An insurance firm wanted to find the effect of driving experience and number of driving violations on the motor insurance premium. A random sample of 15 drivers insured with the company and having similar motor insurance policies was selected. The schedule below lists the monthly motor insurance premiums (in Ghana Cedis) paid by these drivers, their driving experience (in years), and the number of driving violations that each of them has committed during the past five years. Monthly Premium (GHS) Driving experience (Years) Number of driving violations (past 5 years) Gender 58 14 1 Female 60 13 3 Male 35 19 0 Male 46 9 1 Female 99 3 5 Female 43 16 1 Male 57 11 3 Female 74 5 2 Male 38 14 0 Female 50 6 1 Female 63 10 3 Male 97 4 6 Male 55 8 2 Female 73 5 8 Female 80 9 8 Male Using R (or any other statistical software package), a. Find the regression of monthly motor insurance premium on the years of driving experience, the number of driving violations, and the gender of drivers. Using the output obtained to answer the following questions: b. Write the estimated multiple regression c. Explain the meaning of the estimated regression coefficient of the independent variable gender d. What are the values of the standard deviations of errors, the coefficient of multiple determination, and the adjusted coefficient of multiple determination? e. What is the predicted motor insurance premium paid per month by a male driver with 10 years of driving experience and 2 driving violations? f. What is the predicted motor insurance premium paid per month by a female driver with 10 years of driving experience and 2 driving violations? g. Construct a 99% confidence interval for the coefficient of gender h. Using the 1% significance level, can you conclude that the coefficient of gender is different from zero?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
An insurance firm wanted to find the effect of driving experience and number of driving violations
on the motor insurance premium. A random sample of 15 drivers insured with the company and
having similar motor insurance policies was selected. The schedule below lists the monthly motor
insurance premiums (in Ghana Cedis) paid by these drivers, their driving experience (in years),
and the number of driving violations that each of them has committed during the past five years.
Monthly
Premium
(GHS)
Driving
experience
(Years)
Number of
driving
violations (past
5 years)
Gender
58 14 1 Female
60 13 3 Male
35 19 0 Male
46 9 1 Female
99 3 5 Female
43 16 1 Male
57 11 3 Female
74 5 2 Male
38 14 0 Female
50 6 1 Female
63 10 3 Male
97 4 6 Male
55 8 2 Female
73 5 8 Female
80 9 8 Male
Using R (or any other statistical software package),
a. Find the regression of monthly motor insurance premium on the years of driving
experience, the number of driving violations, and the gender of drivers.
Using the output obtained to answer the following questions:
b. Write the estimated multiple regression
c. Explain the meaning of the estimated regression coefficient of the independent variable
gender
d. What are the values of the standard deviations of errors, the coefficient of multiple
determination, and the adjusted coefficient of multiple determination?
e. What is the predicted motor insurance premium paid per month by a male driver with 10
years of driving experience and 2 driving violations?
f. What is the predicted motor insurance premium paid per month by a female driver with 10
years of driving experience and 2 driving violations?
g. Construct a 99% confidence interval for the coefficient of gender
h. Using the 1% significance level, can you conclude that the coefficient of gender is different
from zero?
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