Question

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?
○ 1/2 of a goal
○ 3/4 of a goal
○ 1 goal
○ 4/3 goals

Explanation:

Step1: Recall the meaning of slope

The slope of a regression line represents the rate of change. In this context, it represents the change in goals scored per change in hours of practice.

Step2: Calculate the slope

Let's assume two points on the regression line. For simplicity, if we take two points \((x_1,y_1)\) and \((x_2,y_2)\). Suppose \((x_1 = 0,y_1=1)\) and \((x_2 = 3,y_2 = 3)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the values: \(m=\frac{3 - 1}{3-0}=\frac{2}{3}\approx\frac{3}{4}\) (approximate visual - estimation as we can also pick other points. For example, if we consider a run of \(4\) units (increase in \(x\)) and a rise of \(3\) units (increase in \(y\)) on the line, the slope \(m = \frac{3}{4}\))

Answer:

\(\frac{3}{4}\) of a goal