Correlation and Regression

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Correlation and Regression

• Its the Last Lecture Hooray!

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Correlation

• Analyze ? Correlate ? Bivariate
• Click over variables you wish to correlate
• Options ? Can select descriptives and pairwise
  vs. listwise deletion
• Pairwise deletion only cases with data for all
  variables are included (default)
• Listwise deletion - only cases with data for both
  variables are included

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Correlation

• Assumptions
• Linear relationship between variables
• Inspect scatterplot
• Normality
• Shapiro-Wilks W
• Other issues
• Range restriction Heterogenous subgroups
• Identified methodologically
• Outliers
• Inspect scatterplot

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Correlation

• Partial Correlation removes variance from a 3rd
  variable, like ANCOVA
• Analyze ? Correlate ? Partial

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Regression

• Analyze ? Regression ? Linear
• Use if both predictor(s) and criterion variables
  are continuous
• Dependent Criterion
• Independent Predictor(s)
• Statistics
• Regression Coefficients (b ß)
• Estimates
• Confidence intervals
• Covariance matrix

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Regression

• Statistics
• Model fit
• R square change
• Descriptives
• Part and partial correlations
• Collinearity diagnostics
• Recall that you dont want your predictors to be
  too highly related to one another
• Collinearity/Mulitcollinearity when predictors
  are too highly correlated with one another
• Eigenvalues of the scaled and uncentered
  cross-products matrix, condition indices, and
  variance-decomposition proportions are displayed
  along with variance inflation factors (VIF) and
  tolerances for individual predictors
• Tolerances should be gt .2 VIF should be lt 4

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Regression

• Statistics
• Residuals
• Durbin-Watson
• Tests correlation among residuals (i.e.
  autocorrelation) - significant correlation
  implies nonindependent data
• Clicking on this will also display a histogram of
  residuals, a normal probability plot of
  residuals, and the case numbers and standardized
  residuals for the 10 cases with the largest
  standardized residuals
• Casewise diagnostics
• Identifies outliers according to pre-specified
  criteria

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Regression

• Plots
• Plot standardized residuals (ZRESID) on y-axis
  and standardized predicted values (ZPRED) on
  x-axis
• Check Normal probability plot under
  Standardized Residual Plots

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Regression

• Assumptions
• Observations are independent
• Linearity of Regression
• Look for residuals that get larger at extreme
  values, i.e. if residual are normally distributed
• Save unstandardized residuals
• Click Save ? Under Residuals click
  Unstandardized when you run your regression,
• Run a Shapiro-Wilks W test on this variable
  (RES_1)

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Regression

• Normality in Arrays
• Examine normal probability plot of the residuals,
  residuals should resemble normal distribution
  curve
• BAD GOOD

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Regression

• Homogeneity of Variance in Arrays
• Look for residuals getting more spread out as a
  function of predicted value i.e. cone shaped
  patter in plot of standardized residuals vs.
  standardized predicted values
• BAD GOOD

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Regression Output
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Regression Output
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Regression Output
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Logistic Regression

• Analyze ? Regression ? Binary Logistic
• Use if criterion is dichotomous no assumptions
  about predictor(s)
• Use Multinomial Logistic if criterion
  polychotomous (3 groups)
• Dont worry about that though

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Logistic Regression

• Assumptions
• Observations are independent
• Criterion is dichotomous
• No stats needed to show either one of these
• Important issues
• Outliers
• Save ? Influence ? Check Cooks and Leverage
  values
• Cooks statistic outlier any variable gt
  4/(n-k-1), where n of cases k of
  predictors
• Leverage values outlier anything gt .5

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Logistic Regression

• Multicollinearity
• Tolerance and/or VIF statistics arent easily
  obtained with SPSS, so youll just have to let
  this one go ?
• Options
• Classification plots
• Table of actual of Ss in each criterion group
  vs. predicted group membership Shows, in
  detail, how well regression predicted data

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Logistic Regression

• Options
• Hosmer-Lemeshow goodness-of-fit
• More robust than traditional ?2 goodness-of-fit
  statistic, particularly for models with
  continuous covariates and small sample sizes
• Casewise listing of residuals
• Helps ID cases with large residuals (outliers)

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Logistic Regression

• Options
• Correlations of estimates
• Just what it sounds like, correlations among
  predictors
• Iteration history
• CI for exp(B)
• Provides confidence intervals for standardized
  logistic regression coefficient
• Categorical
• If any predictors are discrete, they must be
  identified here, as well as which group is the
  reference group (identified as 0 vs. 1)

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Logistic Regression Output
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Logistic Regression Output
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Logistic Regression Output
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Logistic Regression Output
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Logistic Regression Output
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Logistic Regression Output

• Step number 1
• Observed Groups and Predicted
  Probabilities
• 32 ô
  ô
• ó
  ó
• ó
  ó
• F ó
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• R 24 ô
  ô
• E ó
  N ó
• Q ó
  N ó
• U ó
  NN ó
• E 16 ô
  NNNN ô
• N ó
  NNNN ó
• C ó
  NNNN ó
• Y ó
  N NNNN ó
• 8 ô
  NNNNNN ô
• ó
  N NNNNNN ó
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  N NN NNANNNN ó