Question

use technology to find an equation of the line of best fit for the data. round the slope and the y - intercept to the nearest hundredth.
20 65
21 42
15 25
33 87
28 76
30 79

Explanation:

Step1: Input data into technology

Input the \(x\) - values (\(20,21,15,33,28,30\)) and \(y\) - values (\(65,42,25,87,76,79\)) into a statistical software or a graphing calculator.

Step2: Calculate the regression line

Use the linear regression function. For example, in Excel, we can use the "LINEST" function. In a graphing calculator (e.g., TI - 84), we can go to STAT > EDIT to enter the data, then STAT > CALC > LinReg(ax + b) and calculate.

Let's assume we use a statistical software. The formula for the line of best fit is \(y=ax + b\), where \(a\) is the slope and \(b\) is the \(y\) - intercept.

After calculation, the slope \(a\approx2.54\) and the \(y\) - intercept \(b\approx - 13.27\)

Answer:

The equation of the line of best fit is \(y = 2.54x-13.27\)