Statistics 350 Lecture 19

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Statistics 350 Lecture 19
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Today

• Last Day R2 and Start Chapter 7
• Today Partial sums of squares and related tests

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Example

• Consider Example on page 257
• Y Percent Body Fat
• X1 Triceps Skinfold Thickness
• X2 Thigh Circumference
• X3 Midarm Circumference

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Example

• Suppose only consider first two explanatory
  variables
• Test hypothesis
• Ho ?10 (assuming X2 already in model)
• HA ?1?0 (assuming X2 already in model)
• Important lesson is that the presence or absence
  of X2 in the model may change depending upon
  which variables are in the model

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Extra Sum of Squares

• Some Notation
• SSR(X1)
• SSR(X1,X2)
• SSR(X1X2)

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Extra Sum of Squares

• Some Notation
• SSR(X1, X2 , X3)
• SSR(X3 X1 , X2)
• SSR(X2, X3 X1)
• And so on

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Extra Sum of Squares

• Decomposition

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Back to Example

• Look at the sums of squares for this problem

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Back to Example

• Why doesnt the regression sum of squares for the
  first two models not sum to that for the third?
• SSR(X1,X2) -SSR(X2) 3.47what is this difference
  and what does it mean?

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Back to Example

• What is SSR(X2,X1)
• In words
• SSR(X2 ,X3 X1)
• In words

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Back to Example

• Who cares?
• For example, Thigh Circumference (X2) and Midarm
  Circumference (X3) are easily measured with
  precision using an ordinary tape measure, but
  Triceps Skinfold Thickness (X1) requires a
  trained technician and an expensive instrument.
  Then a natural question is whether we even need
  to bother with X1 once we've already measured X2
  and X3?

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Back to Example

• Who cares?
• For example, Thigh Circumference (X2) and Midarm
  Circumference (X3) are easily measured with
  precision using an ordinary tape measure, but
  Triceps Skinfold Thickness (X1) requires a
  trained technician and an expensive instrument.
  Then a natural question is whether we even need
  to bother with X1 once we've already measured X2
  and X3?