Question

using the data below, find the equation of the line of best fit using a calculator. round all decimals to the hundredths place. (5, -5), (-6, 21), (-5, 18), (-10, 31), (0, 3), (-3, 16)

Explanation:

Step1: Input Data into Calculator

First, we need to input the given data points \((5, -5)\), \((-6, 21)\), \((-5, 18)\), \((-10, 31)\), \((0, 3)\), \((-3, 16)\) into a calculator (such as a TI - 84 Plus or a graphing calculator with linear regression capabilities). For a TI - 84 Plus, we would press STAT then EDIT and enter the \(x\) - values in L1 and the corresponding \(y\) - values in L2.

Step2: Perform Linear Regression

After entering the data, we press STAT again, move to the CALC menu, and select LinReg(ax + b). This function will calculate the slope \(a\) and the \(y\) - intercept \(b\) of the line of best fit \(y=ax + b\).

When we perform this calculation with the given data:

• The \(x\) - values are \(5,-6,-5,-10,0,-3\)
• The \(y\) - values are \(-5,21,18,31,3,16\)

Using a calculator (either by hand - calculation of the linear regression formula or using a graphing calculator), we find that the slope \(a\approx - 1.98\) and the \(y\) - intercept \(b\approx5.03\)

Answer:

The equation of the line of best fit is \(y=-1.98x + 5.03\)