ECONOMICS 2B03: Analysis of Economic Data I
Department of Economics
McMaster University
Assignment 1, Fall 2014, Due Tuesday September 16
Name and Student ID:
In order to facilitate grading, kindly complete your work in the space provided. It might be
hel
ECONOMICS 2B03: Analysis of Economic Data I
Department of Economics
McMaster University
Assignment 2, Fall 2014, Due Tuesday September 30
Name and Student ID:
In order to facilitate grading, kindly complete your work in the space provided. It might be
hel
ECONOMICS 2B03: Analysis of Economic Data I
Department of Economics
McMaster University
Assignment 3, Fall 2014, Due Tuesday October 21
Name and Student ID:
In order to facilitate grading, kindly complete your work in the space provided. It might be
helpf
Introduction to R
I. Using R for Statistical Tables and Plotting Distributions
The R suite of programs provides a simple way for statistical tables of just about
any probability distribution of interest and also allows for easy plotting of the
form of the
Assignment 3
Brandon Solanki 40033595
20170226
1. Define
1. Binomial Probability Distribution:
The model of probability obtaining one or two outcomes a certain number of times from a fixed
number of trails
2. Interval Estimate:
An interval within which
Assignment 2
Brandon Solanki 40033595
20170129
1. Define the following terms in a sentence (or short paragraph) and state a formula if appropriate
(a)Statistical Inference: Forming a judgement or educated opinion based on data that has been
collected, u
Determining sample sizes for confidence intervals of given widths
Suppose that you are interested in knowing how large a sample size we need before, say , the
value of our estimated parameter lies within 4 unites of the population parameter
By way pf exam
The sampling distrubution of the sample mean x
The sample mean X ~ = n ~1 nSUMi=1 Xi is an estimaaotr of the pipilation mean Omx
Expected value of X
The central limit theorem
The central limit theorem (CLT) is one of the most important theorems in statist
Law of probability: Multiplication
Unconditional probability p(A)
o
The likelihood that a particular event will occur, regardless of where another event
occurs
Joint Probability p(A and B)
o
The likelihood that two or more events will occur simultaneously
Basic rules for probability density functions
If a smooth curve is to represent a probability density functions, then the following tow
requirements must be met:
o
The total area between the curve and the horizontal axis must be unity, i.e., intergral
f(x
Sampling Theory



Recall that sampling from a population is necessary for a umber of reasons
We now turn our attention to problems involving the estimation of means and proportions. We
shall be interested in:
o Estimation
o Testing hypothesis
Estimate
Background: Discrete Probability Distribution
A 'probability distribution' is the theoretical (i.e., analytical) counterpart of the frequency
distrbutions discussed earlier
By applying the laws of prbability we can determine the prbability that a variable
Chapter 3
Origins of Data
Data can originated in a number of ways
Internal Data
Created as byproducts of regular activities
Example: customers, employee, productions records, governments records
External Data (typical source for this course)
Created by e
Chapter 3. continuous
Basic probability concepts
We now lay the foundation for the field of statistical inference by studying the theory of
probability
Statistical inference
The set of techniques used to turn sample evidence into valid conclusions about
s
Econ 2BO3 Assignment 1
Brandon Solanki 40033595
20170118
1. Define the following terms in a sentence (or a short paragraph) and state a formula if appropriate
1. Categorical data
Categorical data is a type of data that is broken down into variable group
Assignment 4
Brandon Solanki 40033595
20170312
1. Define the following terms in a sentence (or short paragraph) and state a formula if appropriate.
(a)Pvalue
Assuming Ho is true, it is the probability that the test statistic would take a value as extre
PROBABILITY TABLES (GENERATED BY R)
1. Standard Normal Cumulative Probability Tables.
Tables 1 and 2 provide values from the N (0, 1) (i.e. standard normal) distribution. Entries in cells are cumulative probabilities
(i.e. P [Z z]). For example, the value
Handout for Regression, Chapter 10
Simple Regression Analysis
The (unknown) population regression line is given by
yi = 0 + 1 xi +
i
The sample regression line is given by
yi = b0 + b1 xi + i
A least squares regression line minimizes the sum of the square
CHEAT SHEET (I.E., STUDY AID) FOR 2B03
(8) For events A and B:
Pr[A B] = Pr[A] + Pr[B] Pr[A B]
= Pr[A] + Pr[B]
Below are some formulas that may help you when studying
for this course. This is in no way meant to be instructive in
nature nor exhaustive. The
Handout for Example, Chapters 79
1
Mendels Pea Data
Mendels experiment resulted in n = 556 observations from which we calculate
Category
1 (RY)
2 (RG)
3 (WY)
4 (WG)
Null probability
Expected
Observed
(j,0 )
Frequency (ej )
Frequency (oj )
1,0 = 9/16
e1 =
Jan 11th
Summary statistics: symbolic expression
population parameter(typically unkown)
summary statistics based on population data
designated by greek letters
Sample statistics (computed from sample)
summary statistics based on sample data
designated
often we are interest in the proportion of successes in a smaple rather than the
number of success
recall that the sample proportion is denoted as P=x/n the random variable must
take on values 0,1 .n so the sample proportion must take on the value 0/n,1/
Cross Tabulations are tabular summaries for two variables
One variable represented by row heads
The other variable represented by column heads
Information for both variables entered in table cells
In R we use the xtabs () function
Crosstabulation is ext
continuous prob density functions
continuous random variables
unlike their discret counterparts, continuous random variables are uncotbale and
can assume any calue on the real number line
rather than looking at p(X=x) (ie the prob of any specific occurre
Statistics can be divided into two broad categories/branches
Descriptive statistics: Which seeks to describe general characteristics of a set of data
Inferential statistics: Which seeks to draw inferences about unknown features of a population
based on a
title: "Assignment 3"
author:
date: "3/1/2017"
output: html_document
`cfw_r setup, include=FALSE
knitr:opts_chunk$set(echo = TRUE)
`
1.
a) Binomial Probability Distribution can be used to determine the
probabilities associated with possible values of a
title: "Assignment 4"
author:
date: "3/15/2017"
output: html_document
1.
a) PValue is the probability, assuming the null is true, that the test
statistic would take a value extreme or more extreme than expected.
b) Power of a test is the probability of
title: "Assignment 2"
author:
date: "2/1/2017"
output: html_document
`cfw_r setup, include=FALSE
knitr:opts_chunk$set(echo = TRUE)
`
1. Definitions:
(a) Statistical Inference
The method of forming theories or judgments about the properties of a
populati
The sampling distribution of the difference between two sample proportion
Frequently we are interested in determining whether the proportion of people or things in on
population that possess a certain characteristic is the same as the proportion possessin