Question

a. 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.)

Period	New Accounts	Period	New Accounts	Period	New Accounts
1	200	6	239	11	281
2	215	7	246	12	275
3	211	8	250	13	283
4	229	9	256	14	288
5	235	10	267	15	319

b.Use trend-adjusted smoothing with α = .2 and β = .1 to smooth the new account data in part a. What is the forecast for period 16? Compute the initial trend estimate (T_t) for Period 5 as follows: (Period 4 data – Period 1 data) / 3. Then compute the initial trend-adjusted forecast (TAF_t) for Period 5 as follows: Period 4 data + Initial trend estimate for Period 5. Then compute all remaining values (including the S_t 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.)

Answer 1

a.

Linear trendline equation:

y = a+bx

where, a is the intercept, x = time period, b is the slope and y is the new period

Hence, the linear trendline equation :

y = 195.25 + 7.21x

The expected values are :

For, y =

16 == 310.62

17 == 317.83

18 == 325.04

19 == 332.25

b.

Initial trend(Tt) = (Period 4 data - Period 1 data)/3

=(229-200)/3 = 9.667

Initial trena adjusted forecast (TAFt) = Period 4 data + Initial trend estimate for Period 5(St)

TAFt = Tt +St

Calculate all values using:

St = TAFt + 0.2(A-TAFt)

Tt = T_t-1 + 0.1(TAFt - TAF_t-1 - T_t-1

Therefore, forecast for period 16 is 361.21