Question

a health food store owner sells home-made peanut butter. she has been observing how many bags of peanuts it takes to make jars of peanut butter. she found that the line of best-fit is jars of peanut butter= 5+ 2.6(bags of peanuts). find and interpret the residual for jars of peanut butter if she made 54 jars of peanut butter from 20 bags of peanuts.
the residual is \boxed{ } (type an integer or a decimal.)

Explanation:

Step1: Recall residual formula

Residual = Observed value - Predicted value.

Step2: Find predicted value

The line of best - fit is \( \text{jars of peanut butter}=5 + 2.6(\text{bags of peanuts}) \). Given bags of peanuts \( x = 20 \), substitute into the equation:
\( \text{Predicted value}=5+2.6\times20 \)
\( = 5 + 52=57 \)

Step3: Calculate residual

Observed value \( y = 54 \), so residual \(=54 - 57=- 3\)

Answer:

\(-3\)