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	212	7	243	12	275
3	211	8	250	13	287
4	222	9	251	14	288
5	235	10	267	15	316

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

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.)

Forecast for period 16 =___  

Answer 1

a)

	Period(x)	New Accounts(y)	xy	x2
	1	200	200	1
	2	212	424	4
	3	211	633	9
	4	222	888	16
	5	235	1175	25
	6	239	1434	36
	7	243	1701	49
	8	250	2000	64
	9	251	2259	81
	10	267	2670	100
	11	281	3091	121
	12	275	3300	144
	13	287	3731	169
	14	288	4032	196
	15	316	4740	225
Total	120	3777	32278	1240

x-bar = Sum(x)/n = 120/15 = 8
y-bar = Sum(y)/n = 3777/15 = 251.8

b = (Sum(xy) – n*x-bar*y-bar)/(Sum(x2) – n*x-bar*x-bar)
= (32278-15*8*251.8)/(1240–15*8*8)
= 2062/280 = 7.364285714 = 7.36 (Rounded to 2 decimal place)

a = y-bar –b*x-bar
= 251.8 - 7.36*8 = 192.92

Regression equation is y = a + bx,
we get following linear trend equation by substituting values of a and b
Regression equation is y =192.92+7.36x

Y16 = 192.92+7.36*16 = 310.68

Y17 = 192.92+7.36*17 = 318.04

Y18 = 192.92+7.36*18 = 325.4

Y19 = 192.92+7.36*19 = 332.76

b)

Period(t)	New Accounts(A(t))	S(t)	T(t)	TAF(t)
1	200
2	212
3	211
4	222
5	235	222	7.333	229.33
6	239	230.46	7.446	237.91
7	243	238.13	7.468	245.60
8	250	245.08	7.416	252.50
9	251	252	7.366	259.37
10	267	257.70	7.199	264.90
11	281	265.32	7.241	272.56
12	275	274.25	7.410	281.66
13	287	280.33	7.277	287.61
14	288	287.49	7.265	294.76
15	316	293.41	7.130	300.54
		303.63	7.439	311.07

Using trend adjusted exponential smoothing, F(t) = TAF(t-1) + alpha*(A(t-1) - TAF(t-1))

T(t) = T(t-1) + beta*(F(t) - TAF(t-1))

and TAF(t) = F(t) + T(t)

Forecast for period 16 = 311.07