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 (LTWL), where y is the size (in number of patients) and x is the corresponding year: 1351 17802741 384047616737744373667597821082068423 8889 * 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 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). (b) How does the LTWL size change in average for a year? Round your answer to the nearest integer (e.g. 9876). B, = patients in the list in 2013. (c) Estimate the number y = (d) Calculate the fitted value of y corresponding to x= 2008. Find the corresponding residual. Round your answer to the nearest integer (e.g. 9876). Round your answer to the nearest integer (e.g. 9876). e

Answer 1

Excel regression output is given below

Regression Analysis
	r²	0.903	n	13
	r	0.950	k	1
	Std. Error	1.268	Dep. Var.	y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	164.31395647	1	164.31395647	102.20	6.63E-07
Residual	17.68604353	11	1.60782214
Total	182.00000000	12
Regression output					confidence interval
variables	coefficients	std. error	t (df=11)	p-value	95% lower	95% upper
Intercept	1,997.8339
x	0.0014	0.00013577	10.109	6.63E-07	0.0011	0.0017

a)

$\hat \sigma^2=MSE=\frac{SSE}{n-2}=1.6078$

b)

$\beta_1=0.0014$

c)

Now that we have the regression equation, we can compute the predicted value for X = 2013, by simply plugging in the value of X = 2013 in the regression equation found above: î = 1997.8339 +0.0014 x 2013 2000.5969

d)

put x=2008

we get y=2000.590

e=7597-2000.590=5596.41