This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: PSTAT 120C: Practice Midterm Solutions May 3, 2006 1. One of the main facts that we have learned is that the residuals are uncorrelated with the parameters in the model and thus the fitted values. Cov( e i , y i ) = 0 = Cov( y i y i , y i ) = 0 = Cov( y i , y i ) Cov( y i , y i ) = 0 . This implies that Cov( y i , y i ) = Var( y i ) = 2 1 n + ( x i x ) 2 n i =1 ( x i x ) 2 from the variance we use in calculating the confidence interval. 2. (a) 1 = n i =1 ( x i x )( y i y ) n i =1 ( x i x ) 2 = 365(5 . 67) 364(100) = 0 . 0569 = y 1 x = 2 15(0 . 0569) = 1 . 147 Thus the linear model is wave height = 1 . 147 + 0 . 0569(wind speed) (b) The variance of the residuals is s 2 e = n 1 n 2 ( s 2 wave 2 1 s 2 wind ) = 364 363 ( . 81 (0 . 0569) 2 (100) ) = 0 . 488 (c) The appropriate t statistic is t = 1 s/ p ( n 1) s 2 wind = . 0569 p . 488 / 36400 = 15 . 546 which means there is a significant relationship. (15which means there is a significant relationship....
View
Full
Document
This note was uploaded on 04/09/2008 for the course PSTAT 120c taught by Professor Idk during the Spring '07 term at UCSB.
 Spring '07
 idk

Click to edit the document details