The number of internal disk drives? (in millions) made at a plant in Taiwan duri
ID: 327166 • Letter: T
Question
The number of internal disk drives? (in millions) made at a plant in Taiwan during the past 5 years? follows: ??????????????????????????????????????????????????????????????????? Year Disk Drives
1 138
2 160
3 190
4 202
5 216
?a) Using simple linear regression?, the forecast for the number of disk drives to be made next year? = 240.6 disk drives
?b) The mean squared error? (MSE) when using simple linear regression? ____________drives2
c) The mean absolute percent error (MAPE) when using simple linear refression=__________%
I was able to wrk through A), but how to I calculate b & c?
Explanation / Answer
Let the linear regression equation isY = a + b.X
Y ( Dependent variable ) = Forecasted number of disk drives
X = Year number
A, b = Constants
We place all the values of Year and disk drives as provided in 2 separate columns in excel and apply the formula LINEST ( ) to obtain values of a and b. Accordingly values of a and b are as per following :
A = 121.8
B = 19.8
Therefore Linear regression equation is : Y = 121.8 + 19.8.X
Y = 121.8 + 19.8.X
To determine forecast for number of disk drives to be made next year, we have to put value of X = 6
Therefore, forecast for number of disk drives to be made next year = 121.8 + 19.8 x 6 = 121.8 + 118.8 = 240.6
Following also may be noted :
Square error =( Forecast – actual )^2
Therefore , Mean Square Error ( MSE ) = Sum of values of Square error / 5 i.e. number of observations
Absolute Percentage error (APE ) = (Absolute difference between values of Forecast vs actual )/Actualx 100
Therefore , Mean absolute Percent Error ( MAPE )
= Sum of values of Absolute Percentage error ( APE ) / 5 I,e, number of observations
Accordingly , please refer below table which calculate values of MSE and MAPE :
Year
Disk drive - actual
Disk drive - Forecast
Square error (SE)
Absolute Percentage error ( APE)
1
138
141.60
12.96
2.61
2
160
161.40
1.96
0.88
3
190
181.20
77.44
4.63
4
202
201.00
1.00
0.50
5
216
220.80
23.04
2.22
SUM =
116.40
10.83
Mean Square error = Sum of Square error / 5 = 116.40/5 =23.28
Mean absolute Percent error = Sum of absolute Percent error / 5 = 10.83/ 5 = 2.17% ( rounded to 2 decimal places )
Year
Disk drive - actual
Disk drive - Forecast
Square error (SE)
Absolute Percentage error ( APE)
1
138
141.60
12.96
2.61
2
160
161.40
1.96
0.88
3
190
181.20
77.44
4.63
4
202
201.00
1.00
0.50
5
216
220.80
23.04
2.22
SUM =
116.40
10.83