"The U.S. Food and Drug Administration (FDA) requires nutrition labeling for most foods. Un FDA regulations, manufacturers are required to list the amounts of certain nutrients in their foods, such as calories, sugar, fat, and carbohydrates. This nutritional information is displayed in the ""Nutrition Facts"" panel on the food's package.
The table shows the nutritional content below for one cup of each of 21 different breakfast
cereals.
C = calories
S = sugar in grams
F = fat in grams
R = carbohydrates in grams

7. Use the equations from Exercise 6 to predict the calories in 1 cup of cereal that has 7 grams of sugar, 0.5 gram of fat, and 31 grams of carbohydrates."

검증된 단계별 안내

Identify the regression equation from Exercise 6, which predicts calories (C) based on sugar (S), fat (F), and carbohydrates (R). The general form of the multiple linear regression equation is:

C = b_0 + b_1 S + b_2 F + b_3 R

, where b_0 is the intercept and b_1, b_2, b_3 are the coefficients for sugar, fat, and carbohydrates respectively.

Substitute the given values for sugar, fat, and carbohydrates into the regression equation:

S = 7, F = 0.5, R = 31

Calculate the predicted calories by multiplying each coefficient by its corresponding variable and adding the intercept:

C = b_0 + b_1 	imes 7 + b_2 	imes 0.5 + b_3 	imes 31

Perform the arithmetic operations step-by-step: multiply each coefficient by the given nutrient amount, then sum all these products with the intercept.

The final sum from step 4 will give the predicted number of calories in 1 cup of cereal with 7 grams of sugar, 0.5 gram of fat, and 31 grams of carbohydrates.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Multiple Linear Regression

Multiple linear regression is a statistical method used to model the relationship between one dependent variable and two or more independent variables. It estimates coefficients that quantify the effect of each predictor on the response, allowing prediction of the dependent variable based on given values of the predictors.

Interpretation of Regression Coefficients

Regression coefficients represent the expected change in the dependent variable for a one-unit increase in an independent variable, holding other variables constant. Understanding these coefficients is essential for making predictions and interpreting the influence of each nutrient (sugar, fat, carbohydrates) on calories.

Prediction Using Regression Equations

Once the regression equation is established, it can be used to predict the dependent variable's value for new observations by substituting the given independent variable values. This process is crucial for estimating calories in cereals with specified amounts of sugar, fat, and carbohydrates.