Question

An analyst must decide between two different forecasting techniques for weekly sales of roller blades: a linear trend equation and the naive approach. The linear trend equation is Ft = 124 + 2.1t, and it was developed using data from periods 1 through 10. Based on data for periods 11 through 20 as shown in the table, which of these two methods has the greater accuracy if MAD and MSE are used? (Round your answers to 2 decimal places.) What is the MAD for Naive and Linear? What is MSE for Naive and Linear?

MAD (Naive)
MAD (Linear)
MSE (Naive)
MSE (Linear)

t	Units Sold
11	148
12	149
13	148
14	145
15	153
16	152
17	152
18	159
19	161
20	165

Answer 1

Calculate the forecast and associated errors (MAD, MSE) as shown below: Linear regression Naive Linear Absolute error ed Error Absolute error Squared Error D342 -04 2 3 11148 4 121149 5 13 148 6 14 145 7 151153 8 16|152 9 17 152 1018|159 11 19 161 12 20 165 124+2.1 A3 EABSIC3-B3) l=124+21°A4 İsAE IC4-84 124+2.1 A5 ABS(CS-B5 124+2.1'A6 EABS(C6-B6) 1=124+2.1*A7-ABS(C7-B |s]24+2.1*A8-ABS(C8-88 124+2.1'A9 EABS(C9-B9) |s]24+2.1"A101-ABS(C10-B1 124+2.1 A11 ABS(C11-B11 124+2.1 A12 EABS(C12-B12 -G4 2 G5 2 ABS(F4-B4 ABS(F5-B5 ABS(F6-B6 ABS(F7-B ABS(F8- ABS(F9-B9 ABS(F10-B10 ABS(F11-811 I-ABS(F12-B -07 2 09 2 010 2 011 2 -D12 2 G8A2 -G9A2 -G10*2 G11A2 G12A2 -B10 -811 AVERAGE(D3:D12) -SUM(E3:E12)/(COUNT(C3:C12)-1) AVERAGE(G3:G12-SUM(H3:H12)/(COUNT(F3:F12)-1) MSE MSE Linear regression Naïve Forecast Linear regression 147.1 149.2 151.3 153.4 155.5 157.6 159.7 161.8 163.9 166.0 Absolute Squared Forecast Absolute Squared Units Sold error Error NAIVE error Error 148 149 148 145 153 152 152 159 161 165 0.81 0.04 10.89 70.56 148 149 148 145 153 152 152 159 161 15 31.36 59.29 7.84 8.41 4 20 4 3.53 21.83 MSE 18.13 MAD MAD MSE

Answer 2

Time::: Unit Sold:::::::Forecast::::::ERRor::::::ErrorBar:::::::Error 2

11:::::::148:::::::::::::::-------:::::::::::::----:::::::::::::----::::::::::::::----

12:::::::149:::::::::::::::148:::::::::::::::1::::::::::::::::::1::::::::::::::1

13:::::::148:::::::::::::::149:::::::::::::-1::::::::::::::::::1::::::::::::::1

14:::::::145:::::::::::::::148::::::::::::::-3:::::::::::::::::3::::::::::::::9

15:::::::153:::::::::::::::145:::::::::::::8:::::::::::::::::::8::::::::::::::64

16:::::::152:::::::::::::::153:::::::::::::-1::::::::::::::::::1::::::::::::::1

17:::::::152:::::::::::::::152:::::::::::::0:::::::::::::::::::0::::::::::::::0

18:::::::159:::::::::::::::152:::::::::::::7::::::::::::::::::7::::::::::::::49

19:::::::161:::::::::::::::159:::::::::::::2::::::::::::::::::2::::::::::::::4

20:::::::165:::::::::::::::161:::::::::::::4:::::::::::::::::4::::::::::::::16

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Total for error bar =27 :::::::::::::::::::Error square:::::::::::145

MAD = $\Sigma$|e| / n

=27 /10 =2.7

MSE= $\Sigma$|e2| /n-1

=145/10-1

=16.11

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Linear

t::::::::::::square of t :::::::::::::::::::::Y:::::::::::::::::::::::tY'

11::::::::::::::::::121::::::::::::::::::::148::::::::::::::::::::::1628

12::::::::::::::::::144::::::::::::::::::::149::::::::::::::::::::::1788

13::::::::::::::::::169::::::::::::::::::::148::::::::::::::::::::::1924

14::::::::::::::::::196::::::::::::::::::::145::::::::::::::::::::::2030

15::::::::::::::::::225::::::::::::::::::::153::::::::::::::::::::::2295

16::::::::::::::::::256::::::::::::::::::::152::::::::::::::::::::::2432

17::::::::::::::::::289::::::::::::::::::::152::::::::::::::::::::::2584

18::::::::::::::::::324::::::::::::::::::::159::::::::::::::::::::::2862

19::::::::::::::::::361::::::::::::::::::::161::::::::::::::::::::::3059

20::::::::::::::::::400::::::::::::::::::::165::::::::::::::::::::::3300

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Totals

155::::::::::::2485:::::::::::::::::::1532:::::::::::::::::::::::23,902

______________________________________________

b=(23,902 - 10( 15.5)(153.20)

_________________________

2485 - 10(15.5)

=23902 - 23746 / 2485 - 155

=156/2330

=0.07

a=153.20 - 0.07 (15.5)

=153.20 -1.1

=152.10

Y=152.10 +0.07X

NOTE: lINEAR DOES NOT USE FOR SHORT TERM SUCH AS MAS AND MAD BUT IT IS USE LEAST SQUARED REGRESSION.