ECONOMETRICS STUDY NOTES FOR FINAL EXAM LEARNING OBJECTIVES 2024
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ECONOMETRICS STUDY NOTES FOR FINAL EXAM LEARNING OBJECTIVES 2024ECONOMETRICS STUDY NOTES FOR FINAL EXAM LEARNING OBJECTIVES 2024ECONOMETRICS STUDY NOTES FOR FINAL EXAM LEARNING OBJECTIVES 2024
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ECONOMETRICS STUDY NOTES FOR FINAL EXAM
LEARNING OBJECTIVES 2024
Chapter 1: Describing Data Graphical
Section 1.1: Decision Making in an Uncertain Environment
Random and Systematic Sampling
- A population is the complete set of all items that interest an investigator
o Population size, N, can be very large or even infinite
- A sample is an observed subset of a population with sample size given by n
- Simple random sampling is a procedure used to select a sample of n objects from a population in
such a way that each member of the population is chosen strictly by chance, the selection of one
member does not influence the selection of any other member (independently selected), each
member of the population is equally likely to be chosen, and every possible sample of a given size,
n, has the same chance of selection.
o This method is so common that the adjective simple is generally dropped, and the resulting
sample is called a random sample
- Suppose that the population list is arranged in some fashion unconnected with the subject
interest. Systematic sampling involves the selection of every jth item in the population, where j is
the ratio of the population size N to the desired sample size n; that is, j=N/n.
o Randomly select a number from 1 to j to obtain the first item to be included in your
systematic sample
o Systematic samples provide a good representation of the population if there is no cyclical
variation in the population
Sampling and Non-sampling Errors
- A parameter is a numerical measure that describes a specific characteristic of a population
- A statistic is numerical measure that describe a specific characteristic of a sample
- Sampling error results from the fact that information is available on only a subset of all the
population members
- Non-sampling errors
o The population actually samples in not the relevant one
o Survey subjects may give inaccurate or dishonest answers
o There may be no response to survey questions
- Descriptive statistics focus on graphical and numerical procedures that are used to summarize and
process data
- Inferential statistics focus on using the data to make predictions, forecasts and estimates to make
better decisions
Section 1.2: Classification of Variables
- A variable is a specific characteristic of an individual or object
- Data are either categorical or numerical
Categorical and Numerical Variables
- Categorical variables produce responses that belong to groups
o Yes/no answers
o “Strongly Agree” or “Strongly Disagree”
- Numerical variables include both discrete and continuous variables
- A discrete numerical variable may have a finite number of values
o Usually comes from a counting process
, o Examples: number of people enrolled, the number of credits earned
- A continuous numerical variable may take on any value within a given range of real numbers and
usually arises from a measurement process
o Examples: height, weight
,Measurement Levels
- With qualitative data there is no measurable meaning to the ‘difference’ in numbers
- With quantitative data there is a measurable meaning to the difference in numbers
- Nominal data are considered the lowest or weakest type of data, since numerical identification is
chosen strictly for convenience and does not imply ranking of responses
o Yes/no, or assigning numbers to responses
- Ordinal data indicate the rank ordering of items, and similar to nominal data the values are words
that describe responses
o Examples: ratings/preferences
Section 1.3: Graphs to Describe Categorical Variables
- A frequency distribution is a table used to organize data
o The left column includes all possible responses on a variable being studied
o The right column is a list of the frequencies, or number of observations, for each class
- A relative frequency distribution is obtained by dividing each frequency by number of observations
and multiplying the resulting proportion by 100%
Tables and Charts
- Tables, pie charts and bar charts are usually used to graph categorical data
- To draw the frequency of each category we will most likely use a bar chart
- The bars do not touch and their height represents the frequency
Cross Tables
- A cross table, sometimes called a crosstab or a contingency table, lists the number of observations
for every combination of values for two categorical or ordinal variables
o The combination of all possible intervals for the two variables defines the cells in a table
o A cross table with r rows and c columns is referred to as an r x c cross table
Pie Charts
- If we want to draw attention to the proportion of frequencies in each category, then we will use a
pie chart
- It will depict the division of a whole into its constituent parts
Pareto Diagrams
- A pareto diagram is a bar chart that displays the frequency of deflect causes
- The bar at the left indicates the most frequent cause and the bars to the right indicate causes with
decreasing frequencies
- It is used to separate the ‘vital few’ from the ‘trivial many’
Section 1.4: Graphs to Describe Time-Series Data
- Data measured at successive points in time are called time-series data
- A time series is a set of measurements, ordered over time, on a particular quantity of interest
o In a time series the sequence of the observations is important
- A line chart, also called a time series plot, is a series of data plotted at various time intervals
o Measuring time along the horizontal axis and the numerical quantity of interest along the
vertical axis yields a point on the graph for each observation
o Joining points adjacent in time by straight lines produces a time-series plot
o Examples: annual enrolment, annual interest rates, GDP over a period of years
Section 1.5: Graphs to Describe Numerical Variables
Frequency Distributions
- Determining the classes of frequency distribution for numerical data requires answers to certain
questions
o Examples: how many classes should be used? How wide should each class be?
- Construction of frequency distribution
o Determine k, the number of classes (or intervals)
, o Classes should be the same width, w; the width is determined by the following equation
largestobservation−smallest observation
▪ w=
number of classes
▪ Always round w upward
o Classes must be inclusive and non-overlapping
- A cumulative frequency distribution contains the total number of observations whose values are
less than the upper limit for each class
o We construct a cumulative frequency distribution by adding the frequencies of all
frequency distribution classes up to and including the present class
- In relative cumulative frequency distribution, cumulative frequencies can be expressed as
cumulative percents
Histograms and Ogives
- A histogram is a graph that consists of vertical bars constructed on a horizontal line that is marked
off with interval for the variable being displayed
o The intervals correspond to the classes in frequency distribution table
o The height of each bar is proportional tot eh number of observations in that interval
o The number of observations can be displayed above the bars
- An ogive is a line that connects points that are the cumulative percent of observations below the
upper limit of each interval in a cumulative frequency distribution
Shape of a Distribution
- The shape of a distribution is said to be symmetric if the observations are balanced, or
approximately evenly distributed about its centre
- A distribution is skewed is the observations are not symmetrically distributed on either side of the
centre
o A skewed-right distribution has a tail that extends farther to the right
o A skewed-left distribution is the opposite
- Distributions of incomes is often skewed-right because incomes tend to contain a relatively small
proportion of high values
Stem-and-Leaf Displays
- A stem-and-leaf display is an exploratory data analysis graph that is an alternative to the histogram
o Data are grouped according to their leading digits, and the final digits are listed separately
for each member of a class
o The leaves are displayed individually in ascending order after each of the stems
- The number of digits in each class indicates the frequency
- The individual digits indicate the pattern of values within each class
Scatter Plots
- A scatter plot is a graph used to investigate possible relationships between numerical variables
- The dependent variable is on the Y axis
- The independent variable is on the X axis
- We can prepare a scatter plot be locating one point for each pair of two variables that represent an
observation in the data set
o The scatter plot provides: the range of each variable, the pattern of values over the range, a
suggestion as to a possible relationship, an indication of outliers
Section 1.6: Data Presentation Errors
Misleading Histograms
- It is never desirable to construct histograms with different widths because it may easily deceive or
distort the findings
Misleading Time-Series
- By selecting a particular scale of measurement, we can, in a time-series plot, create an impression
either of relative stability or of substantial fluctuation over time
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