Question

Reserve Problems Chapter 11 Section 2 Problem 1 The department of health studied the number of patients who need liver transplantation. The following data are the Liver Transplantation Waiting List (LTL), where is the site in number of patients) and is the corresponding year: 1303 1807 2819 3802 4783 6716 749974357658 8354 8430 84948938 * 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Round your intermediate answers to four decimal places (e.p.98.7654) (a) Fit the simple linear regression model using the method of seast squares. Find the estimate of on? Round your answer to the nearest Integer (0.9.9876). (0) How does the LTWL se change in average for a year? Round your answer to the nearest Integer (e.g. 9876) 2.- (c) Estimate the number of patients in the list in 2019. (a) Calculate the fated volue of y corresponding to x = 2011. Find the corresponding residual. Round your answer to the nearest integer (eg. 9876). 9 Round your answer to the nearest Integer leg. 9876)

Answer 1

We have given the liver transplantation data list.

Where y is the no. of patients and x is the corresponding year.

number of dataset,N=13

By using the above data we have

$\bar X=2009, \: \bar Y=6002.92$

Sum of Squares SS_x , $\sum (X-\bar X)^2=182$

Sum of products SP,$\sum(X-\bar X)(Y-\bar Y)=121814$

Regression equation, y=a+bx

$b=\frac{SP}{SS_{x}}=\frac{121814}{182}=669.31$

a =Y – 6X = 6002.92 – 669.31 * 2009 = -1338636.23

Which gives us

$y=-1338636.23+669.31x$

A) We know that the

$\sigma ^2=\frac{\sum (X-\bar X)^2}{N}$

Hence

$\sigma^2=\frac{182}{13}=14$

B) Average change in size (i.e. number of patients) for a year = (Last value-first value)/no. of years

$Average\:change=8938-1303=7635$

Average change for a year would be 7635/13=587.3

i.e. LTWL size change in average for a year=587

C) The regression equation using the analysis is

$y=-1338636.23+669.31x$

No. of patient in 2019=

$y=-1338636.23+669.31*2019=12700.66$

The no. of patients in 2019 would be 12701.

D) Fitted value of 2011 using regression equation

$y=-1338636.23+669.31*2011=7346.18$

Error in 2011=7658-7346=312