1) A paper in a 1998 issue of American Journal of examined data r regarding the

Question

1) A paper in a 1998 issue of American Journal of examined data r regarding the l had on the number of days after arthroscopic shoulder their sport. Computer output for the regression is given below surgery before 10 weight lifters were able to return to p a) Use the computer output at the left to Predictor Constant Age Coef SE Coef -5.054 0.27150.1427 write an equation for the least squares regression line predicting time to return to lifting from an athlete's age. -1.16 1.90 0.279 0.094 4.355 S=1.23063 R-Sq = 31.161% R-Sq (adj) #22.55796 b) One 28 year-old weight lifter took 3 days to return to weight lifting. Find the length of time that would be predicted by the regression line and then calculate this weight lifter's residual. c) Interpret the meaning of the value of s in this context.

Explanation / Answer

a) From output we get intercept = a = -5.054, b = 0.2715

Hence the regression equation is given by

y = a + bx

y = -5.054 + 0.2715 x

b) Here age = x = 28, length of time =y = 3

Fitted value of y is given by

y = -5.054 + 0.2715 *28

= 2.55

Residual = observed value - fitted value

= 3 - 2.55

=0.45

c) The standard error s indicate average distance of observed value from fitted values. If s is small it indicates that obsrved values are closer to fitted values. And model good model of fit.

Here s indicate average distance of observed length of time from fitted value of length of time. Here s shows that how closser the y values are to the regression line. Here s value is smaller which indicate that obsvered values of y and fitted (expected values ) of y are closer.

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