Individual Descriptive Report BUSI 650: Statistical Analysis of Car Insurance Premiums and Age Groups

QUESTION

Your Descriptive Project will consist of researching one and two variable data to answer a topic question, which you will create.

The written report is to be completed in Microsoft Word and all mathematical calculations are to be completed in Microsoft Excel. Both files are to be submitted electronically through the hand-in folder.

Written Report Format

Your report should have the following headings and each bullet should be contained under that heading:

Title Page (1 page)

• Include title of your project, your name, my name, course code and due date.
• Straight forward; clear, concise, to the point.

Table of Contents (Approx. 0.5-1 page)

• Listing of each section in your project.
• Using main categories with sub-categories could be useful.

Introduction (Approx. 0.5-1 page)

• A paragraph describing the purpose and focus of your statistics project as well as why you chose this topic.
• Introduce your main topic question. Be general to allow for as many possible sub-questions as possible.  For example,
  • Why do teenagers pay so much for car insurance?”
• Introduce some sub-questions that you will use to help you research your main topic question. The problems may evolve slightly throughout the life of your project.  For example,
  • What is the relationship of death rates for various age groups?
  • What is the relationship between collisions and various age groups?
  • What is the relationship between insurance rates and age?
• Make a hypothesis as to what the outcome of your research will be. This is just an educated guess, so it is acceptable if you end up proving yourself wrong by the end of the report.

Analysis (Approx. 3 or more pages)

• Measures of Central Tendency
  • Mean, median and mode must be calculated at least once each in your excel file.
  • At least two measures of central tendency must be used for a purpose and explained in report.
• Measures of Spread
  • At least four measures of spread (standard deviation, variance, kurtosis, z-score, percentiles) must be calculated in your excel file and used for a purpose with an explanation in your report.

• Pivot Table Analysis
  • At least one pivot table analysis is explained properly with numbers and charts to prove hypothesis

• Linear Regression, Correlation coefficient r
  • Least-squares method must be used at least once to find a linear regression equation. At least one line of best fit must be used on a scatter plot and visually classified
  • Explain your answers
• Variables
  • As variables are used/manipulated throughout your report, you must describe them as discrete, continuous or categorical and identify which variables are independent or dependent.
  • Variables should also be labeled on each graph correctly.
• Cause and Effect
  • The relationship/factor (cause and effect, common cause factor, reverse cause-and-effect relationship, etc.) between at least one pair of variables must be identified and explained
• Graphs
  • Multiple scatter plots as well as at least one other type of graph (minimum) must be used throughout the report.
  • Be sure to only include graphs which you discuss in the report & serve a purpose.

Conclusion (Approx. 0.5-1 page)

• Draw conclusions by summarizing your findings and directly relate them to your main topic question and sub-topic questions.
• State whether your hypothesis was correct or incorrect with justification.
• Note at least one bias which could have arisen through your study and identify with justification (sampling, judgments, assumptions etc.).

Appendices Excel File (# of pages depends on amount of data collected)

• Your separate Excel file used to collect all of your data, calculate, graph and analyze will be submitted at the same time as your written report.

References (1 page or more)

• Cite all of your information using the APA format. A summary of the APA format can be found at: General Format // Purdue Writing Lab
• Be sure to correctly cite all of your data throughout your report to avoid plagiarism issues.

ANSWER

Introduction

The purpose of this statistics project is to investigate the relationship between car insurance premiums and age groups. Car insurance premiums often vary significantly based on the age of the policyholders, and we aim to explore the underlying patterns and factors influencing these variations. By analyzing one and two-variable data, we seek to answer the main topic question: “What is the relationship between car insurance premiums and age groups?” To facilitate our research, we will consider the following sub-questions:

• What is the distribution of car insurance premiums across different age groups?
• How do measures of central tendency (mean, median, mode) vary for car insurance premiums in different age groups?
• What is the spread of car insurance premiums for each age group (standard deviation, variance, kurtosis, z-score, percentiles)?
• Is there a significant correlation between age and car insurance premiums?
• Can we identify any cause-and-effect relationships between age groups and insurance rates?

Hypothesis: Based on preliminary insights, we hypothesize that car insurance premiums will generally decrease with increasing age. We anticipate that older age groups will have lower insurance rates due to their perceived lower risk and experience as drivers. However, we remain open to discovering any unexpected trends in the data.

Analysis

Measures of Central Tendency: We will calculate the mean, median, and mode of car insurance premiums for each age group using Microsoft Excel. These measures will help us understand the typical insurance rates for different age categories.

Measures of Spread: In the Excel file, we will calculate various measures of spread, including standard deviation, variance, kurtosis, z-score, and percentiles. Analyzing these measures will provide insights into the variability and distribution of insurance premiums within each age group.

Pivot Table Analysis: We will create at least one pivot table in Excel to analyze the relationship between age groups and car insurance premiums. Additionally, we will create relevant charts and graphs to visualize the data and support our hypothesis.

Linear Regression and Correlation Coefficient r: Using the least-squares method, we will determine a linear regression equation to model the relationship between age and insurance premiums. We will also calculate the correlation coefficient (r) to quantify the strength of this relationship.

Variables and Graphs: Throughout the report, we will describe the variables used (e.g., age groups and insurance premiums) as continuous or categorical and identify their independence or dependence. Graphs such as scatter plots and other types will be utilized to visually represent the data and analyze trends.

Cause and Effect: We will explore potential cause-and-effect relationships between age groups and insurance rates. It will help us understand how age impacts insurance premiums and whether it is a significant factor in determining the cost.

Conclusion

In conclusion, our analysis will shed light on the relationship between car insurance premiums and age groups. We expect to find evidence supporting our hypothesis that older age groups generally pay lower insurance premiums. However, we acknowledge the possibility of discovering additional factors that may influence insurance rates.

By summarizing our findings, we will directly address the main topic question and sub-questions, providing valuable insights into the dynamics of car insurance pricing based on age. We will evaluate the correctness of our hypothesis, and any biases encountered during the study will be acknowledged and justified.