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: y 1494 2092 31374094 5125 7061 7958 788279838763 8775 88369275 * 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 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). Ô1 = (c) Estimate the number of patients in the list in 2019. (d) Calculate the fitted value of y corresponding to x = 2012. Find the corresponding residual. Round your answer to the nearest integer (e.g. 9876). ỹ = Round your answer to the nearest integer (e.g. 9876). e =

Answer 1

Solution

we will solve it by using excel and the steps are

Enter the Data into excel

Click on Data tab

Click on Data Analysis

Select Regression

Select input Y Range as Range of dependent variable.

Select Input X Range as Range of independent variable

click on labels if your selecting data with labels

click on ok.

So this is the output of Regression in Excel.

	SUMMARY OUTPUT
	Regression Statistics
	Multiple R	1
	R Square	1
	Adjusted R Square	1
	Standard Error	923
	Observations	13
	ANOVA
		df	SS	MS	F	Significance F
	Regression	1	83806286	83806286	98	0
	Residual	11	9362025	851093
	Total	12	93168310
		Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
	Intercept	-1356928	137383	-10	0	-1659306	-1054550	-1659306	-1054550
	x	679	68	10	0	528	829	528	829

a) σ² = MS Residual = 851093

b) β₁=679

c) number of patients in 2019

y-hat = -1356928+679*x

y-hat= -1356928+679*2019

y-hat = 13973

d)

when x=2012

y-hat = -1356928+679*x

y-hat = -1356928+679*2012

y-hat = 9220

residual e = y-yhat

e = 8763 - 9220

e = -457