Answer: [tex]ŷ=-0.580x+10.671\text{ \lparen option C\rparen}[/tex]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:
[tex]\begin{gathered} ŷ=bx+a \\ b\text{ = slope} \\ a\text{ = y-intercpet} \end{gathered}[/tex][tex]\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}[/tex][tex]\begin{gathered} ŷ=\text{ }bX+a \\ b=\frac{SP}{SSX}=\frac{-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}[/tex][tex]\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}[/tex]
