Question

chicken sandwiches are often advertised as a healthier alternative to beef because many are lower in fat. a researcher collected data on chicken sandwiches from various fast food restaurants. the equation of the line of best - fit is calories = 189.2 + 13.3(grams of fat). find and interpret the residual for a chicken sandwich that has 20 grams of fat and 466 calories.
the residual is 10.8. (type an integer or a decimal.)
the residual is which indicates that the equation the number of calories.
options for the first blank: positive, negative

Explanation:

Step1: Recall Residual Formula

Residual = Observed - Predicted. Observed calories = 466, predicted from \( \text{calories} = 189.2 + 13.3(\text{grams of fat}) \).

Step2: Calculate Predicted Calories

Substitute grams of fat = 20: \( 189.2 + 13.3(20) = 189.2 + 266 = 455.2 \).

Step3: Compute Residual

Residual = 466 - 455.2 = 10.8. Since 10.8 > 0, residual is positive. A positive residual means the observed value is higher than predicted, so the equation underestimated the calories.

Answer:

The residual is 10.8, which is positive, indicating that the equation underestimated the number of calories.