# Giant Slalom

## A More Yet Less Difficult Course

The giant slalom isn't just any regular skiing event. This event involves skiing between sets of poles, otherwise known as gates, that are set apart from each other at a greater distance than in Slalom but less than in Super-G. The giant slalom, along with the slalom, make up the technical events in alpine skiing. This means that these events are normally made of 2 runs that are held on different courses of the same ski run. In a giant slalom course, the vertical drop must be 250-450 meters with a total of 56-70 gates for men and 46-58 gates for women.

## Our Purpose

Since in giant slalom they won't let the men and women compete in the same event, we can gather data from the previous Olympic Games to make observations and inferences of what the outcomes may be. Below is the data that was collected for the individual giant slalom event. By using this data, we can use linear regression, mathematical predictions, and methods of solving a system of equations to recognize patterns in both sets of data (men and women). With these linear models, it is possible to determine if when women's performances will ever surpass the men's or vise-versa.

## The Scatterplot

The picture to the right is the scatterplot for the data points. The pink Xs represent the male competitors and the blue square's represent the female competitors.

## linear regression (lines of best fit)

The picture to the left is a scatterplot that includes the trend lines (lines of best fit) for the 2 sets of data. The blue line represents the male trend line and the red represents the female's trend line.

## The Intersection

The picture above shows the intersection point between the two trend lines. Notice that the women's trend line (red) is increasing while the men's trend line (blue) is decreasing. This means that the woman's gold medal times are increasing over the past Winter Olympic Games and will most likely continue to do so in the future. On the other hand, the men's gold medal times are decreasing over the past Winter Olympic Games. The intersection point is a very important point in the two sets of data because it tells us a great deal of information in the analysis. This means that after the intersection point, the women's times will be greater making them slower than the men's times, which will be lesser, but faster than the women's.

## The X Coordinate

The X axis (independent variable) represents the years of each of the Winter Olympic Games. The X coordinate of the intersection point is at the year of 2008, which is not a Winter Olympic year. However in the next Winter Olympic Year, 2010, is the year that when the men's times appear lesser and faster than the women's in the individual giant slalom event.

## The Y Coordinate

The Y axis (dependent variable) represents the time in seconds. The Y coordinate of the intersection point is at 152 seconds, which converts to approximantly 2 minutes and 53 seconds. This is the approximate gold medal time for both men and women if the Winter Olympics happened in 2008. But since that is not a Winter Olympic year, in the 2010 Winter Olympics, the men's time will be less than but still pretty close to 152 seconds because it's trend line is decreasing. However, the women's time will be greater than but still pretty close to 152 seconds because it's trend line is increasing.