Modelling Change Project-Jon World Transfer Records 1961-2016

I graphed the change in world transfer records in soccer. my x-axis is the years of the transfers and the y-axis is the transfer fee in millions.

Graphs and Data Points

Finding the Lines of Best Fit

So that the y-intercept would not get too confusing, there will be two different equations per group where the x- coordinates in the new equation will be the x-coordinates on the graph - 1950.

Lines for group 1

First Point:(1961,0.25)=(11,0.25)5th point: (1992,10)=(42,10)

slope=9.75/31

Equation of the graph Line: y=9.75x/31-616.52, New Line: y=9.75x/31-3.21

Lines for group 2

First point: (1996,15)=(46,15)

5th point: (2000,37)=(50,37)

Slope:11/2

Equation of the Line: y=11x/2-10963=y=11x/2-238

Lines for Group 3

First Point:(2001,45.6)=(51,45.6)

5th Point: (2016,89)=(66,89)

Slope:43.4/15

Equation of the graph line:y=43.4x/15-5744, New line: y=43.4x/15-102

The Overall Line of Best Fit

I chose a quadratic equation (y=ax^2+bx+c) to make the curve of best fit.

How I found the line

I used the formula y=a(x-h)^2+k where (h,k) is the bottom point of the quadratic smiley face. I knew (h,k) was (1961,.25) so the formula would be: y=a(x-1961)^2+.25.

I then substituted another coordinate (2016,89) for (x,y) to solve for a.

89=a(2016-1961)^2+.25

=a(55)^2+.25

88.75=a(55)^2

88.75/55^2=a

a= .029=1/34

The formula: y=1/34(x-1961)^2+.25, if x2=x-1950, then: y=1/34(x-11)^2+.25

Trends

Predictions

In 50 years, the year will 2067 so x=2067, therefore y=1/34(2067-1961)ˆ2+.25

y=330,7 million pounds

b) in 95 years it will be 2112 so x=2112

y=1/34(2112-1961)ˆ2=.25

y=670,9 million pounds

Analysis

There is a drastic increase of fees from the start of the 21st century because there was more money in soccer from the increase of people paying to watch. For example the English First Division changed to the Premier league and got a lot of money from sponsors. Real Madrid is the richest club in the world with a worth of 3 billion and they also have the third biggest fan base of 450 million. The top 3 richest clubs (Real Madrid, Barcelona and Manchester United) have the 3 biggest fan bases so there is a link there. Recently China and America have grown an interest in soccer and the teams have spent a lot of money on players. Shanghai Shenua FC bought Carlos Tevez from Argentina and he has the biggest salary in the world. With the growing interest in huge countries there will be a lot of money to follow so I think the record transfer fee could reach 500 million in a hundred years.

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