Parametric Statistics: Descriptive Tools for Sun Coast Data

MBA 5652-unit IV scholarly activity
Student Name
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Introduction
Parametric statistics is a branch of data analysis that takes into account the assumption
that a sample data is obtained from a population that can significantly be modeled using a
probability distribution with a fixed set of parameters. In this task the objective is to describe the
Sun Coast data using descriptive tools. For data to be summarized using the parametric tools it is
assumed to adhere to a number of assumptions (Murphy, 2012). Some of the assumptions are
listed below;
The sample was obtained randomly and are independent of each other
The data is normally distributed
The sample data contains no outliers
The data have a homogeneous variance
The sample size is large enough to warrant a parametric test
The data will be described using the excel tool pack. For each of the excel tab an appropriate tool
will be used to describe the observations and an appropriate interpretation made.
Correlation
Under this description, the interest is to analyze the association between two sets of data
(Mahdavi, 2013 (). In this case will apply the excel tool pack to study the relationship between
microns and the mean annual sick days per employee. The result is summarized by the tale
below
Correlation
microns mean annual sick days per employee
microns 1
mean annual sick days per employee -0.715984185 1
From the table the value of the correlation is -0.71598. This is interpreted as a strong
negative correlation, an increase in the number of microns will have a negative impact on the
mean annual sick days per employee.
Simple linear regression
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Simple linear regression is a model that is used to predict the values of the dependent variable
given the independent variable. In this study the independent variable is the lost time hours while
the dependent variable is the safety training expenditure (Rencher & Christensen, 2012). The
study objective is to evaluate how the changes in the lost time hours do impact the safety training
expenditure. Using the excel tool pack the model developed is as described in the table below.
SUMMARY OUTPUTRegression Statistics
Multiple R 0.939559324
RSquare 0.882771723
Adjusted RSquare 0.882241279
Standard Error 161.302987
Observations 223
ANOVA
df
SS
MS
F Significance F
Regression 1 43300521.43 43300521.43 1664.210687 7.6586E-105
Residual 221 5750122.451 26018.65362
Total 222 49050643.88
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 1753.602133 30.36296223 57.75464594 2.5647E-135 1693.764135 1813.440132 1693.764135 1813.440132
lost time hours -6.157394365 0.150935993 -40.79473848 7.6586E-105 -6.45485242 -5.85993631 -6.45485242 -5.85993631
According to the developed model the two variables are described by the relationship
y=1753.60−6.1574 x
Where y is the safety training expenditure and x the lost time hours. The value of the multiple R
is given as 0.9396, This is interpreted as a strong positive association. A change in the values of
lost time house do increase the values of the safety training expenditure. In addition, the R square
value of 0.8828 means that 88.28% of all the changes in the values of y are as a result of the
changes in the values of x. looking at the predictive equation given above the intercept of
1753.60 shows that in case there is no time lost, the safety expenditure will be 1753.60.
The relevance of the model is described by the F statistics, a value less than 0.05 as in the
model proves that at a 95% level of significance, the model is appropriate in estimating the
safety training expenditure.
Multiple linear regression
The model summary is highlighted in the table below
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