Answered: The number of internal disk drives (in…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Question

The number of internal disk drives (in million) made at a plant in Taiwan during the past 5 years follows:

Year Disk Drives

1 142

2 156

3 184

4 204

5 210

a) Using simple linear regression the forecast for the number of disk drives to be made next year= 234.4 disk drives

b) The mean squared error (mse) when using simple linear regression=[___] drives^2 (round your response to one decimal place)

Expert Solution

Step 1

a. Forecast using simple linear regression:

Year (X)	Disks (Y)	$X \times Y$	$X^{2}$
1	142	142	1
2	156	312	4
3	184	552	9
4	204	816	16
5	210	1050	25
15	896	2872	55

N=5

$b = \frac{(N \sum_{} X Y) - (\sum_{} X) (\sum_{} Y)}{(N \sum_{} X^{2} - {(\sum_{} X)}^{2})} b = \frac{(5 \times 2872) - (15) (896)}{(5 \times 55) - 15^{2}} b = \frac{14360 - 13440}{275 - 225} b = \frac{920}{50} b = 18.4$

$a = \frac{(\sum_{} Y - b (\sum_{} X))}{N} a = \frac{896 - 18.4 \times 15}{5} a = \frac{896 - 276}{5} a = 124$

The linear equation is given by

Y = a+bX

Forecast for a period, Y = 124+18.4X

Forecast for the number of disk drives to be made next year, $Y = 124 + 18.4 \times 6 = 124 + 110.4 = 234.4$

Therefore, the forecast for next year is 234.4 disk drives

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