**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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Laetisaric acid is a compound that holds promise for control of fungus diseases in crop plants. Below is the least-squares regression equation to predict fungus growth (mm) from laetisaric acid concentration (µG/ml): ŷ =31.8 -0.712x Which of the following statements is correct? A. Above-average values of laetisaric acid concentration tend to accompany above-average values of fungus growth. B. From the given regression equation, we know the correlation is negative and we can say what the exact value of that correlation is. C. When fungus growth increases by 1 mm, the laetisaric acid concentration decreases by 0.712 µG/ml. D. None of the above.
If the R-squared for a regression model relating the outcome y to an explanatory variable x is 0.9. This implies that there is a positive linear relationship between y and x. True or false?
ANSWER THE FOLLOWING QUESTION.
A study examined the eating habits of 20 children at a nursery school. The variables measured for each child included: calories (the number of calories eaten at lunch), time (the time in minutes spent eating lunch), and sex (male=1, female=0). A multiple linear regression model using Y = calories, X1 = time, and X2 = sex led to the following model: y=547.65-2.85x1+10.67x2 For two children who spend the same amount of time eating, one male and one female, which child is predicted to consume more calories and by how much?
3. Consider the following regression model: Weekly Hours = Bo + B1 × Wage + uj Weekly Hours is the average number of hours the individual worked over the course of the year and Wage is the individual's average hourly wage over the course of the year. A researcher who collects data and regresses Weekly Hours against Wage finds that B1 > 0. The OLS estimator, B, however, likely suffers from omitted variable bias because those individuals who earn high wages may be driven personalities who would work long hours no matter the wage. Because of this omitted variable bias, it is likely the case that B1_B1. A) В)
Consider the following linear regression prediction equation: Y = 12 + -1x. What is the direction of the relationship between these two variables? a. The relationship between the observed X and the predicted Y is negative. b. The relationship between the observed X and the predicted Y is positive. c. There is no relationship between the observed X and the predicated Y. d. There is a weak relationship between the observed X and the predicted Y with no direction.
A company studying the productivity of its employees on a new information system was interested in determingg if the age (X) of data entry opeertors influenced the number of completed entries made per hour (Y). The regression equation is y = 14.374 - 0.145x Suppose the acyual completed entries per hour for an operator who is 35 years old was 8. The residual is:
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
Assume there is a positive linear correlation between the variable R (Return rate in percent of a financial investment) and the variable t (age in years of the investment) given by the regression equation R= 2.3t + 4.8 A. Without further information, can we assume there is a cause-and-effect relationship between the return rate and the age of the investment? B. If the investment continues to grow at a constant rate, what is the expeted return rate when the investment is 7 years old? C. If the investment continues to grow at a constant rate, how old is the investment when the return rate is 30%?

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