Question

Write the equation of the line of best fit. Line of best fit: y =

Answer 1

In order to calculate the line of best fit, let's start calculating the mean value of x and y.

The mean is given by the sum of all values divided by the number of values.

So we have:

`\begin{gathered} \bar{x}=\frac{\sum_{i\mathop{=}1}^nx_i}{n}=(81)/(9)=9\\ \\ \bar{y}=\frac{\sum_{i\mathop{=}1}^ny_i}{n}=(2277)/(9)=253 \end{gathered}`

Now, let's calculate the slope of the line using the formula below:

`m=\frac{\sum_{i\mathop{=}1}^n(x_i-\bar{x})(y_i-\bar{y})}{\sum_{i\mathop{=}1}^n(x_i-\bar{x})^2}=13.95`

And finally, calculating the y-intercept, we have:

`\begin{gathered} b=\bar{y}-m\bar{x}\\ \\ b=253-13.95\cdot9\\ \\ b=253-125.55\\ \\ b=127.45 \end{gathered}`

Therefore the equation is:

`y=13.95x+127.45`