The foopt the 107 Exercise 3. Case Study Instructions: With the same group in Exercise 2, conduct a simple survey on the case of sugar consumption. You may either hold brief interviews or use survey questionnaires to gather data for your case study. Your data gathering may focus on but is not limited to the following: 1. Extent of overconsumption of sugar 2. Awareness of hidden sugar content on food items 3. Food items that contain hidden sugars 4. Agreement or disagreement on the need to regulate the production and consumption of sugar 5. Awareness on the impact of the overconsumption of sugar-based products on the pursuit of human happiness After gathering data, analyze and present your data following the guidelines below. Overall, your case study report should not be more than 10 pages.
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Calories versus Sugar The following data represent the number of calories per serving and the number of grams of sugar per serving for a random sample of high-fiber cereals. $$\begin{array}{|cc|cc|} \hline \text { Calories, } \boldsymbol{x} & \text { Sugar, } \boldsymbol{y} & \text { Calories, } \boldsymbol{x} & \text { Sugar, } \boldsymbol{y} \\ \hline 200 & 18 & 210 & 23 \\ \hline 210 & 23 & 210 & 16 \\ \hline 170 & 17 & 210 & 17 \\ \hline 190 & 20 & 190 & 12 \\ \hline 200 & 18 & 190 & 11 \\ \hline 180 & 19 & 200 & 11 \\ \hline \end{array}$$ (a) Draw a scatter diagram of the data treating calories as the explanatory variable. What type of relation appears to exist between calories and sugar content? (b) Determine the correlation between calories and sugar content. Is there a linear relation between calories and sugar content? (c) Suppose that we add Kellogg's All-Bran cereal, which has 80 calories and 6 grams of sugar per serving, to the data set. Redraw the scatter diagram and recompute the correlation between calories and sugar content. Is there a linear relation between calories and sugar content with All-Bran included in the data set? Is All-Bran an influential observation? (d) Explain why it is necessary to show a scatter diagram with the correlation coefficient when claiming that a linear relation exists between two variables.
Describing the Relation between Two Variables
Diagnostics on the Least-Squares Regression Line
People with diabetes measure their fasting plasma glucose (FPG; measured in units of milligrams per milliliter) after fasting for at least 8 hours. Another measurement, made at regular medical checkups, is called HbA. This is roughly the percent of red blood cells that have a glucose molecule attached. It measures average exposure to glucose over a period of several months. The table below gives data on both $\mathrm{HbA}$ and $\mathrm{FPG}$ for 18 diabetics five months after they had completed a diabetes education class. $$\begin{array}{ccc|ccc}\hline \text { Subject } & \begin{array}{c}\text { HbA } \\\text { (\%) }\end{array} & \begin{array}{c}\text { FPG } \\\text { (mg/mL) } \end{array} & \text { Subject } & \begin{array}{c} \text { HbA } \\\text { (\%) }\end{array} & \begin{array}{c}\text { FPG } \\\text { (mg/mL) }\end{array} \\1 & 6.1 & 141 & 10 & 8.7 & 172 \\2 & 6.3 & 158 & 11 & 9.4 & 200 \\3 & 6.4 & 112 & 12 & 10.4 & 271 \\4 & 6.8 & 153 & 13 & 10.6 & 103 \\5 & 7.0 & 134 & 14 & 10.7 & 172 \\6 & 7.1 & 95 & 15 & 10.7 & 359 \\7 & 7.5 & 96 & 16 & 11.2 & 145 \\8 & 7.7 & 78 & 17 & 13.7 & 147 \\9 & 7.9 & 148 & 18 & 19.3 & 255 \\\hline \end{array}$$ (a) Make a scatterplot with HbA as the explanatory variable. Describe what you see. (b) Subject 18 is an outlier in the $x$ direction. What effect do you think this subject has on the correlation? What effect do you think this subject has on the equation of the least-squares regression line? Calculate the correlation and equation of the least-squares regression line with and without this subject to confirm your answer. (c) Subject 15 is an outlier in the $y$ direction. What effect do you think this subject has on the correlation? What effect do you think this subject has on the equation of the least-squares regression line? Calculate the correlation and equation of the least-squares regression line with and without this subject to confirm your answer.
Describing Relationships
Least-Squares Regression
Managing diabetes People with diabetes measure their fasting plasma glucose (FPG; measured in units of milligrams per milliliter) after fasting for at least 8 hours. Another measurement, made at regular medical checkups, is called HbA. This is roughly the percent of red blood cells that have a glucose molecule attached. It measures average exposure to glucose over a period of several months. The table below gives data on both HbA and FPG for 18 diabetics five months after they had completed a diabetes education class.19 (a) Make a scatterplot with HbA as the explanatoryvariable. There is a positive linear relationship, but it is surprisingly weak. (b) Subject 15 is an outlier in the $y$ direction. Subject 18 is an outlier in the $x$ direction. Find the correlation for all 18 subjects, for all except Subject $15,$ and for all except Subject 18 . Are either or both of these subjects influential for the correlation? Explain in simple language why $r$ changes in opposite directions when we remove each of these points. (c) Add three regression lines for predicting $\mathrm{FPC}$ from HbA to your scatterplot: for all 18 subjects, for all except Subject $15,$ and for all except Subject $18 .$ Is either Subject 15 or Subject 18 strongly influential for the least-squares line? Explain in simple language what features of the scatterplot explain the degree of influence.
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