Question

What is the linear function equation that best fits the data set?

Answer 1

To form an equation for a straight line, we need the value of gradient and the y-intercept

The formula to find gradient is $\frac{S_{xy} }{ S_{xx} }$

$S_{xy}=$∑$(xy)- \frac{(∑x)(∑y)}{n}$
$S_{xy}= 111- \frac{(22)(56)}{8}$
$S_{xy}= \frac{1232}{8}=-43$

$S_{xx}=$∑$x^{2} - \frac{∑x}{n}$
$S_{xx}=75- \frac{22^{2}} {8}$
$S_{xx}=14.5$

$m= \frac{S_{xy}}{S_{xx}}$
$m= \frac{-43}{14.5}=-2.9$≈-3

where m is the gradient

to find c (y-intercept)
$c=mean of y-(m)(mean of x)= \frac{56}{8} -(-3)( \frac{22}{8})=15.25$≈15

Hence the equation of the straight line is $y=-3x+15$