I'm working on a math project about a track and field olympic event. The question is, is the relationship between the years and time values linear or exponential?
So I selected an event and I can see that as the years have passed, the time has decreased, so I consider that linear.
Then I have to find a line of best fit for my data and state what the meaning of the slope from that equation is. I believe the slope represents the change in time in the event each time there is an olympics held. (Is that correct?)
Here is the question that I am really struggling on: does my graph have a y-interecept. Well I know it's not going to have a x-interecept, where the line crosses the x axix because that would mean that they are doing the event in no time which, of course, is impossible.
But what about a y-intercept?
My confusion, I believe, is because the equation of a line is y = mx + b, with b being the y interecept. I have a "b" in my equation, but would there really be a y intercept in this type of scenario?
Thank you.
sure ... b represents the first (modern) olympics
the time in the event is dependent on the year of the games
one would expect the times to decrease as a result of improvement of the atheletes
... better conditioning, better nutrition, ... etc.
I am a little confused by your comments --
My equation of best fit, determined by the computer, is: Y=-.02496x+551.65
My event is 100M mens backstroke, and the first time they did this, in 1906, the time was 1:16.8 which would be 76 secons -- so I don't understand how the b can be the first olympics time.
I understand and agree that the times decrease as time goes on, but I'm still trying to understand this y-intercept thing.
Thank you for clarifying for me.
how have you defined your variables?
winning time in seconds? ... this should be y
year of games? ... or years since 1st "modern" games? ... this should be x
going back in time beyond the "modern" games is probably meaningless
Yes, the years are my x and the time in seconds is my y -
The question is, is there a y-intercept - so technically, there WOULD be a y-intercept since the line would cross the y-axis??
In relation to your math project, determining whether the relationship between the years and time values is linear or exponential is a crucial step. Based on your observation that as the years passed, the time has decreased, it seems reasonable to conclude that the relationship is linear. A linear relationship implies that as the independent variable (in this case, years) increases, the dependent variable (time) changes at a constant rate.
Now, onto finding the line of best fit for your data and understanding the meaning of the slope from the equation. To find the line of best fit, you will typically use a technique called linear regression. This involves finding the equation of the line that minimizes the squared differences between the observed data points and the predicted values on the line.
Once you have the equation of the line, let's say it is of the form y = mx + b, as you correctly mentioned. The slope, represented by 'm,' does indicate the change in time in the event each time there is an Olympic Games held. Specifically, the slope represents the rate at which the time changes per unit increase in years. For example, if the slope is -0.5, it means that for every year that passes, the time in the event decreases by half a unit.
Now, let's address your question regarding the existence of a y-intercept. In the context of your track and field Olympic event, the y-intercept represents the value of time when the years are zero, that is, at the start of the analysis. Unfortunately, since time cannot be negative in a practical sense, it would not make sense to interpret the y-intercept in this scenario. A y-intercept implies the time taken for the event when no time has passed, which is not meaningful.
Taking all these factors into consideration, it seems reasonable to conclude that in this particular track and field Olympic event, the relationship between years and time is best represented by a linear equation.