Question

The department of health studied the number of patients who need liver transplantation. The following data are the Liver Transplantation Waiting List (LTWL), where y is the size (in number of patients) and x is the corresponding year: y | 1367 1934 31114179 5132 | 7181 80107916 8058 8708 8754 8863 9327 * 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Round your intermediate answers to four decimal places (e.g. 98.7654). (a) Fit the simple linear regression model using the method of least squares. Find the estimate of op. Round your answer to the nearest integer (e.g. 9876). (b) How does the LTWL size change in average for a year? Round your answer to the nearest integer (e.g. 9876). B = (c) Estimate the number of patients in the list in 2017. ỹ = (d) Calculate the fitted value of y corresponding to x = 2011. Find the corresponding residual. Round your answer to the nearest integer (e.g. 9876). Round your answer to the nearest integer (e.g. 9876).

Answer 1

prin tet, Fri 1 X = Year assie independent variable size (in noi of patients) jie dependent variable we know that, The fitted peast square regression line is, where in Boes estimate of y-intercept of regression line estimate of slope of regression line Br is Also, på = ý ßď and Bi= ssky 3 Ssac. where, ssay Ssx= I (xi-7² L ( xi - x) (1-7) e cvi-u? ssy = Here, n=13, l'aci= 26117 [yi = 82540 x Tai 2009 LÝ ř = Eyi .63 49.2308 cs

(x1 - x)² (x1=%) (91-ý 30 29893.3846b 11825 tratagy a b 22076.1538 12952.9231 9 6510 6923 77 2434.4615 -8310 7692 O g 1566. 769.2 3417,5385 7670. 3077 9619.0769 V 12568.846213 25 35 47866.6154 Total 182 125151 CS signatd with Come Sister

Here, Ssa= 182, SS Ssxy =125151 ssay ores se - 125151 182 - 687.64286 х and Bol = 7 - Bi 6349.2308 ( 687. 6428 x 2009) - 1375125. 2692. Bo 3 The fitted least square linear regresston line is - 1375125. 2692 + 687 06428x TE CS Sam With CMS

(Yi-y)? 2482 2623.4379. 19494262.7455 10486138 5148 4709gol.5917 1481650. 7450 691840.0533 2758154.4379 2454765. 8225 2919892 2840 5563792 • 2840 5782915. 0533 63190356 7450 8867109.5917 Total 963 52082,3077 12 Here, [(y-7)= 9635208203077. ssy = @ Y = -1375125+ 688 X we have, 3 = rispes. ssres 1-2 and sSpes= Sy- & Say Herse, sst: I (1-1) = 96352082. 2017 - SSpes = 963520 82.3077 - (687.6428 x 125151) sspes = 10292891 · 0934 935117 mspes = 10292891.0934 11 ICS

82- 935717 (b The LTHL LTNL size change in average for a year 688. Here, we have to estimate the no. of patients in the list in 2017. t.e we have to find have to find ŷ when x2 2017 û = -1375)25 +688 (2017) .: 9 - 11850 d we have to calecelate the fitted value of y correspondi to x = 2011. nap ... Y = -1375125 +688 (2011) ů - 7724.5165 7724-5165 7725 Residual le): Y- ☺ 8058-7725 333 e cs