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Unformatted text preview: Statistics 501 Homework 4 Answers Fall 07 1. a. For each of these variables, the pvalue is small for testing that the population beta = 0. In each case, we have statistical significance and conclude that, within this model, the true beta is not 0. b. The null is that all coefficients multiplying xvariables have the value 0. The alternative is that at least one of these coefficients is not 0. These can be written as : H 4 3 2 1 o = = = = versus H a : At least one of 4 3 2 1 , , , is not 0. c. 42 . 380 . 201 588 . 84 SSTO SSR SSTO SSE SSTO R 2 = = = = . The four xvariables (or, the model) explain 42% of the observed variation in hospital infection risks. d. Here, n = 113 and p = 5 (parameters = the four slopes and the intercept) Total df = n 1 = 113 1 = 112 Regression df = p 1 = 5 1 = 4 Error df = n p = 113 5 = 108 Alternatively, one or these might be calculated using df Total = df Regression + df error e. adjusted R2= = 1 113 38 . 201 5 113 791 . 116 1 113 38 . 201 399 . 798 . 1 081 . 1 798 . 1  , or 39.9% 2. a. Source DF SS MS F Regression 6 1 = 5 1300 960 = 340 340 / 5 = 68 68/16 = 4.25 Error 66 6 = 60 960 960/ 60 = 16 Total 66 1= 65 1300 b. pvalue = FDIST(4.25, 5,60) = 0.00225.. If we use the standard .05 significance level, we reject the null hypothesis : H 5 4 3 2...
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This homework help was uploaded on 03/19/2008 for the course STAT 501 taught by Professor Heckard,robertf during the Fall '07 term at Pennsylvania State University, University Park.
 Fall '07
 HECKARD,ROBERTF
 Statistics

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