Statistics Summary Report

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Statistics Summary Report
Descriptive Statistics
To establish the characteristics of the variables in the dataset, summary statistics were
obtained, and the results were as shown in Table 1 (Appendix). Table 1 can be used to examine
the variability of each variable in the study by comparing its mean to the corresponding standard
deviation. From statistical theory, if the mean of a variable is higher than its standard deviation,
then there exists a lower variability of variables within the mean. On the contrary, a standard
deviation that exceeds the mean implies that there is a higher variation. From the table, it is
evident that the mean value of each variable exceeded the standard deviation; hence there was
low variability in the recorded values. In particular, the means (and standard deviations) of each
of the variables were: gender 1.54 (0.52), comfort 4.23 (1.031), ethnicity 2.35 (1.257), insurance
1.42 (0.497), race 2.63 (1.349), ages 27.26 (6.349), and index 10.7436 (2.86237).
Correlation Analysis
In this study, the variable gender was transformed into a numeric value. Pearson’s
coefficient can be adopted in analyses that involve numeric data (Akoglu, 92). Since the
remaining variables were numeric, Pearson’s correlation coefficient was adopted, and the
outcomes were summarized in Table 2 (Appendix). From the table, none of the possible pairs of

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variables have a correlation coefficient that is greater than 0.8; hence, it can be deduced that
there is no multicollinearity. Also, Table 2 indicates that there exist weak associations between
pairs of variables since none of the coefficients is equal to or greater than 0.5.
Regression Analysis
Linear regression a reliable model for exploring the association between two or more
variables (Aggarwal & Ranganathan, 101). Ordinarily, one variable is regarded as a result,
whose occurrence is contingent on two or more other variables. Consequently, regression
analysis is a statistical approach for exploring the extent to which the dependent variable is
affected by some identified independent predictors (Aggarwal & Ranganathan, 101).
Denoting the outcome as y, the corresponding predictors can be denoted by x1, x2, ..., xn.
The linear model that can be used to explain the association between the former and the latter
categories of variables is of the form:
y = β + β₀ 1x1 + β2x2 + ... + βnxn (Li et al., 926).
Where β is a constant and β₀ 1, β2, ... βn are the corresponding coefficients of regression for x1, x2,
..., xn, respectively (Li et al., 926).
The values of β1, β2, ... βn provide reliable metrics for examining how variables are related
in terms of direction and significance. The sign of the coefficient can be either positive or
negative. A positive sign implies that as the value of the predictor rises, then that of the outcome
increases. On the other hand, a negative sign has two implications; when the value of the
predictor rises, that of the outcome declines, and when the value of the independent variable
reduces, then the value of the outcome increases.

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In the current study, if the sign of the coefficient is positive, then an increase in the value
of the variable leads to a rise in the observed index. Conversely, if the sign is negative, then a
rise in the predictor leads to a reduction in the observed index. However, if the value of the
coefficient is 0, then there exists no association between the variable and the value of the index.
Consequently, the hypothesis that a predictor, j, has an insignificant effect on the index
(β̂j = 0) can be tested against the alternative that it has a significant impact on the index (β̂j ≠ 0).
To examine the association between the index as the outcome and gender, race, and
comfort as predictors, the linear regression model was adopted. Particularly, a simple regression
model was formulated with gender as the independent variable, and the result was as
summarized in equation (1):
Index = 8.857 + 1.226*Gender (1)
Subsequently, a multiple linear regression model was fitted to the data with gender as the
controlling variable. The result was as summarized in equation (2):
Index = 5.175 + 1.386*Gender – 0.037*Race + 0.835*Comfort (2)
From equation (2), there exists a positive association between the index and the two variables;
gender and comfort. On the contrary, there is a positive relationship between index and race.
Findings
Table 3 (Appendix) provides a summary of the findings of the analysis. From the table,
the R-squared value for the overall model was 0.46. This metric evaluates the extent to which the
dependent variable is affected by its predictors in a study (Hamilton et al., 152). Specifically,
approximately 46% of the variation in the index was attributable to the variation in gender, race,