Burger King 2010 revisited Recall the Burger Kingmenu data from Chapter 7. BK’s nutrition sheet listsmany variables. Here’s a multiple regression to predict calories for Burger King foods from Protein content (g),Total Fat (g), Carbohydrate (g), and Sodium (mg) perserving:Dependent variable is CaloriesR-squared = 99.8, R-squared (adjusted) = 99.8,s = 8.51 with 111 - 5 = 106 degrees of freedomSource Sum ofSquares df MeanSquare F-RatioRegression 4750462 4 1187616 16394Residual 7678.64 106 72.4400Variable Coefficient SE(Coeff) t-Ratio P-ValueIntercept -5.826 2.568 -2.27 0.0253Protein 3.8814 0.0991 39.1 60.0001Total fat 9.2080 0.0893 103 60.0001Carbs 3.9016 0.0457 85.3 60.0001Na/Serv. 1.2873 0.4172 3.09 0.0026 a) Do you think this model would do a good job of predict-ing calories for a new BK menu item? Why or why not? b) The mean of Calories is 453.9 with a standard devia-tion of 234.6. Discuss what the value of s in the re-gression means about how well the model fits the data. c) Does the R2 value of 99.8% mean that the residuals are allactually equal to zero? How can you tell from this table?
Burger King 2010 revisited Recall the Burger Kingmenu data from Chapter 7. BK’s nutrition sheet listsmany variables. Here’s a multiple regression to predict calories for Burger King foods from Protein content (g),Total Fat (g), Carbohydrate (g), and Sodium (mg) perserving:Dependent variable is CaloriesR-squared = 99.8, R-squared (adjusted) = 99.8,s = 8.51 with 111 - 5 = 106 degrees of freedomSource Sum ofSquares df MeanSquare F-RatioRegression 4750462 4 1187616 16394Residual 7678.64 106 72.4400Variable Coefficient SE(Coeff) t-Ratio P-ValueIntercept -5.826 2.568 -2.27 0.0253Protein 3.8814 0.0991 39.1 60.0001Total fat 9.2080 0.0893 103 60.0001Carbs 3.9016 0.0457 85.3 60.0001Na/Serv. 1.2873 0.4172 3.09 0.0026 a) Do you think this model would do a good job of predict-ing calories for a new BK menu item? Why or why not? b) The mean of Calories is 453.9 with a standard devia-tion of 234.6. Discuss what the value of s in the re-gression means about how well the model fits the data. c) Does the R2 value of 99.8% mean that the residuals are allactually equal to zero? How can you tell from this table?
MATLAB: An Introduction with Applications
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Concept explainers
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Question
Burger King 2010 revisited Recall the Burger King
menu data from Chapter 7. BK’s nutrition sheet lists
many variables. Here’s a multiple regression to predict
calories for Burger King foods from Protein content (g),
Total Fat (g), Carbohydrate (g), and Sodium (mg) per
serving:
Dependent variable is Calories
R-squared = 99.8, R-squared (adjusted) = 99.8,
s = 8.51 with 111 - 5 = 106 degrees of freedom
Source
Total Fat (g), Carbohydrate (g), and Sodium (mg) per
serving:
Dependent variable is Calories
R-squared = 99.8, R-squared (adjusted) = 99.8,
s = 8.51 with 111 - 5 = 106 degrees of freedom
Source
Sum of
Squares df
Squares df
Mean
Square F-Ratio
Regression 4750462 4 1187616 16394
Residual 7678.64 106 72.4400
Variable Coefficient SE(Coeff) t-Ratio P-Value
Intercept -5.826 2.568 -2.27 0.0253
Protein 3.8814 0.0991 39.1 60.0001
Total fat 9.2080 0.0893 103 60.0001
Carbs 3.9016 0.0457 85.3 60.0001
Na/Serv. 1.2873 0.4172 3.09 0.0026
Square F-Ratio
Regression 4750462 4 1187616 16394
Residual 7678.64 106 72.4400
Variable Coefficient SE(Coeff) t-Ratio P-Value
Intercept -5.826 2.568 -2.27 0.0253
Protein 3.8814 0.0991 39.1 60.0001
Total fat 9.2080 0.0893 103 60.0001
Carbs 3.9016 0.0457 85.3 60.0001
Na/Serv. 1.2873 0.4172 3.09 0.0026
a) Do you think this model would do a good job of predict-
ing calories for a new BK menu item? Why or why not?
ing calories for a new BK menu item? Why or why not?
b) The mean of Calories is 453.9 with a standard devia-
tion of 234.6. Discuss what the value of s in the re-
gression means about how well the model fits the data.
tion of 234.6. Discuss what the value of s in the re-
gression means about how well the model fits the data.
c) Does the R2
value of 99.8% mean that the residuals are all
actually equal to zero? How can you tell from this table?
actually equal to zero? How can you tell from this table?
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