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)

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter13: Regression And Forecasting Models
Section13.3: Simple Regression Models
Problem 8P: The management of a technology company is trying to determine the variable that best explains the...
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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×Y X2
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=(NXY)-(X)(Y)(NX2-(X)2)b=(5×2872)-(15)(896)(5×55)-152b=14360-13440275-225b=92050b=18.4

a=(Y-b(X))Na=896-18.4×155a=896-2765a=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+18.4×6=124+110.4=234.4

Therefore, the forecast for next year is 234.4 disk drives

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