Question

what is the equation for the line of best fit for the following data? round the slope and y-intercept of the line to three decimal places.*photo*

Answer 1

Answer:
`ŷ=-0.580x+10.671\text{ \lparen option C\rparen}`Step-by-step explanation:

Given:

Table of values for x and y

To find:

the equation of the line of best fit

To determine the line of best fit, we will use a regression calculator.

The regression equation is in the form:

`\begin{gathered} ŷ=bx+a \\ b\text{ = slope} \\ a\text{ = y-intercpet} \end{gathered}`
`\begin{gathered} Sum\text{ }ofX=42 \\ Sum\text{ }ofY=29 \\ Mean\text{ of }X=8.4 \\ Mean\text{ of }Y=5.8 \\ Sum\text{ }of\text{ }squares\text{ }SSX=125.2 \\ Sum\text{ }of\text{ }products\text{ }SP=-72.6 \end{gathered}`
`\begin{gathered} ŷ=\text{ }bX+a \\ b=(SP)/(SSX)=(-72.6)/(125.2)=-0.57987 \\ \\ a=Mean\text{ of }Y-b(Mean\text{ of }X) \\ a\text{ }=5.8-(-0.58)(8.4)=10.67093 \end{gathered}`
`\begin{gathered} ŷ=-0.5798x+10.67093 \\ \\ Slope\text{ and intercept t}o\text{ 3 decimal place:} \\ ŷ=-0.580x+10.671\text{ \lparen option C\rparen} \end{gathered}`