Problem 3-9 Obtain the linear trend equation for the following data on new check

Question

Problem 3-9

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.)

313

Use trend-adjusted smoothing with = .2 and = .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 (TAFt) for Period 5 as follows: Period 4 data + Initial trend estimate for Period 5. Then compute all remaining values (including the Stvalue 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.)

    

    

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       231 11 281 2 213 7       244 12 275 3 211 8       250 13 286 4 222 9       254 14 288 5 235 10       267 15

313

Y = +  t   Y16 =   Y17 =   Y18 =   Y19 = b.

Use trend-adjusted smoothing with = .2 and = .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 (TAFt) for Period 5 as follows: Period 4 data + Initial trend estimate for Period 5. Then compute all remaining values (including the Stvalue 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 =

    

     

Explanation / Answer

Solution:

a) Y = 192.82 + 7.31t

Y16= 192.82 + 7.31 * 16 = 309.78

Y17= 192.82 + 7.31 * 17 = 317.09

Y18= 192.82 + 7.31 * 18 = 324.4

Y19= 192.82 + 7.31 * 19 = 331.71

Solution B)

Compute the initial trend estimate (Tt) for Period 5 as follows: (Period 4 data – Period 1 data) / 3.

Solution : Forcast for period 16 is 291.08.

(Period 4 data – Period 1 data) / 3 = (222-200)/3 =7.333

Then compute the initial trend-adjusted forecast (TAFt) for Period 5 as follows:

Solution: Period 4 data + initial trend estimate for period 5 = 222 + 7.333 = 229.33

Forcast for period 16 = 312.92

  Y17

=

  Y18

=

  Y19

=

  Y17

=

  Y18

=

  Y19

=

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