Question
In: Economics
Consider the simple regression model ? = ?0 + ?1? + ?) In the following cases,...
Consider the simple regression model ? = ?0 + ?1? + ?)
In the following cases, verify if the ‘zero conditional mean’ and ‘homoscedasticity in errors’ assumptions are satisfied:
a. If ? = 9? where ?(?⁄?) = 0, ???(?⁄?) = ? 2
b. If ? = 5.6 + ? where ?(?⁄?) = 0, ???(?⁄?) = 3? 2
c. If ? = 3?? where ?(?⁄?) = 0, ???(?⁄?) = ? 2 2)
D. In which of the cases above are we likely to get biased estimates of ?1?
Solutions
Expert Solution
Zero Conditional Mean -The error u has an expected value of zero given any values of the independent variables.
Homoskedasticity - The conditional variance of the error term in a regression equation is constant for all values of the independent variables.
An estimator is unbiased if E(b) = 
That’s just saying if the expected value of estimator equals the
parameter, then it’s an unbiased estimator.
a)
Unbiased estimate
b)
Biased estimate
c)
Unbiased estimate
(Homoskedasticity is not required for unbiasedness of estimator)
Rahul Sunny answered 1 year agoRelated Solutions
In the simple linear regression model ? = ?0 + ?1? +?, explain how the variance...
In the simple linear regression model ? = ?0 + ?1? +?, explain
how the variance of the error term u, the sample variance of x, and
the sample size n, affect the precision with which we can estimate
the unknown parameter ?1
Question 1: Consider the simple regression model: !Yi = β0 + β1Xi + ei (a) Explain...
Question 1:
Consider the simple regression model: !Yi = β0 + β1Xi + ei
(a) Explain how the Ordinary Least Squares (OLS) estimator formulas
for !β̂ and !β̂ are derived.
(b) Under the Classical Linear Regression Model assumptions, the
ordinary least squares estimator, OLS estimators are the “Best
Linear Unbiased Estimators (B.L.U.E.).” Explain.
(c) Other things equal, the standard error of β! ̂ will decline
as the sample size increases. Explain the
importance of this.
Question 2:
Consider the following...
(Regression Analysis) Consider the simple linear regression model (I) and the corresponding scatter plot with the...
(Regression Analysis)
Consider the simple linear regression model (I) and the
corresponding scatter plot with the covariates XX (x-axis) vs
residuals (y-axis). What model assumption violations can be
diagnosed by this scatter plot?
Consider the simple linear regression model for which the population regression equation can be written in...
Consider the simple linear regression model for which the
population regression equation can be written in conventional
notation as: yi= βxi+ui as
1- Derive the Ordinary Least Squares estimator (OLS) of β (i.e.
ˆβ) include in your answer details of the
proof.
2- Give an interpretation of ˆβ
Consider the simple linear regression model for which the population regression equation can be written in...
Consider the simple linear regression model for which the
population regression equation can be written in conventional
notation as: yi= βxi+ui as
1- Derive the Ordinary Least Squares estimator (OLS) of β0 (i.e.
ˆβ0) include in your answer details of the
proof.
2- Give an interpretation of ˆβ0
Consider the simple regression model: Yi = β0 + β1Xi + e (a) Explain how the...
Consider the simple regression model: Yi =
β0 + β1Xi + e
(a) Explain how the Ordinary Least Squares (OLS) estimator
formulas for β0 and β1are derived.
(b) Under the Classical Linear Regression Model assumptions, the
ordinary least squares estimator, OLS estimators are the “Best
Linear Unbiased Estimators (B.L.U.E.).” Explain.
(c) Other things equal, the standard error of will decline as
the sample size increases. Explain the importance of this.
Consider the simple regression model: !Yi = β0 + β1Xi + ei (a) Explain how the...
Consider the simple regression model: !Yi = β0 + β1Xi + ei
(a) Explain how the Ordinary Least Squares (OLS) estimator formulas
for β̂0 and β̂1 are derived.
(b) Under the Classical Linear Regression Model assumptions, the
ordinary least squares estimator, OLS estimators are the “Best
Linear Unbiased Estimators (B.L.U.E.).” Explain.
(c) Other things equal, the standard error of β̂1 will decline
as the sample size increases. Explain the
importance of this.
Which of the following is the complete definition of the simple linear regression model?
Which of the following is the complete definition of the simple
linear regression model?
Discuss the underlying assumptions of a simple linear regression model; multiple regression model; and polynomial regression.
Discuss the underlying assumptions of a simple linear regression
model; multiple regression model; and polynomial regression.
1. Consider simple regression model (one independent variable) a) How do you find a confidence interval...
1. Consider simple regression model (one independent
variable)
a) How do you find a confidence interval for the coefficient of
X?
b) How do you conduct a test if the coefficient of X is 10 or
not?
c) How do you find a CI for the mean of the dependent variable
if x=2?
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- [Big Data concept] (10) Give one example of Big Data application you know. Use the detailed...
- Write a program of Binary Search in C++ by using function and arrays with the explanation.
- Consider three jobs you know well, and explain the personality traits necessary for each job using...
- Steven has learned how stress affects his physical health, so now he is trying to reduce...
- You manage a risky portfolio with expected rate of return of 12% and a standard deviation...
- 1) a. Write down a C++ program which will create a list (simple linear linked list)...
- What is the difference between cross-site scripting (XSS) attack and cross-site request forgery (XSRF) attack?
ADVERTISEMENT