EDF 5400

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EDF 5400

• Albert OosterhofJune 5 and 7, 2001

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3-dimensional scatter plots. Supplement 10
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3-dimensional scatter plots. Supplement 10
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Multiple regression.

• Y bX a
• Y b1X1 b2X2 a
• Y b1X1 b2X2 b3X3 a
• Multiple regression with SPSS...

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Back to bivariate correlation and regression...
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Correlations between...

• pretest and posttest?
• pretest and estimated posttest?
• pretest and residual?

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Explained and Unexplained Components of Variance
What variability in weight is explained versus
not explained by variability in height?
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Explained and Unexplained VarianceSupplement 10
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Proportion of Variance Explained and
Unexplainedr2 and 1-r2

• Questions
• On graph, what variance on Y is explained by
  variance on X ? What variance is unexplained?
• On the graph, where is standard error of estimate
  illustrated?
• On the graph, how can we describe the criterion
  of least squares?
• On the graph, what would we see if the
  correlation increased or decreased?

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Proportion of Variance Explained and
Unexplainedr2 and 1-r2

• Not only height and weight
• Study time and test scores (r .7)
• GRE scores and grades (r .4)
• Boat registrations and manatee kills (r .9)
• Heights of husbands and wives (r .6)

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The Bivariate Normal Distribution(Textbook, pp.
118-120)
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The Bivariate Normal Distribution(Textbook, pp.
118-120)

• Frequency is vertical axis

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The Bivariate Normal Distribution(Textbook, pp.
118-120)

• Frequency is vertical axis
• How shape on X and Y axes changes with magnitude
  of correlation

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Characteristics of Bivariate Normal Distribution

• Y scores normally distributed for any given X,
  and vice versa
• Relation between X and Y is linear (Y means for
  various values of X fall in a straight line, and
  vice versa)
• Homoscedasticity (SD of Y values equal for any
  given X, and vice versa)

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Spearman Rank-Order Correlation(Supplement, page
12)
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Spearman Rank-Order Correlation(Supplement, page
12)
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Spearman Rank-Order Correlation...(Supplement,
page 12)

• In contrast to product-moment correlation, is
  sensitive only to rank order
• Actually is a special case of product-moment
  correlation

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Correlation and Covariance(Textbook, p. 112)
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Correlation and Covariance(Textbook, p. 112)

• What is covariance
• Effect on covariance of standard deviation and
  correlation

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Correlation defined in terms of
Covariance(Textbook, p. 112)
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Using Deviation Score Notation(Textbook, p. 112)
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Example Using Covariance to Compute the
Correlation Coefficient(Supplement, page 12)
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Covariance later becomes important with variance
of totaled scores or difference scores
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What level of scaling is required with Pearson
product-moment correlation?
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What level of scaling is required with Pearson
product-moment correlation?

• Correlation has been defined in terms of
• z-scores
• standard deviation and covariance