A researcher would like to analyze the effect of muscle injury on the number of

Question

A researcher would like to analyze the effect of muscle injury on the number of physical therapy intervention programs received. She takes a random sample of 4 patients. For these 4 patients, she finds out how many times each had a muscle injury and how many physical therapy intervention programs they received. These data are presented in the table below: Patient Number of Muscle Injuries Number of Physical Therapy Programs Received 1 1 4 2 2 6 3 1 3 4 0 1 The results of the simple linear regression are provided below. Y= 1+2.5X; S subscript Y X end subscript = 0.5, S subscript b 1 end subscript = 0.35355; 2-tailed p value = 0.0192 (testing beta 1)

Explanation / Answer

Regression Analysis: Number of Physical Therapy Prog versus Number of Muscle Injuries

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 1 12.5000 12.5000 50.00 0.019
Number of Muscle Injuries 1 12.5000 12.5000 50.00 0.019
Error 2 0.5000 0.2500
Lack-of-Fit 1 0.0000 0.0000 0.00 1.000
Pure Error 1 0.5000 0.5000
Total 3 13.0000

Model Summary

S R-sq R-sq(adj) R-sq(pred)
0.5 96.15% 94.23% 93.16%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant 1.000 0.433 2.31 0.147
Number of Muscle Injuries 2.500 0.354 7.07 0.019 1.00

Regression Equation

Number of Physical Therapy Prog = 1.000 + 2.500 Number of Muscle Injuries

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