Patrick Mike Aquino
BSMA 2-2
STATISTICAL ANALYSIS with SOFTWARE APPLICATION
ASSESSMENT NO. 5
1. Insurance companies are known to charge different insurance rate for different categories of
its customers, such as the age of the insured. Table 1 shows the average insurance premium,
the adjusted insurance premium, and the average insurance claim grouped by age.
a. Calculate the correlation coefficient between the premiums (average premium; adjusted
premium) and claim values.
b. Interpret the results of the correlation coefficients.
Analysis
To measure the strength and direction of the relationship between average premium, adjusted
premium, and claim values–pairwise, the Pearson Product Moment Correlation coefficient was
conducted. The correlations procedure from Excel Data Analysis was utilized to calculate the
statistic of correlation coefficients. Also, to assess the strength of the relationship of the
coefficients, criteria of ranges was also used. As contemplated by Mindrila (n.d.), from her book
The Basic Practice of Statistics (6th ed.) under Scatterplots and correlation:
Firstly, the correlation between
Average premium and Adjusted
premium was approximately -0.79
delineating that these insurance
rates have a negative-inverse
relationship; as one variable increases, the other variable decreases. Also, the absolute value of
r reflects that the strength of the correlation is strong. The coefficient indicates that the Average
premium and Adjusted premium have a strong negative correlation. Thus, as Average premium
decreases, Adjusted premium increases based on the ascending interval of the ages of the clients.
Next, Average premium and
Average claims prove their linear
relationship as these insurance
rates scored 0.98, showing they
have
a
positive-direct
correlation. The strength of the relationship based on the absolute value of r is strong. For
instance, the comparison between ages 1-3 receiving Average premium and Average claims of
P9,720 and P36,670, respectively and ages 58-60 with P890 and P13, 890, shows younger clients
have higher premiums and claims than those who are in senior years. Thus, as Average premium
decreases, Average claims also decrease according to the ages of the clients of the insurance
company.
Lastly, the correlation between
Adjusted premium and Average
claims was rounded off as -0.82
which is the least value among the
coefficients. This means that these
insurance rates have a negative-inverse correlation and the strength of their relationship is
strong. It is almost the same with the relationship of Average premium and Adjusted premium,
however their coefficient is approximately ahead of 30 percent. Thus, as Average claims decrease,
Adjusted premium increases based on the ascending interval of the ages of the clients.
Reference
Mindrila, D. (n.d.) Scatterplots and Correlation. The Basic Practice of Statistics (6th ed.).
Retrieved from
https://www.westga.edu/academics/research/vrc/assets/docs/scatterplots_and_correlation
_notes.pdf