STA 3024 Introduction to Statistical 2

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STA 3024Introduction to Statistical 2

• Chapter 12
• Simple Linear Regression

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Examples in Regression from Chapter 3

• GDP (K) and internet use ( population) by
  country (p.105)
• GDP (K) and CO2 emission (metric tons) by
  country (p.112)
• Car weight (lb) and gas mileage (MPG) (p.106)
• Sit up numbers and 40-yard dash speed (sec) of
  female athletes (p. 125)

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The Model
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Correlation (r) and slope (b)
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The Graph
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A Simple Example

• The graph

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The Fit
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The Fitted Straight Line
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SPSS Output (For input see Basic SPSS in the
class website)

• Model Summary (partial)

ANOVA
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Coefficients

• Residual statistics
• Including mean and standard deviation information
  on prediction and residuals
• On way to do residual analysis is to output the
  residuals with save option and plot them.

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Inference on the slope ?
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Good Model?
ANOVA Table 12.8 will be discussed in the next
chapter.
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Possible Patterns in Residuals (p.665)
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Prediction (Middle box p.622)
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Regression toward the Mean (p.600)

• Example. During the screening, we picked a group
  of people with high blood pressure. Then their
  blood pressures tends to be lower when they are
  measured next week, even without treatment.
• Reason If consider the measure during the
  screening as x and the measure next week as y for
  the same person. Then the pair (x, y) will be
  highly corrected when plotted.

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Standardized Residual (p.616)

• It can be seen the discrepancy between the real
  line and the estimate line varies at different
  point of x. Thus the residual accuracy also
  changes with x.

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Caution in Correlation (slope) Interpretation

• Outlier effect
• Stratification effect (Simpsons paradox,
  Exercise 3.58, Murder trials in Florida,
  1976-1987, p.144)

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Stratified data
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Simpsons paradox in regression (Ecological
fallacy, p. 606)
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12.5 Linearize a Nonlinear Model