Referring to the table, the prediction for the number of physical therapy progra

Question

Referring to the table, the prediction for the number of physical therapy programs for a person with 2 muscle injuries is: 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

y = 1 +2.5 *x

hence for every increase in 1 unit of muscle injury, the number of physical therapy is incread by 2.5

p-value of b1 = 0.019419 < 0.05

hence X is significant

the overall model is also significant as significance F = 0.019419 < 0.05

SUMMARY OUTPUT Regression Statistics Multiple R 0.980580676 R Square 0.961538462 Adjusted R Square 0.942307692 Standard Error 0.5 Observations 4 ANOVA df SS MS F Significance F Regression 1 12.5 12.5 50 0.019419 Residual 2 0.5 0.25 Total 3 13 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 1 0.433013 2.309401 0.147197 -0.8631 2.863103 -0.8631 2.863103 x 2.5 0.353553 7.071068 0.019419 0.978783 4.021217 0.978783 4.021217

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