Obtain the linear trend equation for the following data on new checking accounts

Question

Obtain the linear trend equation for the following data on new checking accounts at Fair Savings Bank and use it to predict expected new checking accounts for periods 16 through 19 (Round your intermediate calculations and final answers to 2 decimal places.) 200 218 211 231 246 250 255 267 12 13 14 15 281 275 287 288 312 8 235 10 195.02+ 202.16 209.30 216.44 223.58 7.14 t b. Use trend-adjusted smoothing with a .2 and ß 1 to smooth the new account data in part a. What is the forecast for period 16? Compute the initial trend estimate (Tt) for Period 5 as follows: (Period 4 data - Period 1 data) /3. Then compute the initial trend-adjusted forecast (TAF) for Period 5 as follows: Period 4 data+ Initial trend estimate for Period 5. Then compute all remaining values (including the St value for Period 5) using the textbook formulas or Excel template. (Round the "Trend values (Tt) to 3 decimal places and all other intermediate forecast values (TAFt and St) to 2 decimal places. Round your final answer to 2 decimal places.) Forecast for period 16 References eBook & Resources Worksheet Dificuity 3 Hard Problem 3-9 Learning Objective 03-11 Prepare a inear

Explanation / Answer

We have given the data on new checking accounts at Fair saving bank.

We have to fit trend equation and to find next four forecasts.

We can do this in MINITAB.

steps :

ENTER data into MINITAB sheet -->STAT --> Time series --> Trend analysis --> Variable : Select data column --> Model type : Linear --> Generate forecasts --> number of forecasts : 4 --> ok

Trend Analysis for new

Data new
Length 15
NMissing 0

Fitted Trend Equation

Yt = 195.02 + 7.139×t

Accuracy Measures

MAPE 1.8179
MAD 4.5794
MSD 29.3534

Time new Trend Detrend
1 200 202.158 -2.15833
2 218 209.298 8.70238
3 211 216.437 -5.43690
4 226 223.576 2.42381
5 235 230.715 4.28452
6 231 237.855 -6.85476
7 246 244.994 1.00595
8 250 252.133 -2.13333
9 255 259.273 -4.27262
10 267 266.412 0.58810
11 281 273.551 7.44881
12 275 280.690 -5.69048
13 287 287.830 -0.82976
14 288 294.969 -6.96905
15 312 302.108 9.89167

Forecasts

Period Forecast
16 309.248
17 316.387
18 323.526
19 330.665

Now we have to find forecasts for period 16 using double exponential smoothing with alpha = 0.2 and beta = 0.1

Double exponential smoothing in MINITAB :

steps :

ENTER data into MINITAB sheet --> STAT --> Time series --> Double exponential smoothing --> Variable : select data column --> Specified weights --> For level : 0.2 --> For trend : 0.1 --> Generate foracasts --> no. of forecasts : 1 --> ok

Double Exponential Smoothing for new

Data new
Length 15

Smoothing Constants

? (level) 0.2
? (trend) 0.1

Accuracy Measures

MAPE 1.9861
MAD 5.0060
MSD 36.4916

Forecasts

Period Forecast Lower Upper
16 309.546 297.281 321.810

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