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Background The Glass Slipper restaurant has operated in a resort community near a popular ski area of New Mexico and busiest during the rst 3 months of the year. The Glass slipper oered the ultimate dining experience with breathtaking !iews of the surrounding mountains. "ames and #eena $eltee% the owner% place special attention in setting the perfect ambiance making dining a truly magnicent gourment experience. The Glass Slipper has de!eloped and maintained a reputation as one of the &must !isit& places in that region of New Mexico. Objective 'fter careful analysis of their nancial condition% the $eltee(s decided to sell the Glass Slipper and open a bed and breakfast on a beautiful beach in Mexico. 'lthough not retired yet% this would put them in the retirement setting they ha!e been longing for many years. They would ha!e to hire a manager that would allow them to begin a semi)retirement life in paradise. The Glass Slipper for the right price. The price of the business would be based on the !alue of the property and e*uipment% as well as pro+ections of future income. ' forecast of sales for the next year is needed to help in the determination of the calue of the restaurant. Monthly sales for each of the past 3 years are pro!ided below. Monthly ,e!enue -in /%000s1 Month "anuary 6ebruary March 'pril May "une "uly 'ugust Septembe :ctober No!embe #ecember
ne& illustrate their busiest months% while the lines below season. The graph also shows moderate increase in . =asically% the up and down is more of a seasonality ance.
egression Anal#sis
eression Anal#sis
Forecasting
Simple linear regression
!ata
>f>fthis this is is trend trend analysis analysis then then simply simply enter enter the the past past demands demands in in the the demand demand column. column. > then ottom in thenenter enterthe they%x y%xpairs pairswith withyyrst rstand andenter enteraanew new!alue !alueof ofxxatatthe thebbottom inorder orde
Forecasts and "rror Anal#sis
Month
!emand #3 "an)08
38
%eriod03
Forecast
"rror
Absolute
S$uared
Abs %ct "rr
/
397.;9;
/08.9;3
/08.9;3
//;93./09
0.9;
6eb)08
90
9
398.545
7/.35
7/.35
8340.37
0.9/8
Mar)08
/
3
39;.09
84.578
84.578
;77./
0.907
'pr)08
3/8
394.90
)8.90
8.90
4;.709
0.094
May)08
304
5
395.0;8
)/7.0;8
/7.0;8
343.7;3
0.049
"un)08
90
4
393.7/4
)83.7/4
83.7/4
;0/.88/
0.350
"ul)08
90
;
399.;5
)89.;5
89.;5
488./8
0.35
'ug)08
9/4
8
39/.579
)/05.579
/05.579
///7.58
0.87
Sep)08
/78
7
390.97
)/99.97
/99.97
/788.745
0.4/8
:ct)08
995
/0
3/7.94;
)7.94;
7.94;
8884.3/8
0./7
No!)08
9;0
//
3/8./05
)8./05
8./05
93/./0/
0./;8
#ec)08
3/5
/9
3/4.73
)/.73
/.73
3.;;5
0.004
"an)07
/3
3/5.;8/
/98.9/7
/98.9/7
/40./48
0.987
6eb)07
95
/
3/.4/7
//0.38/
//0.38/
/9/8.07
0.940
Mar)07
93
/5
3/3.54
/07.5
/07.5
//777.;88
0.957
'pr)07
33/
/4
3/9.97
/8.;04
/8.;04
37.703
0.05;
May)07
3/8
/;
3//./39
4.848
4.848
;./48
0.099
"un)07
95
/8
307.7;0
)4.7;0
4.7;0
99/.07;
0.945
"ul)07
955
/7
308.808
)53.808
53.808
9875.980
0.9//
'ug)07
993
90
30;.44
)8.44
8.44
;/4.885
0.380
Sep)07
9/0
9/
304.83
)74.83
74.83
7307.043
0.57
:ct)07
933
99
305.39/
);9.39/
;9.39/
5930.3;
0.3/0
No!)07
9;8
93
30./57
)94./57
94./57
48.309
0.07
#ec)07
399
9
309.77;
/7.003
/7.003
34/.//
0.057
"an)/0
50
95
30/.835
/8./45
/8./45
9/759.7/4
0.397
6eb)/0
38
94
300.4;3
/3;.39;
/3;.39;
/8858.;75
0.3/
Mar)/0
3
9;
977.5//
/3.87
/3.87
/808;.93
0.3/0
'pr)/0
338
98
978.38
37.459
37.459
/5;9.953
0.//;
May)/0
33/
97
97;./84
33.8/
33.8/
//3.3;
0./09
500 400 300 200 100 0 0
5
10 Col
The seasonality is consistent but the slo positi!e performance trend line% the reg raw data is found to be? 4 5 (('..+ - 1' The Slope of the trend line is negati!e w seasonal index in "an and 6eb causes the negati!e slope.
"un)/0
95
30
974.09
)9.09
9.09
/;44.0/7
0./45
"ul)/0
94
3/
97.849
)30.849
30.849
759.55
0.//;
'ug)/0
93/
39
973.;00
)49.;00
49.;00
373/.959
0.9;/
Sep)/0
99
33
979.538
)48.538
48.538
47;.37
0.304
:ct)/0
93
3
97/.3;5
)8.3;5
8.3;5
930./;;
0./77
No!)/0
987
35
970.9/3
)/.9/3
/.9/3
/.;9
0.00
#ec)/0
335
34
987.05/
5.77
5.77
9///.304
0./3;
Total
0.000
934.8;
99;57.373
8.90
Average
'
*)'*+
*(2'.1*
'22.
7ntercept Slope
(('..+ -1'1*2
Bias
MA! S"
Forecast
2.)'.......+
MS"
MA%" .1'..
3; 8orrelation
-'1&
8oe9cient o determination
'2(
f this >f thisisiscausal causalregression regression to toforecast forecasty. y.
Regression
15 mn B
20
25
30
35
40
Linear (Column B)
e is not. $hile the /9)month mo!ing a!erage plotted a ession plotted a negati!e trend line. ' trend line based on the *26 ich would indicate that sales are declining o!er time. The high trend line on the unad+usted data to appear to ha!e a
6orecasted sales for each month of the next year. The gi!es the seasonal indices% the unad+usted forecasts found using the trend line% and the nal -ad+usted1 forecasts for the next year
0 1
2
3
4 "eriod
5
6
#nad$usted
7 %ea
sts and "rror Anal#sis "rror
="rror=
"rror>2
Abs %ct "rr
/3.3/5
/3.3/5
/;;.985
0.030
7.8;5
7.8;5
7;.50;
0.09
4.45;
4.45;
.390
0.0/4
0.857
0.857
0.;3;
0.003
)/.45/
/.45/
9.;9
0.005
/.39/
/.39/
/.;5
0.004
)5.;4;
5.;4;
33.94
0.09
)/.50
/.50
9.949
0.00;
);.479
;.479
57./49
0.037
)3.;97
3.;97
/3.708
0.0/;
)3.;78
3.;78
/.98
0.0/
)3.;45
3.;45
/./;
0.0/9
4.0;0
4.0;0
34.850
0.0/
9.//;
9.//;
.83
0.005
3.0/7
3.0/7
7.//;
0.00;
.05
.05
/4.357
0.0/9
0.85
0.85
0.;97
0.003
)/.09;
/.09;
/.055
0.00
/.484
/.484
9.8/
0.00;
)/./44
/./44
/.340
0.005
)/.7;4
/.7;4
3.70
0.007
)9.;00
9.;00
;.988
0.0/9
)./9/
./9/
/4.789
0.0/5
)4.30
4.30
/.39
0.090
)/./;
/./;
/.3;8
0.003
9.340
9.340
5.5;0
0.005
/.38/
/.38/
/.708
0.003
/.93/
/.93/
/.5/
0.00
.358
.358
/8.770
0.0/3
0.495
0.495
0.370
0.009
3./37
3./37
7.85/
0.0/9
0./;9
0./;9
0.030
0.00/
5.;0
5.;0
39.7;
0.094
0.330
0.330
0./07
0.00/
)/.3
/.3
9.08
0.005
)3.075
3.075
7.5;;
0.007
/8.//
/90./70
488./;5
0.373
0.503
3.337
/7.//4
0.0//
=ias
M'#
MSB
M'@B
SB
5.573
Season /0
Season //
Season /9
0.;9;
0.8;3
/.0/8
0.;53
0.877
/.0/
0.;85
0.73
/.083
0.;55
0.709
/.0;
onal
!
10 &d$us ted
11
12
Forecasting /9 seasons
!ata @eriod
!ecomposition: multiplicative
Enter Enterpast pastdemands demandsin inthe thedata dataarea. area.Do Donot notchange changethe thetime time period numbers! period numbers!
Enter Enter alpha alpha and and beta beta (between (between 00 and and 1, 1, enter enter the the past past demands demands in in the the shaded shadedcolumn columnthen thenenter enter aa starting orecast. I the starting orecast is not in the irst period then delete the error anal"sis starting orecast. I the starting orecast is not in the irst period then delete the error anal"sisor or all allrows rowsabo#e abo#ethe the starting starting orecast. orecast.
Enter Enter alpha alpha (between (between 00 and and 1, 1,enter enter the the past past demands demands in in the the shaded shaded column column then then enter enter aa starting starting orecast. orecast. II the the starting starting orecast orecast is is not not in in the the irst irst period period then then delete delete the the error error anal"sis anal"sisor orall allrows rows abo#e abo#ethe thestarting startingorecast. orecast.
5.30? Asing alpha of 0./ %M'# !alue is .333 while using alpha of 0.3 %M'# !alue is 3.4/8. =ased on this using alpha of 0.3 pro!ides a better forecast since it has a lower M'# !alue.
