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# Problem Analysis Assignment PDF

Added on - 14 Dec 2021

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Problem Analysis
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Problem Analysis2
Factor Analysis
1.
The table of communalities shows how much of the variance to be considered for further
analysis. The communality value needs to be more than 0.5 for consideration. However, the
variables Pers17, Pers20 and Pers38 were below 0.5 and therefore they should be flagged.
2.
The reliability of the items was checked through the reliability statistics table. The
Cronbach’s alpha yield a result of 0.503. This suggest that there is a relatively high level of
internal consistency of the items. However, from the KMO and Bartletts’ Test table, it can be
seen that since theKaiser-Meyer-Olkin (KMO) is more than 0.6, and the Bartlett’s test is also
significant, it can be concluded that the correlation matrix is not an identity matrix.
3.
a.
From the total variance explained table, it is evident that 10 factors will be extracted. The 10
factors are the only ones which meet the cut-off criterion of the extraction method. Evidently,
these are the only factors with eigenvalues greater than 1. The 10 factors also accumulatively
account for 57.53%of the variance in the items' variance-covariance matrix. On the other
hand, all the remaining factors are not significant.
b.
The table named Component matrix shows the loadings of the 44 variables on the ten
extracted factors. Clearly, it can be seen that some of the items did cross-load. For example
pers13 (1 and 4), pers33 (1 and 9), and pers38 (1 and 10). The cross loading of below .3 will
be ignored since they were suppressed. However, items with cross-loading with above 0.3
were eliminated.
4.
After the factor analysis, the next step is assigning a score to each component for each
participant. Questions which are strongly loaded to a particular component whill be given
scores that reflect the subjects of those questions. The scores can be further used for further
analyses such as multiple regression.
Correlational analysis
1.
Influential cases is the presence of outliers. Influential cases need to be checked since their
presence greatly affects the line of regression’s slope and the also the coefficient o
determination.
Problem Analysis3
2.
The first assumption for linear regression is that the dependent variable should be measured
on a scale that is continuous. The dependent variable, resilience mean, is continuous in nature
with a mean of 3.6 and a standard deviation of 0.66. Hence, the first assumption has been
met.
The second assumption for the regression is that there should be two or more independent
variables which can either be categorical or continuous. The second assumption has been met
since in this case, the independent variables mindfulness mean, narcissism mean and
conscientiousness mean are continuous in nature.
The third assumption for linear regression is that there should be an independence of
observations. From the Durbin-Watson statistic on the model summary table, it can be seen
that the statistic is 1.879. Since the statistic is between 1.5 and 2.5, it can be anticipated that
there is no first order linear auto-correlation in the multiple linear regression data.
The forth assumption is that the data must not show multicollinearity. From the coefficients
table, it can be seen that the VIFs are between 1 and 10. Thus, it can be concluded that the
forth assumption has been met since there is no multicollinearity.
The fifth assumption is that the residuals should be approximately normally distributed. From
the histogram, it is evident that this assumption has been met since the residuals can be seen
to be approximately normally distributed.
3.
From the coefficients table, it can be seen that all the predictors (mindfulness mean,
narcissism mean and conscientiousness mean) significantly predict resilience since their p-
values are less than 0.05.
4.
a.
The relationship being tested when mindfulness predicts resilience via conscientiousness is
the interaction effect.
b.
Table 1: Total, Direct, and indirect effects of X on Y  