Question

use the regression line for the data in the scatter - plot to answer the question. on average, how many more goals will a player score for every additional hour of practice?
1/2 of a goal
3/4 of a goal
1 goal
4/3 goals

Explanation:

Step1: Identify slope concept

The slope of the regression - line represents the change in the dependent variable (goals scored) for a unit change in the independent variable (hours of practice).

Step2: Select two points on the line

Let's take two points on the regression line. For example, (2, 2) and (5, 4).

Step3: Calculate the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $x_1 = 2,y_1 = 2,x_2 = 5,y_2 = 4$ into the formula, we get $m=\frac{4 - 2}{5 - 2}=\frac{2}{3}\approx\frac{1}{2}$ (approximate value for comparison with options). Another way, if we take (0, 1) and (3, 3) on the line, $m=\frac{3 - 1}{3-0}=\frac{2}{3}\approx\frac{1}{2}$.

Answer:

$\frac{1}{2}$ of a goal