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: 1447 | 1873 3161 4127 5155 7190 802579258181 88238925 90049421 x 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 o. Round your answer to the nearest integer (e.g. 9876). 959683 (b) How does the LTWL size change in average for a year? Round your answer to the nearest integer (e.g. 9876). 698 (c) Estimate the number of patients in the list in 2019. T11986 y= (d) Calculate the fitted value of y corresponding to x = 2014. Find the corresponding residual. Round your answer to the nearest integer (e.g. 9876). 8497 y = Round your answer to the nearest integer (e.g. 9876). 326

Answer 1

1.

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Using the method of least squares, the estimated regression line is given by

Y=a+bX, where a is the intercept and b is the slope estimate.

slope = b = average(cy) – average(2) * averagely) [average(22) - (average(2))2]

and intercept =a = average(y) - b*average(x)

Substituting the values, we get , b=700.1648 and a= -1401627

Thus, the regression line is Y= -1401627 +700.165X

Now, we calcukate the residuals and then the estimate os variance is given by

σ?, Σy - Y)? η – 2

=9927480.132/(13-2)

= 902498.12

=902498

2. This is the value of the slope , b = 700.165 = 700

3. when x = 2019, Y = -1401627 +700.165*2019 = 12006.14 = 12006

4. When X = 2014, observed y =8823

Estimated Y = 8504.879 = 8505

And e = y-Y = 318.1209 = 318