε Log-Linear Trend Models Y = e^(β0 + β1 * t) + ε ln Y = β0 + β1 * t + ε B1 provides the instantaneous rate of growth for your dependent variable associated with a unit change in your independent variable The compounded growth rate is considered to be a more accurate estimate of the impact of X. compounded growth rate = e^B1-1

Log-transforming Only the Predictor Lin-log model Y = β0 + β1 *ln X + ε Y = β0 + β1 *ln (time) + ε B1 coefficients represent the estimated unit change in your dependent variable for a percentage change in your independent variable.