Stats Project

Introduction

Using a regression analysis we are testing to see if there is a significant correlation between the percentage of licensed drivers under the age of 21 (X variable) and fatal accidents per 1000 licenses (Y Variable).Data was collected by the U.S. Department of Transportation using a sample of 42 cities over a period of one year.

Data

Prior to analyzing the data collected by the U.S. Department of Transportation we sorted the data and then calculated the basic descriptive statistics for both the independent variable (X -% of drivers under 21 years old) and dependent variable (Y - number of fatal accidents). After performing the calculations, we determined that the mean was 12.262 for the independent variable, and its standard deviation was 3.132, while the dependent variable’s mean was 1.922 and its standard deviation was 1.071.

Results and Discussion

After using the proper equations, we have come up with a regression analysis to determine whether there is a relationship between the X and Y variables. As displayed in Exhibit 1, it can be seen from the naked eye that there is a positive correlation between the percent of drivers under the age of 21 and fatal accidents per 1000 licenses. As the percentage of younger driver increases, so do the fatal accidents. A covariance of 2.815 was calculated and this also proves that there is a positive correlation between the X and the Y variable.

Exhibit 1

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But how strong is this correlation? With further calculations, it is concluded that the regression line of this data set is y = 0.2871x- 1.5974. In a perfect ideal situation, all the points of data fall right on top of the regression line. Consequently, the Y variable can be completely explained by the X variable, but this is certainly not the case as the data points are scattered all around the computed equation line.

To further understand the strength of this line, the coefficient of correlation (r) and coefficient of...