crj 604 introduction - arizona state university linear regression (next week) 3. multiple regression...

CRJ 604 Introduction

Do babies delay crawling

when it’s cold outside?

Here’s the raw data for 12 birth-month groups of babies:

Temperature in 6th month Average crawling month

66 6.86

73 7.02

72 6.84

63 7.32

52 6.58

39 7.23

33 7.73

30 7.55

33 7.78

37 7.69

48 7.69

57 7.53

Do babies delay crawling

when it’s cold outside?

Do babies delay crawling

when it’s cold outside?

6.5

77

.58

cra

wl

30 40 50 60 70temp6

“scatter crawl temp6” produces this graph

Do babies delay crawling

when it’s cold outside?

“twoway (scatter crawl temp6) (lfit crawl temp6)” adds a line of “best fit”

6.5

77

.58

30 40 50 60 70temp6

crawl Fitted values

Do babies delay crawling

when it’s cold outside?

-This line of best fit is what linear regression does. It represents our best estimate of

the relationship between our two variables.

- To obtain a quantification of this line in stata: “reg crawl temp6”

Do babies delay crawling

when it’s cold outside?

This regression produces the following relationship between

temperature and crawling month:

-Month start crawling = 8.21-.0177*(avg. temperature)

-So a 1 point decrease in temperature is associated with babies

delaying crawling .018 months (about half a day).

- With a 10 point increase in temp, baby should crawl 5 days

earlier.

-Phoenix babies must be super fast crawlers . . .

Goals

From the syllabus:

1. Students will understand the theoretical issues involved in the basic linear regression model in its simplest form (bivariate regression) and multivariate form (multiple regression).

2. Students will also acquire fluency with the computer application (using Stata) of bivariate and multivariate regressions and probit/logit models, including testing assumptions and applying fixes.

Plan for course

1. Overview of course (today)

2. Simple linear regression (next week)

3. Multiple regression

4. Violations of regression assumptions

5. Limited dependent variables

6. Propensity score matching

Textbook: Wooldridge’s

Introductory Econometrics

“Econometrics” is simply the

term economists use for

statistics.

- Crime examples used in

book. I/we will

supplement these with

more examples.

- Data sets / solutions to

odd-numbered exercises

are online

Online resources, this course

All course documents will be located at the following address:

http://www.public.asu.edu/~gasweete/crj604/

This includes the syllabus, lecture slides, datasets for the exercises, and solutions to odd-numbered exercises.

Statistical package

All analysis for this class should be

done using Stata!

- Stata is installed in this classroom

- Outside of the classroom, you will

have to access Stata via Saguaro

- The details of this access are

forthcoming.

The best place to learn Stata:

http://www.ats.ucla.edu/stat/stata/

A quick introduction:

http://data.princeton.edu/stata/

What I use:

Online resources, Stata

Computer exercise C1.1

Research questions

You will come to understand statistical approaches

to answering questions like these:

Is a particular rehabilitation program effective in

reducing recidivism?

Does gang membership increase crime?

Does juvenile arrest affect high school dropout?

Does inequality increase crime rates?

Types of Data

Your approach to answering research questions is

constricted by the data to which you have

access.

Nonexperimental data: naturally occurring,

preferably collected in a systematic manner

Experimental data: random assignment of cases

to two or more conditions.

Theory

Barring data restrictions, the way you

approach research questions is guided

by criminological theory.

E.g. Social control, strain, differential

association, social disorganization

These theories point to constructs that

account for crime.

For statistical analysis, we create variables

that are supposed to represent theoretical

constructs.

Becker’s model of crime, in theory

Becker’s model of crime, in practice

Causality

Criminologists are often concerned with the causal effect of one variable on another.

Ceteris paribus, meaning “all else equal,” is essential for causal analysis. It’s also difficult to impossible to achieve.

Example: Law enforcement and crime

Causality

Recall: Month start crawling = 8.21-

.0177*(avg. temperature)

Is it reasonable to assume that we have captured a causal relationship between temperature and crawling age?

What else might be correlated with crawling age and temperature?

Next time:

Homework: Problems 1.2, C1.2, C1.4

Note: If I cannot provide access to Stata by

Friday, C1.2 and C1.4 will be done as an

in-class exercise next week.

Read: Wooldridge Chapters 1 & 2, and

appendices A through C if you haven’t

already.