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Summary of hypothesis tests for testing slopes

This summary delves into hypothesis testing for regression slopes in predicting mean arterial blood pressure (BP) among 20 individuals with hypertension. Key predictor variables include age, weight, body surface area (BSA), and duration of hypertension. The regression equation illustrates the contributions of these variables to BP. It discusses hypothesis testing using overall F-statistics, t-tests, and evaluates the significance of individual and subsets of slope parameters through ANOVA. Results indicate the importance of age, weight, and BSA, highlighting their impact on BP.

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Summary of hypothesis tests for testing slopes

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  1. Summary of hypothesis tests for testing slopes

  2. 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)

  3. 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

  4. Testing all slope parameters are 0 • Use overall F-statistic and P-value reported in ANOVA table.

  5. 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.

  6. 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.

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