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 = 182.5 + 13.5(grams of fat). find and interpret the residual for a chicken sandwich that has 20 grams of fat and 448 calories. the residual is \\(\square\\) (type an integer or a decimal.)

Explanation:

Step1: Recall residual formula

Residual is observed value minus predicted value, \( \text{Residual} = y - \hat{y} \), where \( y \) is observed, \( \hat{y} \) is predicted.

Step2: Calculate predicted calories

Given \( \hat{y} = 182.5 + 13.5x \), \( x = 20 \) grams of fat.
Substitute \( x \): \( \hat{y} = 182.5 + 13.5(20) \)
Calculate \( 13.5(20) = 270 \), then \( \hat{y} = 182.5 + 270 = 452.5 \).

Step3: Compute residual

Observed \( y = 448 \), so residual \( = 448 - 452.5 = -4.5 \).

Answer:

-4.5