Question

1. determine the line of best fit. enter it in ( y = mx + b ) format. round to the nearest tenth.

type a response

Explanation:

Step1: Calculate the means of \(x\) and \(y\)

\(\bar{x}=\frac{0 + 4+3+2+1+0}{6}=\frac{10}{6}\approx1.7\)
\(\bar{y}=\frac{-3-2 + 0-1+1+1}{6}=\frac{-4}{6}\approx - 0.7\)

Step2: Calculate the numerator and denominator for \(m\)

Numerator: \(\sum_{i = 1}^{n}(x_{i}-\bar{x})(y_{i}-\bar{y})\)
\((0 - 1.7)(-3+0.7)+(4 - 1.7)(-2 + 0.7)+(3 - 1.7)(0+0.7)+(2 - 1.7)(-1+0.7)+(1 - 1.7)(1+0.7)+(0 - 1.7)(1+0.7)\)
\(=(-1.7)(-2.3)+(2.3)(-1.3)+(1.3)(0.7)+(0.3)(-0.3)+(-0.7)(1.7)+(-1.7)(1.7)\)
\(=3.91-2.99 + 0.91-0.09-1.19-2.89\)
\(=3.91+0.91-(2.99 + 0.09+1.19+2.89)\)
\(=4.82 - 7.16=-2.34\)

Denominator: \(\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}\)
\((0 - 1.7)^{2}+(4 - 1.7)^{2}+(3 - 1.7)^{2}+(2 - 1.7)^{2}+(1 - 1.7)^{2}+(0 - 1.7)^{2}\)
\(=2.89+5.29+1.69+0.09+0.49+2.89\)
\(=13.34\)

\(m=\frac{-2.34}{13.34}\approx - 0.2\)

Step3: Calculate \(b\)

Using \(b=\bar{y}-m\bar{x}\), substitute \(\bar{x}\approx1.7\), \(\bar{y}\approx - 0.7\) and \(m\approx - 0.2\)
\(b=-0.7-(-0.2)\times1.7=-0.7 + 0.34=-0.4\)

Answer:

\(y=-0.2x - 0.4\)