Lecture 15 Homework
Earnings Per Share of Mecta Mining
0.50
0.45
eps
0.40
0.35
0.30
0.25
0.20
Quarter Q1
Year 2005
Q3
Q1
2006
Q3
Q1
2007
Q3
Q1
2008
Q3
Winters' multiplicative model
Data
Length
NMissing
Winters' Multiplicative Model for eps
eps
16.0000
0
Actual
0.6
Predicted
Forecast
Smoothing Constants
Alpha (level):
0.5
Gamma (trend):
0.2
Delta (seasonal): 0.2
Actual
eps
0.5
Accuracy Measures
MAPE: 5.01573
MAD: 0.01555
MSD: 0.00043
Predicted
Forecast
0.4
Smoothing Constants
Alpha (level): 0.500
Gamma (trend):0.200
Delta (season): 0.200
0.3
MAPE:
MAD:
MSD:
0.2
0
10
Time
Row
Period
Forecast
Lower
Upper
1
2
3
4
17
18
19
20
0.468334
0.349298
0.461985
0.563029
0.430235
0.306098
0.413152
0.508195
0.506433
0.392498
0.510818
0.617863
20
5.01573
0.01555
0.00043
Seasonal Indices
Period
Index
1
2
3
4
1.05953
0.779649
0.999138
1.16168
Reference Class is qtr3
Eps = earnings per share of Mecta Mining
Time = 1,2,3,4,5,…,16
qtr1 = 1 if the data is from quarter one
= 0 otherwise
qtr2 = 1 if the data is from quarter two
= 0 otherwise
qtr4 = 1 if the data is from quarter four
= 0 otherwise
0.425
eps
0.275
12.25
time
4.75
0.75
qtr1
0.25
0.75
qtr2
0.25
0.75
qtr4
0.25
7 5 .4 25
0. 2
0
5
5
4. 7 12 .2
5
0. 2
5
0. 7
5
0. 2
5
0 .7
5
0. 2
0 .7
5
Correlations (Pearson)
eps
0.779
0.000
time
qtr1
0.051
0.852
-0.188
0.486
qtr2
-0.595
0.015
-0.063
0.818
-0.333
0.207
qtr4
0.531
0.035
0.188
0.486
-0.333
0.207
time
No MC exists
qtr1
qtr2
-0.333
0.207
Regression Analysis
The regression equation is
eps = 0.232 + 0.0123 time + 0.0296 qtr1 - 0.0702 qtr2 + 0.0577 qtr4
Predictor
Constant
time
qtr1
qtr2
qtr4
Coef
0.23169
0.0123125
0.02962
-0.07019
0.05769
S = 0.01512
StDev
0.01072
0.0008451
0.01082
0.01072
0.01072
R-Sq = 97.4%
T
21.61
14.57
2.74
-6.55
5.38
P
0.000
0.000
0.019
0.000
0.000
R-Sq(adj) = 96.5%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
4
11
15
SS
0.095380
0.002514
0.097894
MS
0.023845
0.000229
F
104.34
P
0.000
Durbin-Watson statistic = 1.44
0----.74---1.93-----------------4
test is inconclusive => more work is needed
Regression Analysis
The regression equation is
eps = 0.196 + 0.0104 time - 0.0011 qtr1 - 0.0901 qtr2 + 0.0427 qtr4
+ 0.205 lag1
15 cases used 1 cases contain missing values
Predictor
Constant
time
qtr1
qtr2
qtr4
lag1
Coef
0.19605
0.010353
-0.00110
-0.09007
0.04274
0.2049
S = 0.01491
StDev
0.04956
0.003873
0.04062
0.03317
0.02470
0.3162
R-Sq = 97.9%
T
3.96
2.67
-0.03
-2.72
1.73
0.65
P
0.003
0.025
0.979
0.024
0.118
0.533
R-Sq(adj) = 96.7%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
5
9
14
SS
0.093160
0.002000
0.095160
Durbin-Watson statistic = 1.95
MS
0.018632
0.000222
F
83.85
P
0.000
Regression Analysis
The regression equation is
eps = 0.197 + 0.0105 time - 0.0892 qtr2 + 0.0434 qtr4 + 0.197 lag1
15 cases used 1 cases contain missing values
Predictor
Constant
time
qtr2
qtr4
lag1
Coef
0.19727
0.010452
-0.089218
0.043362
0.19665
S = 0.01414
StDev
0.01967
0.001318
0.009727
0.009029
0.08407
R-Sq = 97.9%
T
10.03
7.93
-9.17
4.80
2.34
P
0.000
0.000
0.000
0.001
0.041
R-Sq(adj) = 97.1%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
4
10
14
SS
0.093160
0.002000
0.095160
MS
0.023290
0.000200
F
116.45
P
0.000
all variables significant
close or greater than 2 => No AC
Durbin-Watson statistic = 1.94
Residuals Versus the Fitted Values
(response is eps)
0.02
Residual
0.01
0.00
-0.01
-0.02
0.2
0.3
0.4
0.5
Fitted Value
Predicted Values
Qtr1
Qtr2
Qtr3
Qtr4
MSD:
2009
2009
2009
2009
Fit
0.47327
0.38861
0.47254
0.54209
StDev Fit
0.01163
0.01112
0.01070
0.01114
.0020/15 = .000133
(
(
(
(
95.0% CI
0.44736, 0.49918)
0.36383, 0.41338)
0.44870, 0.49639)
0.51728, 0.56690)
(
(
(
(
95.0% PI
0.43248, 0.51407)
0.34852, 0.42869)
0.43303, 0.51206)
0.50198, 0.58220)