Homework Help is Here – Start Your Trial Now!
Math
Statistics
Consider the regression model Y; = B1X11 + B2X2¡ + uj for i = 1,..., n. %3D • Specify the least squares function that is minimized by OLS.

Consider the regression model Y; = B1X11 + B2X2¡ + uj for i = 1,..., n. %3D • Specify the least squares function that is minimized by OLS.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question

Thank you so much !

Consider the regression model Y; = B1X1i + B2X2; + Ui for i = 1, ..., n. • Specify the least squares function that is minimized by OLS. • Compute the partial derivatives of the objective function with respect to B1 and B2. • Compute the second derivatives of the objective function with respect to B1 and B2. Is the least squares function quadratic? • Derive an expression for B1 as a function of the data (Y;, X1i, X2i), i = 1,...,n. • Suppose E-1 X1;X2i = 0. Show that i=D1 n i=1 i=1 • Suppose the equation satisfies MLR.1-MLR.4, please derive E(ß1). • Suppose the equation satisfies MLR.5, please derive Var(Bì). • Suppose that the model contains an intercept. Also suppose that n E(Xli – X1) (X2i – X2) = 0 i=1
Transcribed Image Text:Consider the regression model Y; = B1X1i + B2X2; + Ui for i = 1, ..., n. • Specify the least squares function that is minimized by OLS. • Compute the partial derivatives of the objective function with respect to B1 and B2. • Compute the second derivatives of the objective function with respect to B1 and B2. Is the least squares function quadratic? • Derive an expression for B1 as a function of the data (Y;, X1i, X2i), i = 1,...,n. • Suppose E-1 X1;X2i = 0. Show that i=D1 n i=1 i=1 • Suppose the equation satisfies MLR.1-MLR.4, please derive E(ß1). • Suppose the equation satisfies MLR.5, please derive Var(Bì). • Suppose that the model contains an intercept. Also suppose that n E(Xli – X1) (X2i – X2) = 0 i=1
Show that βΣ(Χ - Χ1) (Y-Υ) /Σ ( Χ- X.). i=1 i=1 How does this compare to the OLS estimator of B1 from the regression that omits X2 ? • Suppose you are interested in B1, the causal effect of X1 on Y. Suppose that X1 and X2 are uncorrelated. You estimate B1 by regressing Y onto X1 (so that X2 is not included in the regression). Does this estimator suffer from omitted variable bias? Explain.
Transcribed Image Text:Show that βΣ(Χ - Χ1) (Y-Υ) /Σ ( Χ- X.). i=1 i=1 How does this compare to the OLS estimator of B1 from the regression that omits X2 ? • Suppose you are interested in B1, the causal effect of X1 on Y. Suppose that X1 and X2 are uncorrelated. You estimate B1 by regressing Y onto X1 (so that X2 is not included in the regression). Does this estimator suffer from omitted variable bias? Explain.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS