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 - 3. (type an integer or a decimal.)
the residual is dropdown which indicates that the equation dropdown the number of jars.

Explanation:

Step1: Recall Residual Formula

Residual = Observed - Predicted. Observed is 54, find predicted using the line of best - fit \( \text{jars}=5 + 2.6(\text{bags}) \).

Step2: Calculate Predicted Jars

Substitute bags = 20 into the formula: \( 5+2.6\times20=5 + 52=57 \).

Step3: Calculate Residual

Residual = \( 54 - 57=- 3 \).

Step4: Interpret Residual Sign

Since residual is - 3 (negative), the predicted value (57) is greater than the observed value (54). So the equation overestimated the number of jars.

Answer:

The residual is \(-3\) (negative), which indicates that the equation overestimated the number of jars.