Question

use the points to describe the data and determine the line of best fit. what type of correlation do the data points represent? negative what is the equation that best represents the data? y = -400x + 3,900 y = -500x + 4,500 y = -100x + 3,100 y = 350x + 3,100

Explanation:

Step1: Analyze the slope of each equation

• For \(y = - 400x+3900\), the slope \(m=-400\)
• For \(y=-500x + 4500\), the slope \(m=-500\)
• For \(y=-100x+3100\), the slope \(m=-100\)
• For \(y = 350x+3100\), the slope \(m = 350\) (positive slope, but we know correlation is negative so we can eliminate this one first)

Step2: Estimate the slope from the scatter - plot

Take two points approximately. Let's assume one point is \((2,3500)\) and another is \((8,1000)\)
The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\)
\(m=\frac{1000 - 3500}{8 - 2}=\frac{-2500}{6}\approx - 416.67\)

• The slope of \(y=-500x + 4500\) is closer in magnitude to our estimated slope (since our estimated slope is about \(-417\)) compared to \(y=-400x + 3900\) (\(m=-400\)) and \(y=-100x+3100\) (\(m=-100\))

Answer:

\(y=-500x + 4500\)