Question

problem 7
the table shows the number of local soccer teams since 1999.

years since 1999	0	2	3	4

regression equation:
using your regression equation approximately how many soccer teams were there in 2000?
using your regression equation approximately how many soccer teams were there in 2020?

Explanation:

Step1: Assume linear regression form

Let the linear - regression equation be $y = mx + b$, where $x$ is the number of years since 1999 and $y$ is the number of teams. When $x = 0$, $y=b$. From the table, when $x = 0$, $y = 119$, so $b = 119$.

Step2: Calculate the slope $m$

We use two points $(x_1,y_1)=(2,143)$ and $(x_2,y_2)=(4,163)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{163 - 143}{4 - 2}=\frac{20}{2}=10$.

Step3: Write the regression equation

The regression equation is $y=10x + 119$.

Step4: Find the number of teams in 2000

For 2000, $x = 2000 - 1999=1$. Substitute $x = 1$ into the equation $y=10\times1+119=129$.

Step5: Find the number of teams in 2020

For 2020, $x = 2020 - 1999 = 21$. Substitute $x = 21$ into the equation $y=10\times21+119=210 + 119=329$.

Answer:

Regression Equation: $y = 10x+119$
Number of teams in 2000: 129
Number of teams in 2020: 329