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: 1346 1862 2876 3849 4823 6813 75927497 | 7716 84868410 8657 8913 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 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 62. 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). ß (c) Estimate the number of patients in the list in 2018. (d) Calculate the fitted value of y corresponding to x=2015. Find the corresponding residual. Round your answer to the nearest integer (e.g. 9876). y = Round your answer to the nearest integer (e.g. 9876). e =

Answer 1

solm cleta x=0 Bared m for 2005, 2,=1 for 2006 Y, = size of patient y =2046-13 +669.747 x, ya~Bo +BqX7 10000 STATISTICS RESIDUALS e plot r2 = 0.9029 r=0.9502 PARAMETERS Bo = 2046.13 Bi = 009.747 2 5000 X1 :yi 0 1346 (2005) (2006) 1 1862 2 2870 3 3849 5 10 15 4 4823 5 6813 6 7592 7 7497 8 7710 (a) based on data we get 8²=0.9029 r=0-9502 9 8486 10 8410 2015 2016 (2017) 11 8057 12 8913 že? std deviation Residual = n-2 = 936-82599 ~ 936.8260 (b) changes per year as we get P ,=669.747 B 7670 per year (9) in 2018, Number of patient x1=13 y =669.747(13) +2046-13 YE 10752-846 Yi z 10753, (d) Based in linear model 2015 x =10 y, =8743.604, 9, ~8744 Residual = Actual-model value = 8410-8744 = - 334 .

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