Question

I Only need Part C, all other parts are correct. Thanks.

As you can see in the following table, demand for heart transplant surgery at Washington General Hospital has increased steadily in the past few years Year Heart Transplants 45.0 52.0 52.0 54.0 58.0 The director of medical services predicted 6 years ago that demand in year 1 would be 41.0 surgeries a) Using exponential smoothing with α of 0.60 and the given forecast for year 1, the forecasts for years 2 through 6 are round your responses to one decimal place Year Forecast 41.0 43.4 48.6 50.8 52.7 55.9 For the forecast made using exponential smoothing with α = 0.60 and the given forecast for year 1, MAD = 4.9 surgeries round your response to one decimal place Using exponential smoothing with α of 0.90 and the given forecast for year 1, the forecasts for years 2 through 6 are round your responses to one decimal place Year Forecast 41.0 44.6 51.3 51.9 53.8 57.6

Answer 1

C) Calculation of regression equation

Year(X) demand(Y) XY X^2 (square of X)

1 45.0 45 1

2 52.0 104 4

3 52.0 156 9

4 54.0 216 16

5 58.0 290 25

$\small \sum$ X = 1+2+3+4+5= 15

$\small \sum$ Y = 45+52+52+54+58 = 261

$\small \sum$ XY = 45+104+156+216+290 = 811

$\small \sum$ X^2 = 1+4+9+16+25 = 55

n = Number of periods = 5

X-bar = $\small \sum$ X / n = 15/5 = 3

Y-bar = $\small \sum$ Y/n = 261/5 = 52.2

b = ( $\small \sum$ XY - nX-bar .Y-bar ) / ( $\small \sum$ X^2 - n. Square of X-bar)

= [811 - (5)(3)(52.2) ] / [55 - (5)(3)(3)]

= (811 - 783) / (55- 45)

= 28 / 10

= 2.8

a = Y-bar - b(X-bar) = 52.2 - 2.8(3) = 52.2 - 8.4 = 43.8

Y = a + bx => Y = 43.8 + 2.8x

So the regression equation is Y = 43.8 + 2.8x

Where x = sequential number of the period

So using the above regression equation the forecast for year 1 through 6 are

• For year 1 = 43.8+2.8x = 43.8+(2.8x1) = 43.8+2.8 = 46.6
• For year 2 = 43.8+2.8x = 43.8+(2.8x2) = 43.8+5.6 = 49.4
• For year 3 = 43.8+2.8x = 43.8+(2.8x3) = 43.8+8.4 = 52.2
• For year 4 = 43.8+2.8x = 43.8+(2.8x4) = 43.8+11.2 = 55.0
• For year 5 = 43.8+2.8x = 43.8+(2.8x5) = 43.8+14 = 57.8
• For year 6 = 43.8+2.8x = 43.8+(2.8x6) = 43.8+16.8 = 60.6