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Economics 240A

Power One

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Outline

Course Organization Course Overview Resources for Studying

I. Organization Lectures are on Tuesdays and Thursdays, 5:00-6:15 PM in North Hall 1105.

Lecture Notes for class will cover the concepts Text: Gerald Keller, Statistics for Management and Economics, Seventh edition (2005)

The Computer Lab is scheduled for Wednesdays, 3:00-3:50. ;400-4:50, & 5:00-5:50 in Leadbetter, Phelps 1530. The capacity is 25 stations.

Software: Excel and EViews Lab Notes will cover the procedures of analysis TA: Stephane Verani, Office, NH 2048 Section: 140A F10:00-10:50 Girvetz 2115, 240A W 6-7:50 Phelps 3505 Exams: Midterm Tuesday, Nov. 6` Final Tuesday, December 13, 7:30-10:30 PM

Problem Sets, Pre-Midterm: #1 Oct. 4, 2007 due Oct 11, 2007 #2 Oct 11, 2007 due Oct 18, 2007 #3 Oct 18, 2007 due Oct 25, 2007 #4 Oct 25, 2007 due Nov.1, 2007 Problem Set, Post-Midterm #5 Nov. 1, 2007 due Nov. 8, 2007 Exercises: as assigned on the Lab Notes

Organization ( Cont.)

Takehome Project: An exercise to test your quantitative and writing skills. You can work collectively but the 2-3 page report must be yours. Last Fall we also did group projects with PowerPoint presentations and I will probably repeat this format.

Your grade for the course will be based on your scores on the midterm(18%), final(37%) and 2 projects(each 18%), and your effort as indicated by problem sets and lab exercises turned in for credit(9%). Of course the latter are more important than the weight indicated. I distribute the grades by letter, weighing the problem sets one third of a grade point, and by total score for the class, and reconcile the course grades.

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Course Overview Topics in Statistics

• Descriptive Statistics• Exploratory Data Analysis• Probability and Distributions• Proportions • Interval Estimation• Hypothesis Testing• Correlation and Regression• Analysis of Variance

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Concepts 1

Two types of data:• Time series• Cross section

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http://research.stlouisfed.org/fred2/

Index 1982-84 =100

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http://research.stlouisfed.org/fred2/

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CPIAUCNS Jan 1921- Aug 2007

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Examples of:1.Graphical Display of

Results2.Cross-Section Data3.Survey Sample of 12,571

1.Men & women2.Ages 15-44

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What is the Message?

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Concepts 2

Population Versus Sample Iowa Caucuses, New Hampshire Primary

• Population: All eligible voters• Sample: Field poll in California

Popsample

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Concepts 3

Different views of the world (universe)• Deterministic• Stochastic

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Statistical Inference and Probability

Deterministic• Newtonian physics: e g. distance = rate*time• Einsteinian(relativistic) physics: E=m*c2

Stochastic (random)• Quantum mechanics

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Statistical Inference and Probability Probability: A tool to understand chance What is chancy about the statistical world

we will study? Example:

• Suppose I number everyone in the class from 1 to 65?

• And draw one number a meeting to ask a question; what is the likelihood I will call on you today?

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Resources for Studying

Keller • Text Readings

• CDROM• Applets

Instructor• Lecture Notes

• Lab Notes & Exercises

• Problem Sets

• PowerPoint Slide Shows

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Keller CDROM

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http://www.duxbury.com/statistics

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Student Book Companion Site

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Concepts 4

Three types of data• Cardinal• Ordinal• Categorical

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Keller & Warrack Slide Show

Excerpts from Ch. 2

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Graphical Descriptive Techniques

Graphical Descriptive Techniques

Chapter 2Chapter 2

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2.1 Introduction

Descriptive statistics involves the arrangement, summary, and presentation of data, to enable meaningful interpretation, and to support decision making.

Descriptive statistics methods make use of• graphical techniques• numerical descriptive measures.

The methods presented apply to both• the entire population• the population sample

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2.2 Types of data and information

A variable - a characteristic of population or sample that is of interest for us.• Cereal choice

• Capital expenditure

• The waiting time for medical services

Data - the actual values of variables • Interval data are numerical observations

• Nominal data are categorical observations

• Ordinal data are ordered categorical observations

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Types of data - examples

Interval data

Age - income55 7500042 68000

. .

. .

Age - income55 7500042 68000

. .

. .Weight gain+10+5..

Weight gain+10+5..

Nominal

Person Marital status1 married2 single3 single. .. .

Person Marital status1 married2 single3 single. .. .Computer Brand

1 IBM2 Dell3 IBM. .. .

Computer Brand1 IBM2 Dell3 IBM. .. .

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Types of data - examples

Interval data

Age - income55 7500042 68000

. .

. .

Age - income55 7500042 68000

. .

. .

Nominal data

With nominal data, all we can do is, calculate the proportion of data that falls into each category.

IBM Dell Compaq Other Total 25 11 8 6 50 50% 22% 16% 12%

IBM Dell Compaq Other Total 25 11 8 6 50 50% 22% 16% 12%

Weight gain+10+5..

Weight gain+10+5..

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Types of data – analysis

Knowing the type of data is necessary to properly select the technique to be used when analyzing data.

Type of analysis allowed for each type of data Interval data – arithmetic calculations Nominal data – counting the number of observation in each

category Ordinal data - computations based on an ordering process

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Cross-Sectional/Time-Series Data

Cross sectional data is collected at a certain point in time • Marketing survey (observe preferences by gender, age)• Test score in a statistics course• Starting salaries of an MBA program graduates

Time series data is collected over successive points in time • Weekly closing price of gold• Amount of crude oil imported monthly

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2.3 Graphical Techniques forInterval Data

Example 2.1: Providing information concerning the monthly bills of new subscribers in the first month after signing on with a telephone company.• Collect data• Prepare a frequency distribution• Draw a histogram

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Largest observation

Collect dataBills42.1938.4529.2389.35118.04110.460.0072.8883.05

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(There are 200 data points

Prepare a frequency distributionHow many classes to use?Number of observations Number of classes

Less then 50 5-750 - 200 7-9200 - 500 9-10500 - 1,000 10-111,000 – 5,000 11-135,000- 50,000 13-17More than 50,000 17-20

Class width = [Range] / [# of classes]

[119.63 - 0] / [8] = 14.95 15Largest observationLargest observation

Smallest observationSmallest observationSmallest observationSmallest observation

Largest observation

Example 2.1: Providing information

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0

20

40

60

80

15 30 45 60 75 90 105 120

Bills

Fre

qu

en

cy

Draw a HistogramBin Frequency

15 7130 3745 1360 975 1090 18

105 28120 14

Example 2.1: Providing information

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nnnn

0

20

40

60

8015 30 45 60 75 90 10

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120

Bills

Fre

qu

ency

What information can we extract from this histogramAbout half of all the bills are small

71+37=108 13+9+10=32

A few bills are in the middle range

Relatively,large numberof large bills

18+28+14=60

Example 2.1: Providing information

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It is generally best to use equal class width, but sometimes unequal class width are called for.

Unequal class width is used when the frequency associated with some classes is too low. Then,• several classes are combined together to form a wider

and “more populated” class.• It is possible to form an open ended class at the higher

end or lower end of the histogram.

Class width

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There are four typical shape characteristics

Shapes of histograms

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Positively skewed

Negatively skewed

Shapes of histograms

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A modal class is the one with the largest number of observations.

A unimodal histogram

The modal class

Modal classes

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Descriptive Statistics

Central Tendency• mode• median• mean

Dispersion• standard deviation• interquartile range (IQR)

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Concepts 5

Normal Distribution• Central tendency: mean or average• Dispersion: standard deviation

Non-normal distributions

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Concepts 6

What do we mean by central tendency? Possibilities

• What is the most likely outcome?• What outcome do we expect?• What is the outcome in the middle?

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Moving from Concepts to Measures

Mode: most likely value.

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Moving from Concepts to Measures

Mode: most likely value. Median: sort the data from largest to

smallest. The observation with half of the values larger and half smaller is the median.

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Moving from Concepts to Measures Median: sort the data from largest to

smallest. The observation with half of the values larger and half smaller is the median.

Mode: most likely value. Mean or average: sum the values of all of

the observations and divide by the number of observations.

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Concepts 7

What do we mean by dispersion? Possibilities

• How far, on average are the values from the mean?

• What is the range of values from the biggest to the smallest?

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Exploratory Data Analysis

Stem and Leaf Diagrams Box and Whiskers Plots

Males: 140 145 160 190 155 165 150 190 195 138 160 155 153 145 170 175 175 170 180 135 170 157 130 185 190 155 170 155 215 150 145 155 155 150 155 150 180 160 135 160 130 155 150 148 155 150 140 180 190 145 150 164 140 142 136 123 155

Females: 140 120 130 138 121 125 116 145 150 112 125 130 120 130 131 120 118 125 135 125 118 122 115 102 115 150 110 116 108 95 125 133 110 150 108

Weight Data

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Box Diagram

First or lowest quartile;25% of observations below

Upper or highest quartile25% of observations above

median

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Whiskers

The whiskers end with points that are not outliers

Outliers are beyond 1.5 times the interquartile range ( in this case IQR = 31), so 1.5*31 = 46.5

1st quartile – 1.5*IQR = 125 – 46.5 = 78.5,but the minimum is 95 so the lower whisker ends with 95.

3rd Quartile + 1.5* IQR = 156 + 46.5 = 202.5; 1st value below =195

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Next Tuesday Only!

Meet in Humanities and Social Sciences, HSSB, 1203 web: www.lsit.ucsb.edu• Exploratory data analysis using JMP