Question

By examining past tournaments, it's possible to calculate the probability that a school wins their first game in the national college basketball tournament. Each school's rank going into the tournament is a strong indicator of their likelihood of winning their first game.

Answer 1

Given:

Rank data

To determine the linear regression equation that models the given data, we first note the regression equation:

$y=bx+a$

where:

b=slope

a=y intercept

Now, we use the process the process below:

Next, we solve for the value of b:

$b=\frac{SP}{SSx}=-\frac{304.5}{47.5}=-6.41$

Then, we solve for a:

$\begin{gathered} a=Mean\text{ of y-b\lparen Mean of x\rparen} \\ a=62.17-(-6.41)(6.5) \\ Calculate \\ a=103.8=104 \end{gathered}$

We plug in a=104 and b=-6.41 into y=bx+a:

$\begin{gathered} y=bx+a \\ y=-6.41x+104 \end{gathered}$

Therefore, the answer is: A

$y=-6.41x+104$