Economic Statistics
A continuous random variable can assume the infinitely many values
corresponding to points on the line interval
The researcher faces the question: how should I model a variable X in the
sample?
Examples of variables for which discrete
clear all
cap log close
cd "/Users/econlab/Desktop/STATA/"
log using HW9.log, replace
*1(a)*
set obs 8
input y
0.1
0.3
0.5
0.8
1.2
1.8
2.5
3.4
input x
1
2
3
4
5
6
7
8
twoway (scatter y x)
*1(b)*
gen x2=x^2
reg y x x2
*99.85% of the total variation is expl
ECON 3230: Homework 3 Solution
1. Multiple Choice: BDBAA
2. Answer:
(a) A person who is one year older increases her weekly earnings by $5.20. There is no meaning
attached to the intercept. The regression explains 5 percent of the variation in earnings.
(
ECON 3230: Homework 2 Solution
1. Multiple Choice: DBCCA
2. (i) Income, age, and family background (such as number of siblings) are just a few possibilities. It seems that each of
these could be correlated with years of education. (Income and education ar
ECON 3230: Homework 4 Solution
1. Multiple Choice: DACDB
2. Answer:
(i) If adults trade off sleep for work, more work implies less sleep (other things equal), so 1 < 0.
(ii) The signs of 2 and 3 are not obvious, at least to me. One could argue that more e
ECON 3230: Homework 4
Due date: Feb 23, 2017
1. Multiple Choice:
(a) Which of the following is true of R2 ?
a. R2 is also called the standard error of regression.
b. A low R2 indicates that the Ordinary Least Squares line fits the data well.
c. R2 usually
ECON 3230: Homework 6 Solution
1. Multiple Choice: BBBDA
2. Answer:
(a) The turnaround point is given by
sales in millions of dollars.
1 /(2| 2 |), or .0003/(.000000014) 21,428.57; remember, this is
(b) Probably. Its t statistic is about 1.89, which is si
ECON 3230: Homework 7
Due date: Apr 13, 2017
1. Multiple Choice:
(a) The major flaw of the linear probability model is that
a. the actuals can only be 0 and 1, but the predicted are almost always
different from that.
b. the regression R2 cannot be used as
ECON 3230: Homework 6
Due date: Mar 21, 2017
1. Multiple Choice:
(a) Which of the following statements is true when the dependent variable, y > 0?
a. Taking log of a variable often expands its range.
b. Models using log (y) as the dependent variable will
ECON 3230 Exam 1: Solution
1. BBCDD CACAB
2. (a) 38.2 percent of the presidents were Republicans and were in the White House while Republicans
controlled the House of Representatives. 44.1 percent of all presidents were Democrats.
(b) E(X) = 0.559. E(X =
Economic Statistics
We need combinatorics to derive the number of simple events in the sample
space and in events.
mn Rule: For any experiment conducted in two stages, with m possible outcomes
in the first stage and n possible outcomes in the second stage
Economic Statistics
Probability is the science of chance.
Two ways to think about probability:
1. Population to Sample: Given a fair coin, probability gives us the chance that
the next flip is heads: 50%.
2. Sample to Population: Test that a coin is fair
Economic Statistics
Parameters: Numerical descriptive measures associated with a population of
measurements
Statistics: Numerical descriptive measures associated with sample
measurements
Arithmetic mean of a set of n measurements is equal to the sum of th
The scores on a national achievement test were approximately normally
distributed, with a mean of 540 and standard deviation of 110.
o
If you achieved a score of 680, how far, in standard deviations, did your
score depart from the mean?
o
What percentage
Let X be a random variable of interest. Can be discrete or continuous
Central Limit Theorem: If random samples of size n observations are drawn from
a population with finite mean and standard deviation , then, when n is
sufficiently large, the sampling d
Consider a binomial random variable X = # successes
o
Let the population proportion of successes be p
o
If we take a random sample of size n then we can calculate the sample
statistic: = x/n
o
The central limit theorem implies that: N(p, (p(1p)/n) if np(
Given a 100(1 )% confidence interval
o
Sampling Error: % of the time, the true value of the population parameter
will not fall in the 100(1 )% confidence interval
Suppose , the population mean is unknown, but we have a large sample n > 30:
o
Derive a 100
Hypothesis Testing: Formal mechanism for drawing conclusions
Statistical process is analogous to the legal system
o
1. Assume the defendant is innocent
o
2. The prosecution then compiles evidence against that assumption
o
3. Original assumption is proved
Suppose = 0.05, n = 16, x N(5.05,0.12), so that the true value of = =
5.05
o
o
Ho : = 5
o
Calculate the power of the following test:
Ha : > 5
Properties of the (1 ):
o
o
Smaller (i.e., higher confidence) implies a lower (1 )
o
Larger n implies larger (1
ECON 3230: Exam 1
Feb 23, 2017
1. Multiple Choice (5 points for each question):
(1). Studying inflation in the United States from 1970 to 2006 is an example of
using
a.
b.
c.
d.
randomized controlled experiments.
time series data.
panel data.
cross-sectio