Middle East Technical University, Department of Economics, Fall 2012-2013
ECON 206 - Statistics for Economics II
Instructor: Dr. Osman Gulseven (A26), [email protected]
Course Assistant: Glsm Akarsu (A218), [email protected]
Schedule: Tuesday 14:40-17
F distribution critical value landmarks
Figure of F distribution (like in Moore, 2004, p. 656)
here.
Table entries are critical values for F *
with probably p in right tail of the
distribution.
p
2
49.50
199.5
799.5
4999
499725
3
53.59
215.7
864.2
5404
54
METU FEAS
Department of Economics
ECON 206-Statistics for Economists II
Instructor: Osman Glseven
Fall 2011
T.A.: Glsm Akarsu
S.A.: Halim mer St, Emel Yavuz
PART I: PROBLEM SET-IX-SOLUTIONS
1. From a sample of 10 families the following quantities were cal
METU FEAS
Department of Economics
ECON 206-Statistics for Economists II
Fall 2012
PROBLEM SET-V-SOLUTIONS
(CHAPTER 11: 11.1-11.4)
1. Assume that we have a model without intercept term:
Yt = Xt + ut
a. Find the normal equation, and .
b. Show that u need no
METU FEAS
Department of Economics
ECON 206-Statistics for Economists II
Fall 2012
PROBLEM SET-VI-SOLUTIONS
(CHAPTER 11)
1. A firm wants to see whether sales can be explained by the number of hours
overtime that their sales people work. Using a spread shee
METU FEAS
Department of Economics
ECON 206-Statistics for Economists II
Instructor: Osman Glseven
Fall 2011
T.A.: Glsm Akarsu
S.A.: Halim mer St, Emel Yavuz
PROBLEM SET-VIII-SOLUTIONS
1. Suppose a researcher wants to estimate the parameters in the simple
METU FEAS
Department of Economics
ECON 206-Statistics for Economists II
Instructor: Osman Glseven
Fall 2011
T.A.: Glsm Akarsu
S.A.: Halim mer St, Emel Yavuz
PROBLEM SET-II-SOLUTIONS
(CHAPTER 8: ESTIMATION)
1. The reading on a voltage meter connected to a
METU FEAS
Department of Economics
ECON 206-Statistics for Economists II
Instructor: Dr. Osman Glseven
T.A.: Glsm Akarsu
S.A.: Halim mer St, Emel Yavuz
Fall 2011
PROBLEM SET-V-SOLUTIONS
(CHAPTER 10: HYPOTHESIS TESTING: 10.5-10.9)
1. A large sample level te
METU FEAS
Department of Economics
ECON 206-Statistics for Economists II
Instructor: Dr. Osman Glseven
T.A.: Glsm Akarsu
S.A.: Halim mer St, Emel Yavuz
Fall 2011
PROBLEM SET-IV-SOLUTIONS
(CHAPTER 10: HYPOTHESIS TESTING: 10.2-10.4)
1. The shopping times of
Middle East Technical University Faculty of Economics and Administrative Sciences Department of Economics Econ 206 Spring 2008 PROBLEM SET # 2
1) A process produces bags of refined sugar. The weights of the contents of these bags are normally distributed
Chapter 11. Linear Regression
Multiple Linear Regression
J.C. Wang
Outline
Multiple Linear Regression
Multiple Linear Regression Modeling
Issues for MLR
Analysis of Real Estate Data
Summary Statistics
Statistical Inferences
Residual Analysis and Model Goo
Middle East Technical University
Department of Economics
Spring 2015-2016
ECON 206
PROBLEM SET 2
1. Let X1, X2 ,., Xn denote a random sample form a Uniform (0,) distribution with
>0 as the unknown parameter. Let X denote the sample mean.
a. Is X an unbias
Middle East Technical University
Department of Economics
Spring 2015-2016
ECON 206
PROBLEM SET 1
1. Let Y1, Y2 ,., Yn be a random sample of size n from a normal distribution with mean and
= 1 ni=1 Yi is normally distributed with mean Y= and variance Y 2
Middle East Technical University
Department of Economics
Fall 2016-2017
ECON 206
PROBLEM SET 1
1. Let Y1, Y2 ,., Yn be a random sample of size n from a normal distribution with mean
= 1 ni=1 Yi is normally distributed with mean Y= and
and variance 2. Sh
Middle East Technical University
Department of Economics
2016-2017 Fall Semester
ECON 206
PROBLEM SET 5
1. Suppose that the length of time
Y
it takes a worker to complete a certain task has the
probability density function given by,
Where
is a positive co
Middle East Technical University
Department of Economics
Fall 2016-2017
ECON 206
PROBLEM SET 3
1. Suppose X1,.,Xn are a random sample from a geometric distribution with parameter p,
f(x,p)=p(1-p)x-1, 0 1, x=1,2,3 Find MLE of .
2. Suppose that Y1,Yn is an
Middle East Technical University
Department of Economics
2016-2017 Fall Semester
ECON 206
PROBLEM SET 4
1. Nutritional information provided by Econ Fried Chicken (EFC) claims that each small bag
of potato wedges contains 4.8 ounces of food and 280 calorie
Middle East Technical University
Department of Economics
2016-2017 Fall Semester
ECON 206
PROBLEM SET 4
1. Nutritional information provided by Econ Fried Chicken (EFC) claims that each small bag
of potato wedges contains 4.8 ounces of food and 280 calorie
Middle East Technical University
Department of Economics
Fall 2016-2017
ECON 206
PROBLEM SET 2
1. Let X1, X2 ,., Xn denote a random sample form a Uniform (0,) distribution with >0 as
denote the sample mean.
the unknown parameter. Let X
an unbiased estim
METU FEAS
Department of Economics
ECON 206-Statistics for Economists II
Instructor: Osman Glseven
Fall 2011
T.A.: Glsm Akarsu
S.A.: Halim mer St, Emel Yavuz
PROBLEM SET-VII-SOLUTIONS
1. The 1980 EPA 49-state (all except California) combined mileage rating
Middle East Technical University Faculty of Economics and Administrative Sciences Department of Economics Econ 206 Spring 2008 PROBLEM SET # 3
1. Let X 1 and X 2 be a random sample of two observations from a population with mean and variance 2 . Consider
Middle East Technical University Faculty of Economics and Administrative Sciences Department of Economics Econ 206 Spring 2008 PROBLEM SET # 4 1. Let X be a Bernoulli random variable. The probability p x (1 - p )1- x , x = 0,1 Find MLE of the parameter p.
Middle East Technical University Faculty of Economics and Administrative Sciences Department of Economics Econ 206 Spring 2008 PROBLEM SET # 5
1. Write the assumptions of the simple linear regression model.
^ ^ 2. Let yx and xy represent the slopes in the
METU FEAS
Department of Economics
ECON 206-Statistics for Economists II
Fall 2012
PROBLEM SET-I
(SAMPLING DISTRIBUTIONS AND CENTRAL LIMIT THEOREM)
1. Suppose that Xi ~ N(,2) i=1,.,n and Zi ~ N(0,1) i=1,.,k and all variables are independent.
State the dist
METU FEAS
Department of Economics
ECON 206-Statistics for Economists II
Fall 2012
PROBLEM SET-II-SOLUTIONS
(CHAPTER 8: ESTIMATION, 8.1-8.4)
1. Let X1,Xn be a random sample from N(,2). Find E(s2), V(s2).
Solution:
n
(X
2
S=
i =1
i
X )2
n 1
(n 1) s 2
E[
2
METU FEAS
Department of Economics
ECON 206-Statistics for Economists II
Fall 2012
PROBLEM SET-III-SOLUTIONS
(CHAPTER 9: Properties of Point Estimators and Methods of Estimation)
1. Let Y1,Y2 and Y3 be a random sample from a normal distribution where both
METU FEAS
Department of Economics
ECON 206-Statistics for Economists II
Fall 2012
PROBLEM SET-IV-SOLUTIONS
(CHAPTER 10: Hypothesis Testing)
1. A single observation of a random variable having an exponential distribution is used to
test the null hypothesis
E 3-1 Listed below are the accounts for Risky Company and a series of transactions. Indicate
the accounts that would be debited and credited for each transaction.
Transaction
Account
Debited
Account
Credited
Mr. Cast, the owner, invested cash in business