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Lecture

# march 26.docx

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University of Saskatchewan

Sociology

SOC 325

Elizabeth Quinlan

Winter

Description

Soc 325
March 26
1
Last two days of our class will be review
Chapter 14 Multiple Regression
• Multivariate analysis
1. Partial correlation
Further insight into a bivariate relationship, a 3rd variable
2. Multiple regression
For the most part interval-ratio variables
Assess the effects of two or more independent variables on the
dependent variable
Expand the number of independent variables but there will always
only ever be one dependent variable
An extension of the linear (bivariate) regression
Multiple regression allows us to
Use more than one independent variable to predict y
Disentangle and examine the separate effects of the independent
variables
We will have a couple of different kinds of B's
Assess the combined effects of the independent variables on Y
Least-squares multiple regression equation
Y = a + b 1 1 b X2 2
For every independent variable you will have a different b
Where, b = the partial slope of the first independent variable on y (formula
14.4)
b = the partial slop of the second independent variable on y
2
(formula 14.5)
a =
The partial slope: shows the effects of each independent variable
on Y while controlling for the effect of the other independent variables
The numerical values of b's indicate the amount of change
in Y for each unite of change in one independent variable while controlling for
the other
Example:
Previously we considered the relationship between the number of
children (x) and husbands contribution of housework (y) for 12 dual-earner
families
Here we will assess the effects of two independent
variables on husbands contribution to housework: number of children (x1)
and SES (measured by the years of education completed by the husband)
(x2)
The partial slope for the first independent variable X1 is
A slope of .65 means that the amount of time the husband
contributes to housekeeping chores increases by .65 hours per week for each
additional child in the family, controlling for the effects of Socio Economic
Status Soc 325
March 26
2
R y1sbands contribution to housework is positively
related to number of children (.50)
R y2sbands in higher ses tend to do less housework
(-.30)
R 12gher ses families tend to have fewer children (-.47)
The partial slope for the second independent variable x2 is
A slope of -.07 means that the amount of time the
husbands contributes to housekeeping chores decreases by .07 hours for
each child
Means calculated by SPSS
Y = 3.3
X1 = 2.7
X2 = 13.7
Rearrange formula and solve for a
A = x - b1x1 - b2x2
= 3.3 - (.65)(2.7) - (-.07)(13.7)
= 3.3 - 1.8 - (-1)
= 3.3 - 1.8 + 1
= 2.5
And then the multiple regression equation:
y = a + b1x1 + b2x2
= 2.5 + (.65)x1 + (-.07)x2

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