Question

3.Write an equation of best fit for the given data.

Answer 1

To find the line of best fit we follow this steps:

1. Calculate the mean of the x -values and the mean of the y -values

`\begin{gathered} \bar{X}=(49.9+48.6+46.3+45.8+44.3+43.6)/(8) \\ \\ \Rightarrow\bar{X}=34.8125 \end{gathered}`
`\begin{gathered} \bar{Y}=(177.5+174.6+165.6+164.7+165.3+164.6+155.8+156.7)/(8) \\ \\ \Rightarrow\bar{Y}=165.6 \end{gathered}`

2. The following formula gives the slope of the line of best fit:

`\begin{gathered} m=\frac{\sum ^n_(i\mathop=1)(x_i-\bar{X})(y_i-\bar{Y})}{\sum ^n_{i\mathop{=}1}(x_i-\bar{X})^2} \\ \\ \end{gathered}`

In our case, such computation will yield as a result: