**3. Problem Statement:**Suppose that a population equation is given by:\[ \mathbf{Y} = \mathbf{X}\boldsymbol{\beta} + \mathbf{Z}\boldsymbol{\gamma} + \mathbf{u} \]Instead, you estimated the following linear regression model:\[ \mathbf{Y} = \mathbf{Xb} + \boldsymbol{e} \]Assume: \[ \text{E}[\mathbf{u} \mid \mathbf{X}, \mathbf{Z}] = 0 \]It is well known that the estimator of \(\boldsymbol{\beta}\) typically will suffer from omitted variables bias. Derive the bias and state the condition(s) under which the estimator will be still unbiased.

Answered: **3. Problem Statement:** Suppose that…

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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Look at the following regression table where the dependent variable is the demand for illegal massage services in a city in the United States. Specifically, the dependent variable is the number of customers per hour (Models 1 and 2) or per day (Models 3 and 4). (a) Explain why the coefficient for Population/1,000 in Model 2 is very different from the one in Model 4?(b) Can you reject H0 in Model 1 if H0 : βP opulation/1,000 = 0.01, H1 : βPopulation/1,000 6= 0.01, and α = 0.01?
Suppose we have the following data on a dependent variable (Y) and a single explanatory variable (X): XY 0 20 5 40 10 90 What is the value of the intercept of the simple regression equation? Report your answer as a whole number. N
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Solve Qg, h , i. Slove Qg and h without using Excel. Qi using Rstudio.
ANSWER THE FOLLOWING QUESTION.
Consider a simple linear regression model with predictor variable x and response variable y, where the regression line is represented by the equation y = β0 + β1x. If β0 = -5 and β1 = 3, what is the predicted value of y for a given x = 4?
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The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.7 8.1 6.7 3.3 2.7 2.3 2.2 0.3 yy 13.8 10.7 9.9 6.6 6.1 5.9 6.1 4.5 xx = thousands of automatic weaponsyy = murders per 100,000 residents Determine the regression equation in y = ax + b form and write it below. (Round to 2 decimal places) A) How many murders per 100,000 residents can be expected in a state with 6.4 thousand automatic weapons? Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 6.7 thousand automatic weapons? Answer = Round to 3 decimal places.
Suppose the analyst constructs the simple linear regression model In(y) = a + Bx+e. She estimates it to be In() = -1- 1.3x. What is the residual in Excel output for the pair of observations x= 1.5 and y = 27 O a. 6. O b. 1.98 O c. -2. O d. 403.43 e. 4.29
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