The accompanying data on x= Average energy density (calories per 100 grams) and y=Average cost (in dollars) for eight different food groups are from the paper (The cost of U.S. Foods as Related to Their Nutritional Value' (American Journal of Clinical Nutrition [2010]: 1181-1188). The authors were interested in the relationship between average cost and the average energy density of foods. Food Group Average Cost Average Energy Density Milk and milk products 0.40 182 Eggs 0.32 171 Dry beans, legumes, nuts and seeds 0.50 330 Grain products 337 0.47 Fruit 0.28 67 Vegetables 0.33 83 Fats, oils, and salad dressings 0.37 390 Sugars, sweets and beverages 0.40 242 The equation of the least squares regression line is given as :

The accompanying data on x= Average energy density (calories per 100 grams) and y=Average cost (in dollars) for eight different food groups are from the paper (The cost of U.S. Foods as Related to Their Nutritional Value' (American Journal of Clinical Nutrition [2010]: 1181-1188). The authors were interested in the relationship between average cost and the average energy density of foods. Food Group Average Cost Average Energy Density Milk and milk products 0.40 182 Eggs 0.32 171 Dry beans, legumes, nuts and seeds 0.50 330 Grain products 337 0.47 Fruit 0.28 67 Vegetables 0.33 83 Fats, oils, and salad dressings 0.37 390 Sugars, sweets and beverages 0.40 242 The equation of the least squares regression line is given as :

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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

The accompanying data on x= Average energy density (calories per 100 grams) and y=Average
cost (in dollars) for eight different food groups are from the paper (The cost of U.S. Foods as
Related to Their Nutritional Value (American Journal of Clinical Nutrition [2010]: 1181-1188).
The authors were interested in the relationship between average cost and the average energy
density of foods.
Food Group
Average Cost
Average Energy Density
Milk and milk products
0.40
182
Eggs
0.32
171
Dry beans, legumes, nuts and seeds
0.50
з30
Grain products
0.47
337
Fruit
0.28
67
Vegetables
0.33
83
Fats, oils, and salad dressings
0.37
390
Sugars, sweets and beverages
0.40
242
The equation of the least squares regression line is given as :
Y=0.27970+0.0004619x , where y is the predicted average cost in dollars, and x is
the average energy density in calories per 100 grams.
-Construct a residual plot and comment on any unusual features of the residual plot.
-Calculate and interpret the value of r2.
-Calculate and interpret the value of se.
-Based on your answers in the parts above, do you think it is appropriate to use the least
squares regression line to predict average cost for a food group based on its average
energy density? Explain.
-The meat, poultry, and fish food group has an average energy density of 196. What
average cost would you predict for this food group?

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