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SOCY 211
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Lecture

# SOCY211 Week 10, Lecture 2

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Queen's University

Sociology

SOCY 211

Carl Keane

Winter

Description

BIVARIATE REGRESSION
- Allows us to make predictions
- Ex. How much extra do you expect to earn by spending an extra year in the
education system
- LINEAR REGRESSION LINE/LEAST SQUARES LINE
- When we look at a scatter graph you try to impose a straight line that fits the
pattern of the dots
o Called least squares line
- (OLS - Ordinary Least Squares regression)
- The Least Squares Line is the line that minimizes the sum of the squared distances
between the line and the dependent variable score of each case.
- Goal is to predict as accurately as possible
- The distance is sometimes called the error or the residual
- Regression Equation: Y = a + b (x)
- Y = Dependent variable score that we want to predict
- a = the value of Y where the regression line crosses the Y-axis. i.e. the value of Y
when x is zero. (This is called Y Intercept or the constant.)
- b = the change in the dependent variable (Y), for every one-unit change in the
Independent Variable (X). (This is called the SLOPE, or sometimes the
STEEPNESS of the line.)
- x = the score on the Independent Variable
- Hypothetical regression equation for Education (X) and Income (Y)
a b
Y = $5,000 + $1,000 (x)
- a (Intercept) = $5,000 - this means that even with no education you will earn
something ($5,000)
- b = $1,000 - this means that, on average, every additional year in school will
result in an additional $1,000 in income
- x = Independent Variable score - this is the score we “plug” in. So, for example,
we can predict that someone with 10 years of education will earn:
Y = $5,000 + $1,000 (10)
Thus: Y = $5,000 + $10,000
Thus: Y = $15,000
*You should always look at the scattered graph
- regression line is the best predictor in general
- you can break it up into samples of males and samples of females
o suggest that the line is steeper for males than for females
- there may be a possibility of earnings discrimination
- similarly it can also be broken down into subgroups of whites and non whites
1 a b
Males $5,000

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