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Use trend projection with regression to forecast sales for weeks 10-13. What are the error measures (CFE, MSE, sigma MAD, and MAPE) for this forecasting procedure? How about r^2? Obtain the trend projection with regression forecast for weeks 10-13. (Enter your responses rounded to two decimal places.) Obtain the error measures. (Enter your responses rounded to two decimal places.)
Expert Answer
Least square method is applied to determine to a linear trend line which is given by following equation:
Y = a + bx
Where,
y = Sales
x = quarter number
Y = demand computed using regression equation
a = y-axis intercept
b = slope of the line
| x | y | x2 | x*y | y2 |
| 1 | 47 | 1 | 47 | 2209 |
| 2 | 50 | 4 | 100 | 2500 |
| 3 | 46 | 9 | 138 | 2116 |
| 4 | 51 | 16 | 204 | 2601 |
| 5 | 55 | 25 | 275 | 3025 |
| 6 | 57 | 36 | 342 | 3249 |
| 7 | 63 | 49 | 441 | 3969 |
| 8 | 60 | 64 | 480 | 3600 |
| 9 | 61 | 81 | 549 | 3721 |
| 45 | 490 | 285 | 2576 | 26990 |
The regression line is given by formula:
Y = a + bx = 43.94 + 2.1x
Forecast value for the next months are:
| x | Y = 43.9 + 2.1x |
| 10 | Y = 43.9 + 2.1*10 = 64.94 |
| 11 | Y = 43.9 + 2.1*11 = 67.04 |
| 12 | Y = 43.9 + 2.1*12 = 69.14 |
| 13 | Y = 43.9 + 2.1*13 = 71.24 |
Calculating Errors:
| Forecast | Error | Absolute | Sum of % E | ||||
| x | y | yc=43.9+2.1x | E = y-yc | |E| | CSE | E2 | 100|E|/y |
| 1 | 47 | 46.0444 | 0.9556 | 0.9556 | 0.9556 | 0.9131 | 2.0331 |
| 2 | 50 | 48.1444 | 1.8556 | 1.8556 | 2.8111 | 3.4431 | 3.7111 |
| 3 | 46 | 50.2444 | -4.2444 | 4.2444 | -1.4333 | 18.0153 | 9.2271 |
| 4 | 51 | 52.3444 | -1.3444 | 1.3444 | -2.7778 | 1.8075 | 2.6362 |
| 5 | 55 | 54.4444 | 0.5556 | 0.5556 | -2.2222 | 0.3086 | 1.0101 |
| 6 | 57 | 56.5444 | 0.4556 | 0.4556 | -1.7667 | 0.2075 | 0.7992 |
| 7 | 63 | 58.6444 | 4.3556 | 4.3556 | 2.5889 | 18.9709 | 6.9136 |
| 8 | 60 | 60.7444 | -0.7444 | 0.7444 | 1.8444 | 0.5542 | 1.2407 |
| 9 | 61 | 62.8444 | -1.8444 | 1.8444 | 0.0000 | 3.4020 | 3.0237 |
| Total | 0.0000 | 16.3556 | 0.0000 | 47.6222 | 30.5947 | ||
Forecast sales for each month are calculated by formula: yc = 43.94 + 2.1x
Forecast Error (E) for each month = E = y – yc
Cumulative forecast error= CFE = ∑( y – yc ) = 0
Mean Squared Error (MSE) = [∑( y – yc )2]/n = [∑E2]/9 = 47.622/9 =5.2913
MSE = 5.2913
Mean Absolute Deviation = [∑|y – yc|]/n = [∑|E|]/9 = 16.3556/9 = 1.8172
Mean Absolute Percent Error = MAPE = (1/n) x (∑100|E|/y) = (1/9)x(30.5947)=3.34
Standard Error of Estimate (Sy,x ) = Standard deviation of regression (σ)
