Question

3. The data in the table gives the number of barbeque sauce bottles (y) that are sold with orders of chicken wings (x) for each hour on a given day at Vonn's Grill. Use technology to write an equation for the line of best fit from the data in the table below. Round all values to two decimal places.

Answer 1

1) Let's visualize the points

2) To find the equation for the line of best fit we'll need to follow some steps.

2.1 Let's find the mean of the x values and the mean of the Y values

2.2 Now It's time to find the slope, with the summation of the difference between each value and the mean of x times each value minus the mean over the square of the difference of the mean of x and x.

To make it simpler, let's use this table:

The slope then is the summation of the 5th column over the 6th column, we're using the least square method

`m=(939.625)/(1270.875)=0.7393\cong0.74`

The Linear coefficient

`\begin{gathered} b=Y\text{ -m}X \\ b=14.625-0.73(19.875) \\ b=0.11625\cong0.12 \end{gathered}`

3) Finally the equation of the line that best fit is

`y=0.73x+0.12`