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 .
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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