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Regression Statistics

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cheryse jackson

on 5 December 2013

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Transcript of Regression Statistics

The Power of Prediction

Linear Regression In Action
Critical Research Points
What It All Means...
Beveridge, S., & Fabian, E. (2007) Vocational rehabilitation outcomes: Relationship
between individualized plan for employment goals and employment outcomes.
Rehabilitation Counseling Bulletin, 50(
4), 238-246.

Salkind, N. J. (2011).
Statistics for people who (think they) hate statistics.

Thousand Oaks, CA: Sage Publications, Inc.

Tabachnick, B. & Fidell, L. (1989).
Using multivariate statistics.
(2nd edition).
New York: HarperCollins

Rose Willis
Cheryse Jackson
Brittney Sears
Maristella Vismele
Charles Carter

Special Thanks To Our Very Own, Dr. Kri Watson

Given data on relationships between specific X (independent/predictor) variables and Y (dependent) variables, LINEAR REGRESSION allows for the prediction of an unknown Y based on a known X.
Selected Research Article:

Vocational Rehabilitation Outcomes:
Relationship between Individualized Plan for
Employment Goals and Employment Outcomes

Examine the relationship between attaining a job congruent with the Individualized Plan for Employment (IPE) vocational rehabilitation goal and vocational rehabilitation outcomes.

Purpose of the Study
Independent Variables:

Disability category
Job satisfaction
Dependent Variable:

Congruent employment
Sample Size:

171 vocational rehabilitation clients served by the Maryland
State Department of Education Division of Rehabilitation

Y= variable to predict
X= variable used to predict Y
a= the intercept
b= slope
Attempts to determine the strength of the relationship between one dependent variable (usually Y) and a series of other changing variables (known as independent variables).

Inferential Statistics:
• Regression analysis is used when
you want to predict a continuous dependent variable from a number of independent variables.
• Casual relationships among the variables cannot be determined. While the terminology is such that we say X "predicts" Y, we cannot say that X "causes" Y (Tabachnick & Fidell, 1989).

• Regression analysis is used with naturally-occurring variables, as
opposed to experimentally
manipulated variables.
Research Question

For those clients who obtained a successful employment outcome congruent with their vocational rehabilitation goal, did their weekly wages differ significantly from those of clients who did not obtain an outcome congruent with the vocational goal?

There is a positive relationship between weekly wages and obtaining an employment
outcome congruent to the
vocational rehabilitation goal.

Regression Process:
STEP 1: Make a scatter plot

STEP 2: Conduct a regression analysis to visually assess if there is a linear relationship between variables

STEP 3: Draw a regression line (diagonal) on scatter plot, noting degree of error

STEP 4: Interpret analysis

Y= variable to predict
X= variable used to predict Y
a= the intercept
b= slope

Independent Variables:
Dependent Variable:
DORS- Congruent Employment
*Table 3 identifies values of Y regressed variables (Beveride & Fabian, 2007).
Linear Regression:
Introduction to
Linear Regression

Conclusion Cont.
• The analysis showed that persons with a physical disability
earned higher weekly wages ($539.29) than participants with
sensory ($463.47) and mental disabilities ($352.75).
• The other independent variables in the weekly wages linear
regression model were not statistically significant; however,
race and gender did affect the participant’s weekly wages
(Beveridge & Fabian, 2007).
o In terms of:
 Race: Caucasians earned $470.65 a week, compared
to weekly earnings of $394.21 for African Americans.
 Gender: Men earned $452.43 a week, and
women earned $429.26.

• The purpose of the research question was to determine
whether obtaining a vocational rehabilitation employment outcome congruent with the vocational rehabilitation goal increased the participant’s weekly wages.
• The data shows a positive relationship between weekly
wages and obtaining an employment outcome congruent
with the vocational rehabilitation goal.
• Participants who obtained a congruent VR employment outcome earned a higher weekly wage than those not
• The education variable indicated, the more education
obtained increased the participant’s weekly wages. (Beveridge & Fabian, 2007)

• The independent variables used in regression can be either continuous
or dichotomous (Tabachnick & Fidell, 1989).
• Independent variables with more than two levels can also be used in regression analysis, but they first
must be converted into variables that have only two levels.
Analysis Cont.
Analysis Cont.
Table 5 identifies the impact of X predictor/IV (which is employment/wages) on Y/DV, which is congruent employment (Beveridge, S. & Fabian, 2001.
(Salkind, 2011).
Full transcript