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	138138
2	156156
3	184184
4	204204
5	210210

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

disk drives ​(round your response to one decimal​ place).

b) compute the mean squared error (MSE).

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

Answer 1

PERIOD (X)	DEMAND (Y)	X	Y	X * Y	X^2
1	138	1	138	138	1
2	156	2	156	312	4
3	184	3	184	552	9
4	204	4	204	816	16
5	210	5	210	1050	25
SIGMA		15	892	2868	55

MANUAL CALCULATION FOR INTERCEPT AND SLOPE VALUES

INTERCEPT = (SIGMA(Y) * SIGMA(X^2) - SIGMA(X) * SIGMA(XY)) / (N * SIGMA(X^2) - SIGMA(X)^2)

INTERCEPT = (892 * 55) - (15 * 2868) / ((5 * 55) - 15^2) = 120.8

SLOPE = ((N * SIGMA(XY)) - (SIGMA(X) * SIGMA(Y))) - (N * SIGMA(X^2) - SIGMA(X)^2)

SLOPE = ((5 * 2868) - (15 * 892) / ((5 * 55) - 15^2) = 19.2

LINE EQUATION = A + B(x), WHERE A IS THE INTERCEPT, B IS THE SLOPE, x IS THE PERIOD = 120.8 + (19.2 * X)

FOR THE VALUE OF X = 6 FORECAST = 120.8 + (19.2 * 6) = 236.0

FORECAST ERROR

PERIOD	ACTUAL DEMAND	FORECAST	DEVIATION(D - F)	ABS DEVIATION	(ABS DEV / DEMAND) * 100	DEVIATION ^2
1	138	140	-2	2	1.45	4
2	156	159.2	-3.2	3.2	2.05	10.24
3	184	178.4	5.6	5.6	3.04	31.36
4	204	197.6	6.4	6.4	3.14	40.96
5	210	216.8	-6.8	6.8	3.24	46.24
SIGMA			0	24	12.92	132.8

MSE = SIGMA(DEVIATIONS^2) / N, WHERE N = 5

MSE = 132.8 / 5 = 26.56

MAPE = SIGMA(ABSOLUTE DEVIATION / DEMAND * 100) / N, WHERE N = 5

MAPE = 12.92 / 5 = 2.58

**Please leave a thumbs-up if you found this answer helpful.