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model is very close to that of the corrected estimate
of the true population.
According to ANOVA both the F-ratio (F = 9.667,
p < 0.003 and F = 5.729, p < 0.005) are significant
and unlikely to have happened by chance. This
indicates that the improvement due regression model
is greater than inaccuracy within the model.
Therefore, the ability to predict the outcome variable
will be significantly improved by the model, and the
model is a significant fit of the data overall due
to the significant F-ratio (significance value is less
than 0.05).
The result also shows that 30.4% (R square =
0.304) of the variance in TAISUS is explained by the
model. This includes the TPU (R square = 0.294),
and TPEOU (R square = 0.010). Adjusted R square
is 0.292, which shows shrinkage of
1.2% =
. This means that the
percentage of the variance explained by the model in
not so much away from the corrected estimate of the
true population. TPU causes R
2
to change from zero
to 0.294, which this change in the amount of
variance explained gives rise to a significant F-ratio
of 46.751 with a probability of less than 0.001.
Addition of TPEOU causes R
2
to increase by 0.010,
and the change in the amount of variance that it can
explain gives rise to an F-ratio of 1.5430, which is
not significant with a probability less than 0.217.
According to ANOVA, both the F-ratio for model 1
(F = 46.751), and F-ratio for model 2 (F = 24.261)
are very significant (p < 0.001 for both the cases),
and therefore, it is unlikely to have happened by
chance. These results show that both models 1 (with
TPU as the independent variable) and model 2 (with
addition of TPEOU as second independent variable)
are significant fit of the data overall, and they
significantly improves our ability to predict the
outcome variable, because the F-ratios are
significant (probability less than 0.05).
5.2.3 Model parameters
Summary of the regression model indicates that
the TSQ, with standardised beta of 52.3%, makes a
stronger unique contribution in explaining TPU,
when the variance explained by the TSE is
controlled for. The standardised beta value for TSE
is showing a less contribution with 40.5%. Further,
TSQ and TSE both with a significance value of
0.001 are making a unique, and statistically very
significant, contribution to the prediction of the TPU
scores. This also means no overlap between TSQ
and TSE.
Confidence interval for TSQ is between 0.452
and 0.972, and for TSE is between 0.148 and 0.411,
which both are relatively narrow, and do not cross
Zero. This indicates that the parameters for these
variables are significant and they have positive
relationships.
Further, the zero-order correlations are 0.504 for
TSQ and 0.380 for TSE. The part correlation
coefficients are 0.523 for TSQ and 0.405 for TSE,
indicating that TSQ uniquely explains 27% (0.523
2
)
and TSE uniquely explains 16% (0.405
2
) of the
variance in TPU scores.
In the case of TPEOU, TSQ with β value of 0.367
has 36.7% a unique contribution in explaining
TPEOU, when the variance explained by the TSE is
controlled for. The TSE with β value of 0.150 has
less contribution with 15.0%. The results also
indicate that TSQ with a significance value of 0.002
making a unique, and statistically very significant,
contribution to the prediction of the TPEOU scores.
However contribution of TSE with significance
value of 0.198 is not significant that may be due to
some degrees of overlap between TSQ and TSE.
Confidence interval for TSQ is between 0.219
and 0.955, which is relatively narrow and does not
cross zero. Confidence interval for TSE is between -
0.065 and 0.308, which is narrow but it does cross
zero. This indicates that only the parameters for TSQ
are significant, and it has a positive relationship, but
the parameters for TSE are not significant and it has
a negative relationship.
The zero-order correlation for TSQ is 0.360 and
for TSE is 0.132. These values correspond to the
same values of the Pearson correlation coefficients.
TSQ (with part correlation coefficients of 0.367),
and TSE (with part correlation coefficients of 0.150)
each uniquely explain 13.5% (0.367
2
), and 2.3%
(0.150
2
) of the variance in TPEOU scores,
respectively, when the effects of the other predictors
on the outcome are controlled for.
TPU with β value of 49.9% makes a stronger
unique contribution in explaining TAISUS, when the
variance explained by the TPEOU is controlled for.
The standardised beta value for TPEOU is only
showing a contribution of 10.8%. TPU with a
significance value of 0.001 is making a unique and
very significant contribution to predict TAISUS
scores. But TPEOU with significance value of 0.217
does not make such a unique and statistically
significant contribution to TAISUS scores
prediction, which may be due to some overlap
between TPU and TPEOU.
Confidence interval for TPU is between 0.449
and 0.921, which is relatively narrow and does not
cross zero. The range of confidence interval for
TPEOU is between -0.75 and 0.325, which despite
being narrow, it crosses zero. These confidence
intervals indicate that the parameters for TPU are