UCLA ECON 103 - Econ-103-Lecture-04 (80 pages)

Previewing pages 1, 2, 3, 4, 5, 38, 39, 40, 41, 42, 43, 76, 77, 78, 79, 80 of 80 page document View the full content.
View Full Document

Econ-103-Lecture-04



Previewing pages 1, 2, 3, 4, 5, 38, 39, 40, 41, 42, 43, 76, 77, 78, 79, 80 of actual document.

View the full content.
View Full Document
View Full Document

Econ-103-Lecture-04

210 views


Pages:
80
School:
University of California, Los Angeles
Course:
Econ 103 - Introduction to Econometrics
Introduction to Econometrics Documents

Unformatted text preview:

Lecture Note 4 Interval Estimation Hypothesis Testing Moshe Buchinsky UCLA Fall 2014 Buchinsky UCLA Econ 103 Lecture 4 Fall 2014 1 80 Topics to be Covered 1 Interval Estimation 2 Hypothesis Tests 3 Rejection Regions for Speci c Alternatives 4 Examples of Hypothesis Tests 5 The p value 6 Linear Combinations of Parameters Buchinsky UCLA Econ 103 Lecture 4 Fall 2014 2 80 Interval Estimation Interval Estimation There are two types of estimates point estimates and interval estimates Point estimates The estimate b2 is a point estimate of the unknown population parameter in the regression model Interval estimates Interval estimation proposes a range of values in which the true parameter is likely to fall Providing a range of values gives a sense of what the parameter value might be and the precision with which we have estimated it Such intervals are often called con dence intervals We prefer to call them interval estimates because the term con dence is widely misunderstood and misused Buchinsky UCLA Econ 103 Lecture 4 Fall 2014 3 80 Interval Estimation The normal distribution of b2 the least squares estimator for 2 is 2 b2 N 2 N 2 i 1 xi x A standardized normal random variable is obtained from b2 by subtracting its mean and dividing by its standard deviation Z r Buchinsky UCLA b2 2 2 N i 1 xi Econ 103 Lecture 4 N 0 1 x 3 1 2 Fall 2014 4 80 Interval Estimation We know that Pr 1 96 Substituting 0 B Pr B 1 96 r 1 96 95 Z b2 2 2 N i 1 xi 1 C 1 96C A 95 x 2 Rearranging Pr b2 1 96 s 2 x 2 N i 1 xi s b2 1 96 Buchinsky UCLA Econ 103 Lecture 4 2 2 N i 1 xi x 2 95 Fall 2014 5 80 Interval Estimation The two end points b2 interval estimator 1 96 r 2 N i 1 xi x 2 provide an In repeated sampling 95 of the intervals constructed this way will contain the true value of the parameter 2 This easy derivation of an interval estimator is based on the assumption SR6 and that we know the variance of the error term 2 Buchinsky UCLA Econ 103 Lecture 4 Fall 2014 6 80 Interval Estimation b2 creates a



View Full Document

Access the best Study Guides, Lecture Notes and Practice Exams

Loading Unlocking...
Login

Join to view Econ-103-Lecture-04 and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Econ-103-Lecture-04 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?