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 + 2.4(bags of peanuts). find and interpret the residual for jars of peanut butter if she made 51 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 - Predicted. First, find predicted value using the line of best - fit equation \( \hat{y}=5 + 2.4x \), where \( x \) is bags of peanuts and \( \hat{y} \) is predicted jars of peanut butter.

Step2: Calculate Predicted Value

Given \( x = 20 \) (bags of peanuts). Substitute into the equation: \( \hat{y}=5+2.4\times20 \). Calculate \( 2.4\times20 = 48 \), then \( \hat{y}=5 + 48=53 \).

Step3: Calculate Residual

Observed value \( y = 51 \). Residual \( = y-\hat{y}=51 - 53=- 2 \).

Answer:

\(-2\)