Math Problem Statement

Suppose a researcher wants to determine if the amount of Fat in​ fast-food hamburgers can be used to predict the amount of Calories. The data are given below. Complete parts a through g. Fat​ (g) 21 30 32 33 37 40 45

Calories 420 600 600 580 620 690 650 Question content area bottom Part 1 ​a) Create a scatterplot of Calories vs. Fat. Choose the correct graph below. A. 300 800 10 60 Calories Fat (g)

A scatterplot with horizontal axis labeled "Calories" from 300 to 800 in intervals of 100 and vertical axis labeled "Fat (grams)" from 10 to 60 in intervals of 10 contains points whose general pattern is a line that falls from left to right. The approximate points are as follows: (490, 45), (450, 40), (520, 37), (560, 33), (540, 32), (540, 30), and (720, 21). B. 10 60 300 800 Fat (g) Calories

A scatterplot with horizontal axis labeled "Fat (grams)" from 10 to 60 in intervals of 10 and vertical axis labeled "Calories" from 300 to 800 in intervals of 100 contains points whose general pattern is a line that rises from left to right. The approximate points are as follows: (21, 420), (30, 600), (32, 600), (33, 580), (37, 620), (40, 690), (45, 650). Your answer is correct.C. 300 800 10 60 Calories Fat (g)

A scatterplot with horizontal axis labeled "Calories" from 300 to 800 in intervals of 100 and vertical axis labeled "Fat (grams)" from 10 to 60 in intervals of 10 contains points whose general pattern is a line that rises from left to right. The approximate points are as follows: (420, 21), (600, 30), (600, 32), (580, 33), (620, 37), (690, 40), (650, 45). D. 10 60 300 800 Fat (g) Calories

A scatterplot with horizontal axis labeled "Fat (grams)" from 10 to 60 in intervals of 10 and vertical axis labeled "Calories" from 300 to 800 in intervals of 100 contains points whose general pattern is a line that falls from left to right. The approximate points are as follows: (21, 720), (30, 540), (32, 540), (33, 560), (37, 520), (40, 450), (45, 490). Part 2 ​b) Interpret the value of Upper R squared in this context. Select the correct choice below and fill in the answer box to complete your choice. ​(Round to one decimal place as​ needed.) A. The value of Upper R squared is    enter your response here​%, which is​ 100% minus the percentage of the variation in Fat that can be accounted for by a linear model on the amount of Calories. B. The value of Upper R squared is    enter your response here​%, which is​ 100% minus the percentage of the variation in Calories that can be accounted for by a linear model on the amount of Fat. C. The value of Upper R squared is    enter your response here​%, which is the percentage of the variation in Calories that can be accounted for by a linear model on the amount of Fat. D. The value of Upper R squared is    enter your response here​%, which is the percentage of the variation in Fat that can be accounted for by a linear model on the amount of Calories.

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Regression
Scatterplots
Correlation
R-squared (R²)

Formulas

Linear regression formula: y = mx + b
R-squared formula: R² = 1 - (SSres / SStot)

Theorems

Linear regression model
Least squares method

Suitable Grade Level

Grades 10-12