Question

asked Sep 27, 2021 96.9k views

1 Answer

Madonna Remon · Answer 1 · 2021-10-03T11:03:59+0000

Answer:

m=-(7600)/(8250)=-0.921

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

$\bar x= (\sum x_i)/(n)=(550)/(10)=55$

$\bar y= (\sum y_i)/(n)=(1042)/(10)=104.2$

And we can find the intercept using this:

$b=\bar y -m \bar x=104.2-(-0.921*55)=104.707$

So the line would be given by:

y=-0.921 x +104.707

Explanation:

For this case we have the following data given:

Demand (x): 10,20,30,40,50,60,70,80,90,100

Price (y): 141 , 133,126, 128,113,97, 90, 82,79,53

We want to construct a linear model like this:

y = mx +b

For this case we need to calculate the slope with the following formula:

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:

$\sum_(i=1)^n x_i =550$

$\sum_(i=1)^n y_i =1042$

$\sum_(i=1)^n x^2_i =38500$

$\sum_(i=1)^n y^2_i =115882$

$\sum_(i=1)^n x_i y_i =49710$

With these we can find the sums:

$S_(xx)=\sum_(i=1)^n x^2_i -((\sum_(i=1)^n x_i)^2)/(n)=38500-(550^2)/(10)=8250$

$S_(xy)=\sum_(i=1)^n x_i y_i -\frac{(\sum_(i=1)^n x_i)(\sum_(i=1)^n y_i)}=49710-(550*1042)/(10)=-7600$

And the slope would be: