Introduction to Econometrics

1. Introduction to Econometrics • Week 2 Lecture 2 • More on bivariate regression models • A recap on sampling distributions and standard errors • The story of the t-distribution • An introduction to forecasting with a simple regression model

2. Sampling distributions and standard errors

3. The Standard Error of the Estimate

4. The Standard Error of the X coefficient (1)

5. The Standard Error of the X coefficient (2)

6. The sales-advertising model on a spreadsheet: regression output

7. A digression on the t distribution and its history

8. The t distribution and the normal distribution The t distribution approaches the normal distribution asymptotically as the number of degrees of freedom increase

9. The t tables

10. Forecasting using the simple regression model (1) Once a model has been estimated (and carefully validated using economic and statistical tests) it can be used for prediction or forecasting. For example our estimated relationship between sales and ads is (approximately) sales = -75 + 1.929 ads + residual We can use this to predict sales for some particular level of advertising, say ads = 70 The disturbance term is assumed to take its expected value so we put the residual = 0.

11. Forecasting using the simple regression model (2) sales(ads=70) = -75 + 1.9292 * 70 = 60.04 This is just a point forecast. We can create a forecast confidence interval by taking 95% forecast interval = point forecast  sF  tn-2, 0.025 Here that would give 60.04  2.58097 * 2.228 = 60.04  5.75 i.e. [54.29, 65.79]

12. Forecasting using the simple regression model (3) This interval is quite large because it is based on a rather small sample. Hence both sF and tn-2, 0.025 will be fairly large. Forecasts based on larger samples will be more precise.

13. More on the standard error of the forecast