Question

The amount of money 'y' made at a laundromat after 'x' months can be represented by the linear function: y = 8.50x - 5. After 2 months, the laundromat made 20 dollars, but the linear function predicted they would make 12 dollars. What is the residual value for this data?

Answer 1

`\hat y = 8.5*2 -5 = 12`

And the residual is defined as:

`e_ i = y_i -\hat y_i`

And replacing we got:

`e_i = 20-12 = 8`

Explanation:

For this case we know that the amount of money 'y' made at a laundromat after 'x' months can be represented by the linear function:

`y = 8.50 x -5`

And fter two months we know that the laundromat made 20 dollars. And if we use the linear function we got:

`\hat y = 8.5*2 -5 = 12`

And the residual is defined as:

`e_ i = y_i -\hat y_i`

And replacing we got:

`e_i = 20-12 = 8`