To improve the model, we would like to delete those
observation and recompute the
line.
Step 5:
Checking the validity of the assumptions:
We made the assumptions that the all the error terms are identically and independently
normally distributed with mean 0 and common variance sigma –square.
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View Full DocumentResidual
Percent
5.0
2.5
0.0
2.5
5.0
99
90
50
10
1
Fitted Value
Residual
120
90
60
30
0
5.0
2.5
0.0
2.5
5.0
Residual
Frequency
6
4
2
0
2
4
6
6.0
4.5
3.0
1.5
0.0
Observation Order
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
5.0
2.5
0.0
2.5
5.0
Normal Probability Plot of the Residuals
Residuals Versus the Fitt ed Values
Histogram of t he Residuals
Residuals Versus the Order of the Data
Residual Plots for Weight
Interpretation:
1.
the graph on top left checks the assumption of normality of error terms. In this
case we see that most of the points are clustered around blue line indication that
the error terms are approximately normal. Thus our assumption of normality is
valid.
2.
The graph on top right plots the error terms against the fitted values. There are
approximately half of them are above and half are below the zero line indicating
that our assumption of error terms having mean zero is valid.
3.
On the same graph we see the clear cyclic pattern among the error terms
indicating that they are violating the assumption of independence of error. Error
terms are not independent. May be there is another factor present in this
example which we need to find out.
4.
The bottom left graph again reemphasizes the normality assumption. Though
our sample size is just 15.
5.
The bottom right graph is also important in this case because data is a time
series and order of the data is important. A clear cyclic pattern indicates that
error terms are dependent on the time variable.
Step VI:
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 Spring '13
 MRR
 Math, Statistics, Regression Analysis, Errors and residuals in statistics, error terms, R Sq, ne Pl ot

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