Question

the following data were collected.

x	15	18	22	25	30
y	32	28	25	24	20

use technology to write an equation that models the data.

• $hat{y} = 42.380x + 0.754$
• $hat{y} = -0.754x + 42.380$
• $hat{y} = 42.380x - 0.754$
• $hat{y} = 0.754x - 42.380$

Explanation:

Step1: Analyze the trend of data

As \(x\) increases (\(15\to18\to22\to25\to30\)), \(y\) decreases (\(32\to28\to25\to24\to20\)). So the slope of the regression line should be negative.

Step2: Check the general form of linear regression equation

The general form of a linear regression equation is \(\hat{y}=mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.
Since the slope \(m\) should be negative, we can eliminate the equations \(\hat{y}=42.380x + 0.754\), \(\hat{y}=42.380x-0.754\) and \(\hat{y}=0.754x - 42.380\) (because their slopes \(42.380\), \(42.380\) and \(0.754\) are positive).

Answer:

\(\hat{y}=- 0.754x + 42.380\)