econ1203 lecture 1 notes

5/27/2018 Econ1203 Lecture 1 Notes

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Statistics


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Week 1 topics

Administrative details

Descri tive statistics Frequency distributions & histograms

Shapes of distributions

Describing bivariate relations

Key references Course outline Keller Chs 1-3

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Administrative details: Staff

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Administrative details:

Teaching & Learning

Keller 9th ed. provides detail

& basic reference material Lectures provide

Overview

Some worked examples

Tutorials rovide

Review & discussion

opportunities Learning cycle

Preview participate

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Administrative details: What

youre expected to know

BES will utilize prior knowledge from high school

mathematics Basic algebra

Basic calculus

Basic probability

mathematics instruction in BES

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Assessment

Online quizzes designedAssessmentComponent

Percentageof total

Weeks 3,6, & 12

In-tutorial test

mark

Feedbackquizzes

6

Week 8 EXCEL important but no

direct com utin mark

In-tutorialtest

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Project 20

Some tutorial problemshave computing part

Ma or ro ect re uires

Final

examination

60

EXCEL

Weekly tutorials (Weeks-

Total 100

6

Final examination


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Lectures

Lecture notes will be sparse Lecture discussion will be

more expansive

Worked eg on frequency

distributions There should be benefit in

attending lectures Use textbook to fill any So its robabl a ood idea to

rema n ng gaps Textbook provides

extensive referenceprint out the lecture slides so youcan fill in the answers as they

Worked examples in lectureswill appear with space for ananswer

.

Statistics in action (SIA) willuse real case studies

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Administrative details: Why

BES?

Its a Faculty requirement!

BES covers basic statistics a s cs = co ec ng, ana yz ng n erpre ng a a

Statistical information & analysis is pervasive in

Provides skills for real-world decision making Provides foundation for all 2nd year econometrics subjects n erp ns quan a ve ana ys s across a sc oo s

, ,finance, management & marketing students the sexy job in the next 10 years will be statisticians. And

8

m no ng. a ar an, e econom s oog e


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Administrative details: Statistical

& generic skills developed

By end of BES you should be able to

Identify appropriate statistical methods for describing data& making inferences about population parameters

Apply appropriate statistical methods to samples of data

Use statistical reasoning to aid in problem solving Use EXCEL to apply appropriate statistical methods

r e a as c us ness repor ocumen ng s a s caanalyses

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Statistics in action (SIA)

Case studies using real, contemporary data

Motivating examples in lectures Suggest prototype project problems

Examples may include Baby bonus Private health insurance

Petrol prices Migrant wealth Sydney housing prices

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SIA: Baby bonus

bonus in July 1, 2004

,

Analysis based on Gans & Leigh (2008)

If so by how much?

Data?

-Bureau of Statistics (ABS)

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SIA: Baby bonus

Heres (part of) the data

BUT need descri tivestatistics in order to

Summarize data

Facilitate interpretation Analyse the research

question

Extract information

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SIA: Baby bonus

1000

y

Panel A: Raw Data

Figure 1: The Introduction Effect

600

800

Numberofbirthsperda

4

00

June3

June10

June17

June24

July1

July7

July14

July21

July28

Panel B: Controlling for Day-of-Week Effects

600

700

800

90

erof

birthsperday

400

500

Numb

June3

June10

June17

June24

July1

July7

July14

July21

July28

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1975-2003 2004


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SIA: Baby bonus

What are the key

features of these data?

-newborns per dayvariable

-Data are observed in time(time series data)

Statistical concepts? Population

Parameter

Statistic

Statistical inference

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Statistical concepts

A population consists of all subjects that are studied.

A parameteris a numerical measure of population.- Note: parameters are often unknown

A sample is a subset of the population that is being

studied.A statistic is a numerical measure that describes acharacteristic of a sample.

Inferential statistics uses the information from asamp e to raw conc us ons a out t e popu at on.

Or, inferential statistics computes/uses a statistic to infera ou a parame er o e popu a on.

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Statistical concepts

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Worked example: diabetes

data

The data set consists of observations on 442 patients

about their 4 variables: a quantitative measure ofdisease progression, height, weight and gender.

What is the population?

What is the sample? The average height of all diabetes patients is a

parameter (unknown)

The average height of all patients in the data set is astatistic (known)

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Types of data A variable is a characteristic of a population or of a sample from

a population We observe values or observations of a variable A data set contains observations on variables

Variables may be

Discrete example - football scores, number of newborns per day Continuous example - time remaining in football game, height, weight

Scores, time, height, weight are quantitative Gender, colour are qualitative

Quantitative is also referred to as interval or numerical.Qualitative is also referred to as nominal or categorical.

Ordinal data are qualitative but there is an ordering This course is oor ood ver ood

18 Standard & Poors ratings AAA > AAA- > AA+ > AA


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Types of data

Type of observation can also be used to classify data

Time series data refer to measurements at different points in

Eg: SIA Baby bonus births per day

Cross sectional data are measurements at single point in time g: y ney ous ng pr ces y su ur , a e es a a

Data type can influence what is appropriate by way of analysis Total number of births per day makes sense

Suppose marital status is coded as Single =1, Married =2,Divorced =3, Widowed=4; Does it make sense to total the marital status of a sam le of

individuals?

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Descriptive statistics

Difficult to determine key features of data

Need to organize & summarize data in order to extractn orma on

This is role of descriptive statistics

Note: descriptive statistics is about organizing and summarizingdata while inferential statistics is for inferring about the populationparame ers

There is a vast range of tools & techniques ,

Type of data may impact on which to use

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Frequency distributions (for

categorical data)

Want to summarize categoricaldata with associated counts

Mode oftransport to

campus

Frequency RelativeFrequency

variable along with the numberof observations for each value

Resident

Walk

UNSW interested in transportissues

How do eo le travel to

Cycle

Carcampus?(http://www.facilities.unsw.edu.

au/ ettin -uni

Bus

Other Categories need to be mutually

exclusive & exhaustiveTotal 100

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Bar charts & pie charts

Provide graphical

representation offrequency distributions

2011 UNSW Travel 25003000

BarchartofmodeoftransporttoUNSWcampus

urvey samp e o 47 (0.8%) Resident 1500

2000

.

210 (3.6%) Bike

1032 (17.5%) Car 0

500

1188 (20.2%) Bus

2776 (47.2%) Other

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Bar charts & pie charts

Pie charts show relative

frequencies

Resident

1% Walk

11%

Bike

4%

PiechartofmodeoftransporttoUNSWcampus

Whats in the Other

Car17%

Other

47%

category?

Bus20%

Resident

ModifiedpiechartofmodeoftransporttoUNSWcampus

to summarize

uantitative data?

1% Walk

11%

Bike

4%

CarBus&train17%

BusOther

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20%2%


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Fre uenc distributions for

quantitative data)

table that

with the corresponding frequencies

Each interval has the same width determined by

width =(largest value-smallest value)/(number of classes) The intervals need to be mutually exclusive &

exhaustive

How many classes? (EXCEL calls them bins)

Too few no information No set rules althou h more observations more classes Usually at least 5 and no more than 15

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Worked example: Keller Ex

3.3: Business Statistics Marks65 81 72 59

71 53 85 66

66 70 72 71

Lets use 5 classes

=79 76 77 68

65 73 64 72

82 73 77 75

Frequency distribution?

80 85 89 7486 83 87 77

64 67 79 60

62 78 59 92

67 67 84 69

72 62 74 73

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Histograms A graph of a frequency distribution (for numerical data) is

called a histogram The horizontal axis shows the class limits or class mid oints The vertical axis shows frequencies

uss e ar s s ogram

30

35

y

5

10

15

20

Frequenc

0

49 64 74 84 100

Marks

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Histograms

Beware of EXCEL

features Histogram for Example 2.6

incorrect

Should be no gapsbetween bars for 25

30

Classes defined by upper-

10

15

Freque

ncy

points may be morenatural

0

50 60 70 80 90 More

Bin

Bar areas should beproportional to

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,

p 265)


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Other distributions & displays

Can convert information in frequency distributions

into: Cumulative frequency or (cumulative) relative frequency

distributions

Aussie marks eg - How many students got a credit orbetter?

Stem-and-leafdisplays

Do examiners avoid marks close to borderline?

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Key features: Shapes of

histograms

Symmetry

Left half of histogram is a mirror image of right half Famous bell-shape is symmetric

Skewness symme r c s ogram

Long tail to the right (posit ively skewed)

May be associated with outliers

Number of modal classes Modal class is class with highest frequency

Histograms may be unimodal or multimodal, orno mode

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Key features: Shapes of

histograms

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A key feature: Shapes of

histograms .

Histogram of returns on

Modal class is

No. of modal classes?

Therefore histogram is

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Bivariate relations

Want to extend univariate analyses to

characterize relationshi s between variables Contingency table (Cross-tabulation table)

For relationship between qualitative variables

Scatter plots For relationship between quantitative variables, e.g. height

and weight

If one of the variables is time we get a time series plot (line

chart

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Mode of transport example:

Staff/student differences? Want to understand if there is

a relation between commuter

Commuter type

Mode Staff Student Total

Resident 0 47 47

Walk 97 531 628

What does the bar graphhighlight?

Cycle 52 158 210

Car 472 560 1032

Bus 186 1002 1188

Bus & train 230 2439 2669

Other 25 82 107

Total 1062 4819 5881

3000

Modeoftransportbycommutertype

Is there a better

representation? 1000

1500

2000

Frequency

0

500

Resident Walk Bike Car Bus Bus&train

Other

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Staff Students


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Scatter plots

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SIA: Cars in China

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SIA: Cars in China

What are the key


.

How does this graph rate

in terms ofcharacteristics forgraphical excellence?

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Time series plot

Bivariate relationship between variable Y &

With time series data order matters

growth or contraction

: a y onus

Relatively sophisticated time plot

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SIA: Petrol prices

160

180

Monthlyunleadedpetrolpricesforselectedcapitalcities

120

140

sperlitre)

60

80

100

rageprice

(cent

20

40Av

0

SYDNEY METRO BRISBANE METRO MELBOURNE METRO

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SIA: Petrol prices

What are the key


motorists about the

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SIA: Petrol prices

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SIA: Petrol prices Pattern representative of daily price movements in

Sydney in winter 2006

ons er a y a a une un ay - u y2006 Notable rice variation from da to da

Determine day of weekly peak and trough Common day for prices to peak was Thursday

o pea s or roug s on on ay, ues ay, r ay,Saturday or Sunday

Common day for prices to trough was Tuesday Consider longer period of daily data (not shown)

No troughs on Wednesday, Thursday, Friday or Saturday

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SIA: Petrol prices

Would bar or pie charts

be useful in displayingthe weekly peak &trough data?

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econ1203 lecture 1 notes

Documents

lectures lecture notes

bes55272018 econ1203

staff35272018 econ1203

lecture slides

sparse lecture discussion

basic statistics

baby bonus bonus

ana yz ng n erpre ng