PRINCIPLES OF MULTIPLE REGRESSION

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PRINCIPLES OF MULTIPLE REGRESSION
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ON RESEARCH PROJECTS

• Papers due at Week 10 section meeting
• Hard copy only (4-6 pages tables, graphs)
• See handout on course website
• Lateness policy
• 5 off for 24 hours lateness
• 10 off for 48 hours lateness
• 20 off for 72 hours lateness
• NOT ACCEPTED after 72 hours
• If completed over weekend, send electronic copy
  to TA and submit a hard copy on Monday, June 2

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Postscripts

• Calculating intercept a
• a Y b X (note b positive or negative)
• Defining t-ratio or t statistic
• t (b ß)/SE, where b is sample slope and ß is
  population parameter
• In null hypothesis, ß 0, thus
• t b/SE, and
• If t gt 2, can reject the null hypothesis

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READINGS

• Pollock, Essentials, ch. 7 (pp. 165-176)
• Pollock, SPSS Companion, ch. 9
• Course Reader, Selections 5-6 (Smith Ziegler,
  Governmental Performance, and Inglehart, Mass
  Support for Democracy)

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OUTLINE

• Purposes of Multiple Regression
• The Basic Model
• Key Concepts
• An Illustration

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• Purposes of Multiple Regression
• Incorporating more than one independent variable
  into
• the explanation of a dependent variable
• Measuring the cumulative impact of independent
  variables
• on a dependent variable
• Determining the relative importance of
  independent
• variables

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The Basic Model Y a b1X1 b2X2 b3X3 .
bkXk Note Signs can be positive or
negative! PRE R2 Standardized regression
coefficient (beta) bi (st.dev.Xi/st.dev
Y) Partial correlation coefficient rYX2.X1,
or r13.2
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Key Concepts Measuring the cumulative impact on
Y of X1 and X2 (via PRE or R2) Examining
relationship between Y and X2, controlling for
the effects of X1 (via partial correlation
coefficient) Detecting the identifiable impact
of independent variables (Xs) on Y (via beta
weights) Assessing significance of overall
relationship and of individual regression
coefficients (via significance tests, including
standard errors)
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Visualizing a Plane of Least Squares
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Detecting Relationships

• Spurious relationship between Y and X1 vanishes
  (i.e., approaches zero) with X2 in equation
  check correlation between X1 and X2
• Enhancement cumulative strength of relationship
  (R2) much higher with X1 and X2 in equation than
  with just X1
• Specification see use of dummy variables next
  time

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An Illustration of the Principles Problem
Effects of public health expenditures Y
infant mortality rate X1 health
expenditures X2 nonwhite population
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Since a Y bX Y 0 (as mean value of
residuals) X 0 (as mean value of
residuals) the value of a for this equation
0 so there is no intercept.
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