Question

asked Jul 17, 2021 132k views

1 Answer

Charleyh · Answer 1 · 2021-07-22T17:51:58+0000

Answer:

m=-(13)/(20.8)=-0.625

Nowe we can find the means for x and y like this:

$\bar x= (\sum x_i)/(n)=(16)/(5)=3.2$

$\bar y= (\sum y_i)/(n)=(35)/(5)=7$

And we can find the intercept using this:

$b=\bar y -m \bar x=7-(-0.625*3.2)=9$

So the line would be given by:

y=-0.625 x +9

Explanation:

We have the following data:

X: 3,3,2,1,7

Y:6,7,8,9,5

We want to find an equationinf the following form:

y= bX +a

a=m=(S_(xy))/(S_(xx))

Where:

$S_(xy)=\sum_(i=1)^n x_i y_i -((\sum_(i=1)^n x_i)(\sum_(i=1)^n y_i))/(n)$

$S_(xx)=\sum_(i=1)^n x^2_i -((\sum_(i=1)^n x_i)^2)/(n)$

So we can find the sums like this:

$\sum_(i=1)^n x_i = 3+3+2+1+7=16$

$\sum_(i=1)^n y_i =6+7+8+9+5=35$

$\sum_(i=1)^n x^2_i =72$

$\sum_(i=1)^n y^2_i =255$

$\sum_(i=1)^n x_i y_i =99$

With these we can find the sums:

$S_(xx)=\sum_(i=1)^n x^2_i -((\sum_(i=1)^n x_i)^2)/(n)=72-(16^2)/(5)=20.8$

$S_(xy)=\sum_(i=1)^n x_i y_i -\frac{(\sum_(i=1)^n x_i)(\sum_(i=1)^n y_i)}=99-(16*35)/(5)=-13$

And the slope would be: