Summary of hypothesis tests for testing slopes

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Summary of hypothesis tests for testing slopes
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Example

• Measured mean arterial blood pressure (BP) of 20
  individuals with hypertension.
• Also, measured four possible predictor variables
• age (X1)
• weight (X2)
• body surface area (X3)
• duration of hypertension (X4)

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The regression equation is BP - 12.9 0.683
Age 0.897 Weight 4.86 BSA
0.0665 Duration Predictor Coef SE
Coef T P Constant -12.852
2.648 -4.85 0.000 Age
0.68335 0.04490 15.22 0.000 Weight
0.89701 0.04818 18.62 0.000 BSA
4.860 1.492 3.26
0.005 Duration 0.06653 0.04895
1.36 0.194 Analysis of Variance Source
DF SS MS F P Regression
4 557.28 139.32 768.01 0.000 Error
15 2.72 0.18 Total 19
560.00 Source DF Seq SS Age
1 243.27 Weight 1 311.91 BSA
1 1.77 Duration 1 0.34
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Testing all slope parameters are 0

• Use overall F-statistic and P-value reported in
  ANOVA table.

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Testing one slope parameter is 0.

• Can use t-test and reported P-value.
• Or, use partial F-statistic, obtained by dividing
  appropriate sequential sum of squares by MSE.
  Determine the P-value by comparing F-statistic to
  F distribution with 1 numerator d.f. and n-p
  denominator d.f.

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Testing a subset of slope parameters are 0

• Let s number of slope parameters testing.
• Use partial F-statistic, obtained by dividing the
  appropriate sequential mean square by MSE.
  Determine the P-value by comparing F-statistic to
  F distribution with s numerator d.f. and n-p
  denominator d.f.