Question 1168826: Researchers recorded facts about 77 breakfast cereals, including the calories and sugar content (in grams) of a serving. Based on the data, the following least squares regression equation can be used to predict the number of calories in a cereal by using the amount of sugar in the cereal.
predicted calories=89.5+2.5(sugar grams)
One popular brand of cereal contains 19 grams of sugar, and has a residual of +53 calories for one serving. What is the actual number of calories contained in one serving of this cereal?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break this down step-by-step:
**1. Predicted Calories**
* We're given the least squares regression equation:
* predicted calories = 89.5 + 2.5(sugar grams)
* The cereal contains 19 grams of sugar.
* Let's plug that into the equation:
* predicted calories = 89.5 + 2.5(19)
* predicted calories = 89.5 + 47.5
* predicted calories = 137
**2. Residual**
* The residual is the difference between the actual value and the predicted value.
* We're given a residual of +53 calories.
* residual = actual calories - predicted calories
* 53 = actual calories - 137
**3. Actual Calories**
* To find the actual calories, we can rearrange the residual equation:
* actual calories = residual + predicted calories
* actual calories = 53 + 137
* actual calories = 190
**Therefore, the actual number of calories contained in one serving of this cereal is 190.**
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