JESTION IIConsider an econometrics model set to investigate the relationship between variables X and Y based on thepopulation regression function given as;Y₁ = B₁ + B₂X₁ + U₁a) Obtain the OLS estimators for B₁ and B₂for the above modelb) State and provide the proof of the mathematical/numerical properties of these estimatorsc) Demonstrate that Ordinary Least Squares Estimator B₂ is be BLUE

A simple linear regression model is given depicting the relationship between the independent…

Answered: IN II Consider an econometrics model…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Can you help me solve sub-part C
Q.1) The table below gives the readings from a laboratory experiment. 2 Time (t) Reading (y) 7 Fit: (i) a curve of the form y = ea(t-b), and (ii) a curve of the form y = a(1-bt) to the above data by method of least squares. (iii) determine which of the two (i) and (ii), is a best approximation. 3 17 5 49 6 71 9 161
13) Identify the terms in the master equation that we used, which is given beiow, in our linear least-squares fitting procedure
Please solve d-e, first parts asked in diffirent question. Consider the one-variable regression model Yi = β0 + β1Xi + ui, and suppose it satisfies the least squares assumptions in Key Concept 4.3. Suppose Yi is measured with error, so the data are ?"i = Yi + wi, where wi is the measurement error, which is i.i.d. and independent of Yi. Consider the population regression ?"i = β0 + β1Xi + vi, where vi is the regression error, using the mismeasured dependent variable ?"i.a) Showthatvi =ui +wi.b) Show that the regression ?"i = β0 + β1Xi + vi satisfies the least squares assumptions in KeyConcept 4.3. (Assume that wi is independent of Yj and Xj for all values of i and j and has afinite fourth moment.)c) Are the OLS estimators consistent?d) Can confidence intervals be constructed in the usual way?e) Evaluate these statements: “Measurement error in the X’s is a serious problem.Measurement error in Y is not.”
Match the answers
A certain experiment produces the data (2,7.3), (3,5.3), and (4, -0.2). Describe the model that produces a least-squares fit of these points by a function of the form y = A cos x + B sinx. The model is y=XB+e, where y = (Type an exact answer.) X=B= and ε = E₁ 82 £3
6. Consider the regression model Yi = βXi + ui, where ui and Xi satisfy the least squares assumptions in Key Concept 4.3. Let β ̄ denote an estimator of β that is constructed as β ̄ = Y ̄/X ̄, where Y ̄ and X ̄ are the sample means of Yi and Xi, respectively. (a) Show that β ̄ is a linear function of Y1 , ..., Yn . (b) Show that β ̄ is conditionally unbiased.
Example 15.11) The following table shows the marks obtained in two tests by 10 students: Marks in Ist Test (X) 8 8. 10 4 7 Marks in 2nd Test (Y) 8 7 7. 10 5 8. 10 6. (a) Find the least square regression line of Y on X. / 7,
Prove that b is an unbiased estimator for ß. What are the essential conditions to prove ordinary least squares (OLS) estimator is unbiased? E(b) = ß
If beta1_hat = 0.4571 use the data below to find beta0_hat for the simple linear model using the method of Least Squares. Y 17 2 3 11 4 20 15 18 13 13.07 50.88 24.57 32.11

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