Class Outline

Class Outline PowerPoint PPT Presentation


  • 177 Views
  • Updated On :
  • Presentation posted in: General

Regression Through the Origin. The intercept is absent or zero. It can be shown that:. Regression Through the Origin. Characteristics of this model:In calculating the parameter we use raw and cross products instead of mean-adjusted sums of squares and cross productsThe degrees of freedom are n-1 rather than n-2The formula for r2 includes an intercept. Therefore you should not use this formula, or you will obtain nonsensical results, like negative r2The sum of the residuals is always zero,9462

Download Presentation

Class Outline

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


1. Class Outline Functional Forms of Regression Models Regression Through the Origin Log Linear Model Comparing Linear and Log Linear Models Multiple Log-Linear Models The Semilog Model The Lin-Log Model Reciprocal Models Polynomial Regression Models Summary of Functional Forms Reading: Chapter 6

3. Regression Through the Origin Characteristics of this model: In calculating the parameter we use raw and cross products instead of mean-adjusted sums of squares and cross products The degrees of freedom are n-1 rather than n-2 The formula for r2 includes an intercept. Therefore you should not use this formula, or you will obtain nonsensical results, like negative r2 The sum of the residuals is always zero, but in the case of a model with intercept this could not be the case.

4. Log-Linear Model Remember our example with the Lotto regression. Assume that our expenditure function is as follows: Where Y is the expenditure on Lotto and X is personal disposable income. The model is nonlinear in the variable X

5. Log-Linear Model We can transform the equation in logarithms: For estimation purposes we can write this model as

6. Log-Linear Model This is a linear regression model for the parameters ?1 and ?2. Observe that the slope coefficient ?2 measures the elasticity of Y with respect to X, that is, the percentage change in Y for a given percentage change in X.

7. Log-Linear Model We can define the elasticity as:

8. Log-Linear Model

9. Comparing Linear and Log-Linear Models Assume we run a linear model and a log linear model for the same dataset, which one to choose? Plot the data and see if you can determine the functional form We cannot compare r2 of log linear and linear models. By definition in the linear model r2 measures the proportion of the variation in Y explained X, while in the log linear model r2 explains the proportion of the variation of lnY explained by lnX. These measures are different

10. Comparing Linear and Log-Linear Models The variation in Y is a absolute change, while the variation in log of Y measures the relative or proportional change. Even if the dependent variables of two models is the same, we should not choose our models based on the highest r2 criterion. This is because this measure changes with the addition of variables.

11. Multiple Log-Linear Regression Models Example: The Cobb Douglas Production Function

12. How to Measure the Growth Rate: The Semilog Model When we are interested on the growth rate of some economic variables we can use this model. Example: we want to measure the growth rate of population over the period 1970-1999 Y0: beginning value of Y Yt: Y’s value at time t r: the compound rate of growth over time

13. How to Measure the Growth Rate: The Semilog Model Let’s transform this equation as follows:

14. The Lin-Log Model: When the Explanatory Variable is Logarithmic In this case, the independent variable, X, is expressed in logarithm Example: we want to find how expenditure on services (Y) behaves if total personal consumption expenditure (X) increases

15. The Lin-Log Model: When the Explanatory Variable is Logarithmic This equation states that the absolute change in Y is equal to ?2 times the relative change in X.

16. Reciprocal Models These models are used when the functional form have some asymptotic characteristics

17. Reciprocal Models

18. Polynomial Regression Models We can estimate this model with OLS. The only problem is the presence of multicollinearity, but usually this problem should not be too important in this case because the explanatory variables are not linear functions of X.

19. Polynomial Regression Models

20. Summary of Functional Forms

  • Login