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

YEAR DISK DRIVES
1 140
2 160
3 190
4 200
5 210
a) Forecast the number of disk drives to be made next year, using linear regression.

b) Compute the mean squared error (MSE) when using linear regression.

c) Compute the mean absolute percent error (MAPE).

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ammad472

Answer:

As given in question

Years=X=1 ,2,3,4,5

Drives=Y= 140,160,190,200,210

Sum of X = 15

Sum of Y = 900

Mean X = 3

Mean Y = 180

Sum of squares (SSX) = 10

Sum of products (SP) = 180

Regression Equation = ŷ = bX + a

b = SP/SSX = 180/10 = 18

a = MY - bMX = 180 - (18*3) = 126

ŷ = 18X + 126

So number of drives that will be made next year will be,

a) Disk Drive for 6th Year= 234.

For calculating the mean Squared error,

consider all the 6 values .

140,160,190,200,210,234

Mean value= 189

Error= -49,-29,1,11,21,45

Sum of Squared error= 5830

MSE = Sum of Squared error/Number of years

MSE= 5830/6

b) Mean Squared error = 971.66

For Mean Absolute Percent error,

As forecast is y= 18X+126

Actual Forecast Percent Error

140             144 -3%

160             162 -1%

190             180 5%

200             198 1%

210             216 -3%

234             234 0%

c) Mean Percent error is 2.2 %

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