Conclusions
The non-interaction model looked like this:
Current SCC = 33159.253(Injection Binary) - 15598.810(Non-injected binary)
-473.830(Age) - 0.423(Average production) +
1.146(previous SCC) + 6722.368(body score)
To illustrate the significance of this model, it is helpful to use an imaginary
situation. If two animals had the same age, average production, previous SCC,
and body score, the only difference in their predicted scores would come from the
coefficients of the two binary variables. If the animal had been treated with
BST, there would be a ³1² as the value for the ³Injection² predictor and a ³0² as
the value for the ³non-injected² predictor. If the other animal had not been
injected, it would have a value of ³0² as the ³Injection² predictor and a value
of ³1² as the ³non-injection² predictor. Therefore, there would be around a
48,748.063 somatic cell difference between the predicted SCC of the injected and
non-injected animals. This value was obtained from model one (see appendix), and
the t-test applied to the injection binary gave a value of .012, which means the
hypothesis that there is no difference in the scores is rejected. This means
that there is a significant difference between the predicted scores of the
experimental and control groups while controlling for other measurable factors.
This was the original model, and was used to gauge the predicted difference
in somatic cell count between the two groups. There were other questions that
had to be solved as well, however.
The first additional question that arose following the first regression model
was: are the co-variables necessary in analyzing the observed data? This
question was answered with the following model:
Current SCC = 243904.118(Constant) + 89751.152(Non-injected)
The t-test value of the binary variable was .266, and this value accepts the
hypothesis that there is no significant difference between the means of the two
groups. Therefore, it can be concluded that the co-variables are necessary for
accurate prediction because there was a significant difference between the two
groups with the co-variables in the model, but when they were removed there was
not a significant difference.
The next question to be looked at concerned the variables used as
co-variables in the experiment. Were they all necessary to ensure accurate
prediction? Based upon the t-tests applied to all the variables in the original
model, it was determined that the pre-test SCC was the only significant factor
in determining an animal¹s response to BST. It was significant at the .05 level,
with a value of .000. (see appendix) In all models, the only variable that was
found to be significant in predicting the response variable was the pre-test
value.
The final question that came up in analyzing the data was a question of
interaction. This question was solved with a command file that executed an
F-test on the observed data. The F-test failed to reject the hypothesis that
there was no interaction. The probability that there is interaction was .390.
This is not significant, and the interaction model (model 3, see appendix) is
rejected.
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