Question

Sales of​ Volkswagen's popular Beetle have grown steadily at auto dealerships in Nevada during the past 5 years​ (see table​ below).

                                                    

Year	Sales
1	460
2	495
3	516
4	555
5	590

​a) Forecasted sales for year 6 using the trend projection​ (linear regression) method are ____ sales ​(round your response to one decimal​ place).

​b) The MAD for a linear regression forecast is _____ sales ​(round your response to one decimal​ place)

​c) The MSE for the linear regression forecast is ______ sales ​(round your response to one decimal​ place).

Answer 1

PERIOD (X)	DEMAND (Y)	X	Y	X * Y	X^2
1	460	1	460	460	1
2	495	2	495	990	4
3	516	3	516	1548	9
4	555	4	555	2220	16
5	590	5	590	2950	25
SIGMA		15	2616	8168	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 = (2616 * 55) - (15 * 8168) / ((5 * 55) - 15^2) = 427.2

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

SLOPE = ((5 * 8168) - (15 * 2616) / ((5 * 55) - 15^2) = 32

LINE EQUATION = A + B(x), WHERE A IS THE INTERCEPT, B IS THE SLOPE, x IS THE PERIOD = 427.2 + (32 * X)

FOR THE VALUE OF X = 6 FORECAST = 427.2 + (32 * 6) = 619.2

OTHER FORECASTS CAN BE CALCULATED IN USING THE SAME:

PERIOD	DEMAND	FORECAST
1	460	459.2
2	495	491.2
3	516	523.2
4	555	555.2
5	590	587.2

FORECAST ERROR

PERIOD	ACTUAL DEMAND	FORECAST	DEVIATION(D - F)	ABS DEVIATION	DEVIATION ^2
1	460	459.2	0.8	0.8	0.64
2	495	491.2	3.8	3.8	14.44
3	516	523.2	-7.2	7.2	51.84
4	555	555.2	-0.2	0.2	0.04
5	590	587.2	2.8	2.8	7.84
SIGMA			0	14.8	74.8

MAD = SIGMA(ABSOLUTE DEVIATION) / N, WHERE N = 5

MAD = 14.80 / 5 = 3

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

MSE = 74.80 / 5 = 15