Question

The following is the recent historical sales of Sony HDTV at a local BestBuy store.

Month	Jan	Feb	Mar	April	May
Actual HDTV sales	60	65	70	55	62

Use simple linear regression y=a+bx, to first calculate the parameter value of b , then the parameter value of a , and finally to forecast sales for June.

There should be 3 separate answers for each part .

Answer 1

PERIOD (X)	DEMAND (Y)	X	Y	X * Y	X^2
1	60	1	60	60	1
2	65	2	65	130	4
3	70	3	70	210	9
4	55	4	55	220	16
5	62	5	62	310	25
SIGMA		15	312	930	55

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

SLOPE = ((5 * 930) - (15 * 312) / ((5 * 55) - 15^2) = -0.6

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

INTERCEPT = (312 * 55) - (15 * 930) / ((5 * 55) - 15^2) = 64.2

LINE EQUATION = A + B(x), WHERE A IS THE INTERCEPT, B IS THE SLOPE, x IS THE PERIOD = 64.2 + (-0.6 * X)

FOR THE VALUE OF X = 6 FORECAST = 64.2 + (-0.6 * 6) = 60.6

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