Question

read the following description of a data set. aisha wants to ensure that the new board game shes designing is accessible to a wide age range. to test this, she had several children of various ages play the board game against each other. each child played the game the same number of times. for each child, aisha recorded his or her age, x, and the number of games that child had won, y. the least squares regression line of this data set is: y = 3.185x - 32.395. how many games does the line predict would have been won by a 12 - year - old? round your answer to the nearest integer.

Explanation:

Step1: Identify the regression - line formula

The regression line is $y = 3.185x-32.395$.

Step2: Substitute the value of $x$

We want to find the number of games won by a 12 - year - old, so we substitute $x = 12$ into the equation.
$y=3.185\times12 - 32.395$.

Step3: Calculate the value of $y$

First, calculate $3.185\times12=38.22$. Then, $y = 38.22-32.395=5.825$.

Step4: Round the result

Rounding $5.825$ to the nearest integer gives $6$.

Answer:

6