An insurance firm wanted to find the effect of driving experience and number of driving violationson 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 5 14 1 F 60 13 3 M 35 19 0 M 46 9 1 F 99 3 5 F 43 16 1 M 57 11 3 F 74 5 2 M 38 14 0 F 50 6 1 F 63 10 3 M 97 4 6 M 55 8 2 F 73 5 8 F 80 9 8 M 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. Construct a 99% confidence interval for the coefficient of gender c. 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 violationson 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 |
| 5 | 14 | 1 | F |
| 60 | 13 | 3 | M |
| 35 | 19 | 0 | M |
| 46 | 9 | 1 | F |
| 99 | 3 | 5 | F |
| 43 | 16 | 1 | M |
| 57 | 11 | 3 | F |
| 74 | 5 | 2 | M |
| 38 | 14 | 0 | F |
| 50 | 6 | 1 | F |
| 63 | 10 | 3 | M |
| 97 | 4 | 6 | M |
| 55 | 8 | 2 | F |
| 73 | 5 | 8 | F |
| 80 | 9 | 8 | M |
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. Construct a 99% confidence interval for the coefficient of gender
c. Using the 1% significance level, can you conclude that the coefficient of gender is different from zero?
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