Question

understanding slope
use the regression line for the data in the scatterplot to answer the question. on average, how many more goals will a player score for every additional hour of practice?
$\frac{1}{2}$ of a goal
$\frac{3}{4}$ of a goal
1 goal
$\frac{4}{3}$ goals

Explanation:

Step1: Recall the meaning of slope in regression line

The slope of the regression line represents the change in \(y\) (goals scored) for a unit change in \(x\) (hours of practice).

Step2: Select two points on the regression line

Let's take two points \((2,2)\) and \((6,6)\) (approximate points on the regression line).

Step3: Calculate the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1 = 2,y_1=2,x_2 = 6,y_2 = 6\), we get \(m=\frac{6 - 2}{6 - 2}=\frac{4}{4}=1\).

Answer:

1 goal