false

Class Notes
(839,079)

Canada
(511,183)

Simon Fraser University
(12,459)

Criminology
(2,192)

CRIM 320
(64)

Patrick Lussier
(11)

Lecture

School

Simon Fraser University
Department

Criminology

Course Code

CRIM 320

Professor

Patrick Lussier

Description

Simple and Multiple Regression
Simple regression
Is it possible to predict a certain outcome (Y) with only one predictor (X)?
Simple regression
Research question:
o Is age a good predictor of the total number of crimes committed in
adulthood?
Research hypothesis:
o H1: older offenders have had more opportunities to offend and, therefore,
have committed more crimes in adulthood
Null hypothesis
o H0: age is not related to the number of crimes committed by offenders in
adulthood
Simple regression
Equation:
o Y= a + b(x) + e
o Y=the predicted value for a given value of x (independent variable)
o X=the predictor, the variable expected to predict the value of y (dependent
variable)
o A=intercept or the mean value of y when x=0
o B=regression coefficient or the weight given to X in order to predict the
value of Y
The change in x associated with one-unit of change in Y
o E=residuals
Represents the prediction error or the gap between the predicted
value of Y and the actual value of Y
The regression line uses Y to best fit the data at each value of x: the ordinary least
squares regression…
Residual variance: “gap” between regression line and each Y
Regression variance/residual variance how well the regression line “explains” all
observations
The bigger the slope, the stronger the relationship
Multiple Regression
Multiple Regression
Improve the prediction of y by using multiple (several) independent variables (Xi)
Looking for the combination of weights for the IV (Xi) to get predicted values of
Y as close as possible from the actual values of YPurpose of multiple regression
How good is the prediction of the DV (Y) base don this set of predictors (Xi)?
Is there a significant relationship between the predictors (Xi) and the DV (Y)?
o What are the predictors of the criminological phenomenon
Is it possible to improve our ability to predict the value of the DV (Y) by adding
another IV (Xi)?
Is one set (block) of predictors better at predicting the value of the DV?
Multiple regression
Equation:
o Y=a + b1(x1) + b2(x2) + b3(x3) + b4(x4) + ……. + e
Different types of regression
Standard multiple regression
Hierarchical (sequential) regression
Statistical (stepwise) regression
Standard multiple regression
All the IVs are entered into the regression equation at once
Each IV evaluated in terms of what it adds to the prediction of the DV that is
different from the variance explained by all the other IVs
Determine the unique contribution (weight) of each variable in the prediction of
the dependent variable
The single best procedure to simply assess relationships among variables
Hierarchical (sequential) regression
IVs are “entered” into the equation in an order specified by the researcher or a
theory
Estimation of the variable’s (or group of variables) contribution over or above the
contribution of variables (or group of variables) already in the equation
Based on theoretical ground, a certain variable (or set of variables) may be given
priority as to the explained variance of the DV
Allow the researcher to control the advancement of the regression process
Statistical (stepwise) regression
The order of entry of variables is based only on statistical criteria
Minor differences in these statistics can have profound effect on the apparent
importance of an IV (e.g., which variable is entered first in the equation)
Typically used to develop a subset of IVs that is useful in predicting the DV, and
to eliminate those IVs not providing additional predicting value to those IVs
already in the equation
Model-building rather than model-testing procedure (exploratory purpose)
Least interesting of the three approaches General Considerations
A rough guide to multiple regression
Selection of ID variables (intevcal/ratio, dichotomous) and DV (interval/ratio)
Descriptive analysis (univariate outliers, skewness)
Analysis of the correlation matrix
Selection of method (enter, block, stepwise)
Regression
Look for multicollinearity (level of tolerance)
Distribution of multivariate outliers
Analysis and interpretation
Variables
Theory should guide the selection of variables
Linear relationship between IVs and DV
Only one dependent variable
DV data should be interval/ratio
IVs data should be interval/ratio/dichotomous
Sample size
Standard regression and hierarchical regression, a minimum of 20 cases per
variables used
Stepwise regression, a minimum of 40 variables per cases
More cases required when the effect size is small, the DV is nor normally
distributed, or measurement error is high
Multicollinearity
Regression will be best when each IV is strongly correlated with the DV but
uncorrelated with other IVs
OLS regression inspects for unique variance accounted by each IV
If two IV share the same “variance,” nothing unique about those will be captured
by the analysis
o Inspection of tolerance level in SPSS output
o Tolerance varies from 0-1.00
o Value close to 0 indicate a problem of multicollinearity
o A problem when getting closer to .30 (or lower) SPSS examples
The 2d:4d ratio
A proxy measure of prenatal exposure to testosterone
Low ratio linked to “masculinisation” of the brain
Research suggests that LOW ratio is predictive of emoti

More
Less
Unlock Document

Related notes for CRIM 320

Only pages 1 and half of page 2 are available for preview. Some parts have been intentionally blurred.

Unlock DocumentJoin OneClass

Access over 10 million pages of study

documents for 1.3 million courses.

Sign up

Join to view

Continue

Continue
OR

By registering, I agree to the
Terms
and
Privacy Policies

Already have an account?
Log in

Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.