Question

Reserve Problems Chapter 11 Section 2 Problem 1 x Your answer is incorrect. Try again. 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 | 1460 | 1972 29824001 49306887 7619 7520 7791 842384928615 | 8901 x 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 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 o. Round your answer to the nearest integer (e.g. 9876). 820156 (b) How does the LTWL size change in average for a year? Round your answer to the nearest integer (e.g. 9876). 655 (c) Estimate the number of patients in the list in 2020. 12675 <a (d) Calculate the fitted value of y corresponding to x = 2013. Find the corresponding residual. Round your answer to the nearest integer (e.g. 9876). 8088 ỹ= Round your answer to the nearest integer (e.g. 9876). 335 e =

Answer 1

let, Fit 1 X = Year ie independent variable Y = size con noi of patients) i:e dependent variable fitted reast square regression line is we know that the - + Baix where, Bo és estimate of y-intercept of regression line Bi is estimate Of slope of regression line ro 91so, Pivo e pia Bô = Ý - ß, π and Bi= ssiry S Sae. A where, Ssxy = a (xi-*) Lyin ) ,852= (xi-*)2 SSy & cri-9 j² cs Staats with CAMS823

n=13, Eai= 26130 Eyi= 79593 Here, ..x = Exil 26130 = 2010 ý = Eyi 6/22. 5385 79593 13 35 25 (xi-x) lyi- 279750 2308 207520 6923 12502. 1538 6364.6154 238500769 -764.400 g - (Yi-J? 21739284.9013 17226969. 1207 9862981-8284 4500925. 4438 1422147 9822 584401, 4438 22393970 1361 1952898. 7515 2783765.9053 52921236 2899 501437409822 6212364, 5207 7719848.5207 8715143502308 9 9 1397.4or 33360 9231 6901.3846 9477.8962 12462.3077 166707692 119522 25 total 182 Ssx=182, ssy 8715143502308 - 19522 ssay Biassay 119522 182 ssa B = 656.7843 657. and Bå = 7 - Bi i = 6122.5385- (656-7143 X 2010 : Pô - - 1313873:1758-1313873 cs

@ The fitted simple linear regression equation is, Y = -1313873 + 6 5 7 X Here, we have to find, ² 32 F MsRes. and sspes = sst - B9 say Here, SS7 = {Hi-T² = ssy sspes= Elti-1² sspes = 87151455. 2308 – ( 657 x 9522) 87151435.2308 isspes: 865963063737 MISRes= ssRes 8659630.3737 11 Pipes 787239 62 = 787231 b 6 8 = 657 Here, we have to find when X=2010 .: û = -1313873 +657(2010) :: = 6123 CS

d Here, we have to find value of ↑ When H = 2013. Y = -1313873 + 657(2013) .: 8093 Residual le) - Y - Ý :e=8423 8093 e=330 CS SAL WE CASA