Guidelines for the analysis. HW3 Q2
ST512
Sum2 2011
1. Create a table that summarize each regression model considered
Model
Overall F test
RSquared
AdjRsq
Significant
Reg coeff.
2. Look at the residual plot for each model. Do the residuals look randomly distributed? Is
ther signs of heterogeneous variances?
3. Decide the best fit. Best looking residuals, high R squared, high Adj Rsq.
4. After selecting the best model, we run again this model to get the predicted in data set
feedp and plot the predicted and observed so that we can demonstrate the goodness of fit
of the selected model. Note that since Cu has only two distinct values, we plot two curves,
one for each level of Cu. What are the regression equations for these two curves? Note that
they are parallel which means that the intercept for Cu=0 is different from Cu=400. These
two equations should show that.
5. 5 Finally, let’s look at the residual plot for the best fitted model once more. Do you see
anything out of order? What about a point far away from the rest? Is it an outlier?
6. What changes should you expect if we drop the supposed outlier? Compare the average
for Cu=0 vs Cu=400, and then look at significance for X2 in the best fit? How much the
means change if we drop the outlier?
N
Cu
Obs
N
Mean
Std Dev
Minimum
Maximum
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0
30
30
2.7373333
1.0687987
1.3000000
5.0600000
400
30
30
2.8193333
1.1028394
1.1400000
5.0900000
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Outlier is identified
Obs
Cu
52
0
Additive
100
Feed
Eff
Ratio
3.87
x1
x2
100
0
x3
x4
10000
1000000
x5
0
x6
x7
0
0
pred
resid
4.76733
-0.89733
New calculation for means without outlier
Analysis Variable : FeedEffRatio
N
Cu
Obs
N
Mean
Std Dev
Minimum
Maximum
_________________________________________________________________________________________
0
30
29
2.6982759
1.0657059
1.3000000
5.0600000
400
30
30
2.8193333
1.1028394
1.1400000
5.0900000
7.
models to choose from
The REG Procedure
Model: x1_x3_x4
Dependent Variable: FeedEffRatio
Number of Observations Read
60
Number of Observations Used
60
Analysis of Variance
Source
DF
Sum of
Squares
Mean F Value
Square
Model
3
66.77523
22.25841
Error
56
1.72460
0.03080
Corrected Total
59
68.49983
722.76
Root MSE
0.17549
R-Square 0.9748
Dependent Mean
2.77833
Adj R-Sq
Coeff Var
6.31635
Pr > F
<.0001
0.9735
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard t Value Pr > |t|
Error
Intercept
1
1.45560
0.05438
26.77
<.0001
x1
1
0.05411
0.00528
10.24
<.0001
x3
1
-0.00115
0.00013124
-8.75
<.0001
x4
1
0.00000942
8.617338E-7
10.93
<.0001
The REG Procedure
The REG Procedure
The REG Procedure
models to choose from
The REG Procedure
Model: x1_x3_x2
Dependent Variable: FeedEffRatio
Number of Observations Read
60
Number of Observations Used
60
Analysis of Variance
Source
DF
Sum of
Squares
Mean F Value
Square
Model
3
63.19591
21.06530
Error
56
5.30393
0.09471
Corrected Total
59
68.49983
Pr > F
222.41
<.0001
Root MSE
0.30775
R-Square 0.9226
Dependent Mean
2.77833
Adj R-Sq
Coeff Var
0.9184
11.07696
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard t Value Pr > |t|
Error
Intercept
1
1.64068
0.09674
16.96
<.0001
x1
1
0.00248
0.00415
0.60
0.5518
x3
1
0.00026522
0.00003982
6.66
<.0001
x2
1
0.00020500
0.00019865
1.03
0.3065
The REG Procedure
The REG Procedure
The REG Procedure
models to choose from
The REG Procedure
Model: x1_x3_x2_x5_x6
Dependent Variable: FeedEffRatio
Number of Observations Read
60
Number of Observations Used
60
Analysis of Variance
Source
DF
Sum of
Squares
Mean F Value
Square
Model
5
63.22065
12.64413
Error
54
5.27918
0.09776
Corrected Total
59
68.49983
129.34
Root MSE
0.31267
R-Square 0.9229
Dependent Mean
2.77833
Adj R-Sq
Coeff Var
Pr > F
<.0001
0.9158
11.25387
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard t Value Pr > |t|
Error
Intercept
1
1.65857
0.12673
13.09
<.0001
x1
1
0.00267
0.00596
0.45
0.6565
x3
1
0.00025786
0.00005721
4.51
<.0001
x2
1
0.00011554
0.00044807
0.26
0.7975
x5
1
-9.11607E-7
0.00002107
-0.04
0.9657
x6
1
3.683036E-8
2.022777E-7
0.18
0.8562
The REG Procedure
The REG Procedure
The REG Procedure
models to choose from
The REG Procedure
Model: x1_x3_x4_x2
Dependent Variable: FeedEffRatio
Number of Observations Read
60
Number of Observations Used
60
Analysis of Variance
Source
DF
Sum of
Squares
Mean F Value
Square
Model
4
66.87609
16.71902
Error
55
1.62374
0.02952
Corrected Total
59
68.49983
Pr > F
566.31
<.0001
Root MSE
0.17182
R-Square 0.9763
Dependent Mean
2.77833
Adj R-Sq
Coeff Var
6.18434
0.9746
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard t Value Pr > |t|
Error
Intercept
1
1.41460
0.05768
24.52
<.0001
x1
1
0.05411
0.00517
10.46
<.0001
x3
1
-0.00115
0.00012850
-8.93
<.0001
x4
1
0.00000942
8.43723E-7
11.16
<.0001
x2
1
0.00020500
0.00011091
1.85
0.0699
The REG Procedure
The REG Procedure
The REG Procedure
Selected model y= x1 x3 x4 x2
The REG Procedure
Model: x1_x3_x4_x2
Dependent Variable: FeedEffRatio
Number of Observations Read
60
Number of Observations Used
60
Analysis of Variance
Source
DF
Sum of
Squares
Mean F Value
Square
Model
4
66.87609
16.71902
Error
55
1.62374
0.02952
Corrected Total
59
68.49983
Pr > F
566.31
<.0001
Root MSE
0.17182
R-Square 0.9763
Dependent Mean
2.77833
Adj R-Sq
Coeff Var
6.18434
0.9746
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard t Value Pr > |t|
Error
Intercept
1
1.41460
0.05768
24.52
<.0001
x1
1
0.05411
0.00517
10.46
<.0001
x3
1
-0.00115
0.00012850
-8.93
<.0001
x4
1
0.00000942
8.43723E-7
11.16
<.0001
x2
1
0.00020500
0.00011091
1.85
0.0699
Selected model y= x1 x3 x4 x2
The REG Procedure
Model: x1_x3_x4_x2
Dependent Variable: FeedEffRatio
Selected model y= x1 x3 x4 x2
Ob
s
52
C Additiv
u
e
0
100
FeedEffRat
io
x1
x
2
x3
x4
x
5
x
6
x
7
pred
resid
3.87
10
0
0
1000
0
100000
0
0
0
0
4.7673
3
0.8973
3