As part of a study on transportation safety, the U.S. Department of Transportation collected data on the number of fatal accidents per 1000 licenses and the percentage of licensed drivers under the age of 21 in a sample of 42 cities. Data collected over a one-year period follow. These data are contained in the file Safety.
Managerial Report
Develop numerical and graphical summaries of the data.
Use regression analysis to investigate the relationship between the number of fatal accidents and the percentage of drivers under the age of 21. Discuss your findings.
What conclusion and recommendations can you derive from your analysis?
Initial post prompt: Your Managerial Report serves as your initial post to the discussion forum. After responding to the requirements posed by the Managerial Report, also provide an example in your career in which you believe one of the lessons learned from the Case has been/could be applicable. Alternatively, if you don’t have/foresee direct experience relevant to your current position, what type of scenario can you anticipate occurring where you can utilize one of the lessons learned from examining this case?
Response post prompt: Consider Managerial Reports posted by two of your peers. One or both of your responses may be to Managerial Reports for a case problem different from your own. Think critically and ask open-ended questions. If you agree, consider their position and expand upon their ideas. Provide an additional perspective. If you disagree, provide your reasoning. Always be professional and courteous in your responses.
Post by classmate 1
In question 1 I created a scatter plot and a regression data analysis chart to summarize the data found by the US department of transportation safety. As we can see from the scatter plot there is a positive linear relationship between the number of fatal accidents per 1000 licenses and percent of drivers under 21. I also included a dotted line to further show the positive regression between the two. In my regression data analysis chart we find important values R squared and the intercept and x variable. All values are also displayed on the plot and provide us more information of the relationship between X and Y.
Question 2 asks us to discuss our findings. Using our intercept and x variable value displayed in my regression analysis we then find our estimated regression equation. Our equation is written as y = 0.2871x - 1.5974 or y = -1.5974 + 0.2871x. The regression equation tells us when the percentage value of drivers under the age of 21 increases, the fatal accident per 1000 licenses increases by 0.2871. Now we consider R squared to determine how well the equation fits the data and if it accurately depicts the changes in the dependent variable. From my regression analysis chart I found a R squared or coefficient of determination value of +0.7046. Our textbook explains that a positive value indicates that in a linear regression, variables x and y have a strong relationship because the value is positive. Furthermore, a R squared value can be written as a percentage and in this case is 70.5%. This means the scatter plot values around the regression line are small in difference and more significant in fitting the linear regression.