# [POL242Y5] - Midterm Exam Guide - Comprehensive Notes for the exam (22 pages long!)

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POL242Y5
MIDTERM EXAM
STUDY GUIDE
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Pol242 January 9, 2017 Multiple Regression
Multiple Regression
Just regression with more variables!
o Instead of one independent variable, two or more
Age causes income
But lots of things causes income; age, education, gender,
immigrant status we are looking at it at the same time
Instead of line have plan going through it different
dimensions
Interpreting Multiple Regression
Multiple slopes, one intercept
o Each has own p-value, confidence interval
Useful for controlling for other variables
Adjusted r squared (hoe closely the dots fit the line)
o If you add more variables the r squared goes up even
if it does not make sense so do not use r squared for
multiple regression
Calculate predicted value of Y by setting a value of all the
variables (Xs)
o Pick a spot on the line if x is this y is going to be…
Bivariate: if X is one higher, Y increases by (coefficient)
Multivariate: If X1, is one unit higher, and other Xs are the
same, Y increases by (coefficient)
The regression coefficient (slope) is the change in Y for a
one unit change in X holding the other variables constant
o For each one unit increase in IV, holding everything
else constant, what is increase in DV?
o For one year older, if education stays the same, what
is the increase in income?
Example
Hypothesis: Older people earn more money than younger
people
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Theory: Older people get paid more BECAUSE their
bosses respect them more, and they get taken more
seriously
Pull apart age and experience
Interpreting Multiple Regression
Y=bX+a Income=Age + intercept
Y=2X+20 One unit increase in Age means
two unit increase in Income
Y=b1X1+b2X2+a Income= Experience +Age+
intercept
Y=1Xx+3X2+5 b1: one unit increase in Age means
a one unit increase in
Income…HOLDING Age THE SAME
b2: One unit increase in Experience
means a three unit increase in
Income…HOLDING Age THE SAME
Slope: If x changes by 1 unit y changes by for example y=2xt20
so increases by 2,
What is a one unit change?
Dependent variable has to be interval
Binary Variables
Only two possibilities
Binary variables are either 0 or 1
Can be nominal
Only for IV, not DV!!
Vote/not vote
Student/not student
Male/female
Always one unit increase for binary
Better to have ordinal do not turn it into a binary (need
more or less of it)
Regression with a binary variable
Y=bX+a Test Mark = Hours studying + intercept
Y=3X+40 One unit increase in studying means a 3
unit increase in Test Mark
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