Option B. [tex]y=-0.18x+10.06[/tex]
Step-by-step explanation:
Given: The nine coordinates can be written as [tex](0,10), (1,9.9),(2,9.6), (3,9.5), (4,9.4)[/tex][tex], (5,9.2), (6,9), (7,8.7), (8,8.6)[/tex]
The equation that best fits the data can be found using the formula [tex]y=ax+b[/tex] where a and b can be found using the formula
[tex]a=\frac{\left(N * \sum x y\right)-\left(\sum x * \sum y\right)}{\left(N * \sum x^{2}\right)-\left(\sum x * \sum x\right)}[/tex] and [tex]b=\frac{\left(\sum x^{2} * \sum y\right)-\left(\sum x * \sum x y\right)}{\left(N * \sum x^{2}\right)-\left(\sum x * \Sigma x\right)}[/tex]
Here, [tex]N=9[/tex]
The values of a and b can be found using the values found from the table which is attached below. The values from the table are given by
[tex]\sum x=36[/tex],
[tex]\sum y=83.9[/tex],
[tex]\sum x y=324.9[/tex],
[tex]\sum x^{2}=204[/tex], and
[tex]\sum y^{2}=784.07[/tex]
Now, we can find the values of a and b, by substituting these values in the formulas of a and b.
[tex]\begin{aligned}a &=\frac{\left(N * \sum x y\right)-\left(\sum x * \sum y\right)}{\left(N * \sum x^{2}\right)-\left(\sum x * \sum x\right)} \\&=\frac{(9 \cdot 324.9)-(36 \cdot 83.9)}{(9 \cdot 204)-(36 \cdot 36)} \\&=-0.18\end{aligned}[/tex]
and
[tex]\begin{aligned}b &=\frac{\left(\sum x^{2} * \sum y\right)-\left(\sum x * \sum x y\right)}{\left(N * \sum x^{2}\right)-\left(\sum x * \sum x\right)} \\&=\frac{(204 \cdot 83.9)-(36 \cdot 315)}{(9 \cdot 204)-(36 \cdot 36)} \\&=10.06\end{aligned}[/tex]
Thus, the values of a and b are found. Now, substituting the two values in the equation [tex]y=ax+b[/tex] , we get,
[tex]y=-0.18x+10.06[/tex]
The correct option is [tex]y=-0.18x+10.06[/tex]
