STAT 501 HW 4 - Statistics 501 Homework 4 Answers Fall 07 1 a For each of these variables the p-value is small for testing that the population beta

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Unformatted text preview: Statistics 501 Homework 4 Answers Fall 07 1. a. For each of these variables, the p-value 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 x-variables 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 x-variables (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. p-value = 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.

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STAT 501 HW 4 - Statistics 501 Homework 4 Answers Fall 07 1 a For each of these variables the p-value is small for testing that the population beta

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