Math215 Statistical Concepts Names: __________________________ Correlation and Regression Worksheet Review the Health data given in the Excel spreadsheet. The variables of Health Services, Safe Water and Sanitation represent the percentages of people who have access to those in a given country. The variable of Infant Mortality is the number of infant deaths in thousands in that country. The variable of Daily Calories represents the average number of calories consumed by an individual of the country. (This data is taken from World Health Organization in 2011) All groups should complete Part I and then each group should complete a section in Part II. Part I: One Variable Statistics All groups should complete this part. Compare the three distributions that describe the percentages of people who have access to health services, safe water, and sanitation. Using your calculator or Excel, calculate the One Variable Statistics and record the information below. Health Services Safe Water Sanitation Mean Standard deviation Five-number summary Which of the three categories has the greatest need for overall improvement? Why? Use your findings above to discuss your answer. 1 081214 Math215 Statistical Concepts Names: __________________________ Part II Group 1. 1. Create a scatterplot to see the relationship between the variables Sanitation and Life Expectancy. What is the independent variable? Dependent variable? 2. Find the correlation coefficient, r and describe the relationship between Sanitation and Life Expectancy. 3. Find the equation of the linear regression line. Write the equation below and draw it on the scatter plot. 4. Interpret the slope of the equation. What does it tell you about the relationship between Sanitation and Life Expectancy? Be specific. 5. Interpret the y-intercept of the equation. What does it tell you? Be specific. 6. What percent of the variation in the dependent variable can be explained by this linear relationship? What is this number called? 7. If the 90% of the people in a country have access to Sanitation, what would you predict the Life Expectancy of that country to be? 8. If the Life Expectancy of a country is 73 years, what would you expect the Sanitation rate of that country to be? 2 081214 Math215 Statistical Concepts Names: __________________________ Group 2. 1. Create a scatterplot to see the relationship between the variables Safe Water and Life Expectancy. What is the independent variable? Dependent variable? 2. Find the correlation coefficient, r, and describe the relationship between Safe Water and Life Expectancy. 3. Find the equation of the linear regression line. Write the equation below and draw it on the scatter plot 4. Interpret the slope of the equation. What does it tell you about the relationship between Safe Water and Life Expectancy? Be specific. 5. Interpret the y-intercept of the equation. What does it tell you? Be specific. 6. What percent of the variation in the dependent variable can be explained by this linear relationship? What is this number called? 7. If the 85% of people in a country have access to Safe Water, what would you predict the Life Expectancy of that country to be? 8. If the Life Expectancy of a country is 73 years, what would you expect the Safe Water rate of that country to be? 3 081214 Math215 Statistical Concepts Names: __________________________ Group 3. 1. Make a scatterplot to see the relationship between the variables Health Services and Life Expectancy. What is the independent variable? Dependent variable? 2. Find the correlation coefficient, r and describe the relationship between Health Services and Life Expectancy. 3. Find the equation of the linear regression line. Write the equation below and draw it on the scatter plot. 4. Interpret the slope of the equation. What does it tell you about the relationship between Health Services and Life Expectancy? Be specific. 5. Interpret the y-intercept of the equation. What does it tell you? Be specific. 6. What percent of the variation in the dependent variable can be explained by this linear relationship? What is this number called? 7. If only 35% of people in a country have access to Health Services, what would you predict the Life Expectancy of that country to be? 8. If the Life Expectancy of a country is 73 years, what would you expect the Health Services rate of that country to be? 4 081214 Math215 Statistical Concepts Names: __________________________ Group 4. 1. Make a scatterplot to see the relationship between the variables Infant Mortality and Life Expectancy. What is the independent variable? Dependent variable? 2. Find the correlation coefficient, r and describe the relationship between Infant Mortality and Life Expectancy. 3. Find the equation of the linear regression line. Write the equation below and draw it on the scatter plot 4. Interpret the slope of the equation. What does it tell you about the relationship between Infant Mortality and Life Expectancy? Be specific. 5. Interpret the y-intercept of the equation. What does it tell you? Be specific. 6. What percent of the variation in the dependent variable can be explained by this linear relationship? What is this number called? 7. If the number of infant deaths in a country is 50 (thousands) , what would you predict the Life Expectancy of that country to be? 8. If the Life Expectancy of a country is 73 years, what would you expect the number of Infant Mortality of that country to be? 5 081214 Math215 Statistical Concepts Names: __________________________ Group 5. 1. Make a scatterplot to see the relationship between the variables Daily Calories and Life Expectancy. What is the independent variable? Dependent variable? 2. Find the correlation coefficient, r and describe the relationship between Daily Calories and Life Expectancy. 3. Find the equation of the linear regression line. Write the equation below and draw it on the scatter plot 4. Interpret the slope of the equation. What does it tell you about the relationship between Daily Calories and Life Expectancy? Be specific. 5. Interpret the y-intercept of the equation. What does it tell you? Be specific. 6. What percent of the variation in the dependent variable can be explained by this linear relationship? What is this number called? 7. If the average number of calories consumed by an individual in a country is 2550, what would you predict the Life Expectancy of that country to be? 8. If the Life Expectancy of a country is 73 years, what would you expect the average number of daily calories consumed in that country to be? 6 081214 Life Daily Country Expectancy Calories Algeria 66 2866 Angola 46 1807 Benin 51 2305 Botswana 68 2375 Cambodia 51 2166 Central Africa Rep. 47 2036 China 71 2639 Egypt 62 3336 Ethiopia 49 1667 Ghana 55 2248 Guinea 44 2132 Indonesia 60 2750 Iran 65 3181 Iraq 64 2887 Jordan 70 2634 Kenya 59 2163 Kuwait 75 3195 Liberia 55 2382 Libya 63 3324 Madagascar 51 2158 Malaysia 71 2774 Mongolia 64 2479 Mozambique 47 1680 Niger 46 2308 Nigeria 52 2312 Papua New Guinea 56 2493 Philippines 65 2375 Rwanda 46 1971 Saudi Arabia 69 2874 Senegal 48 2369 Singapore 75 3198 Somalia 49 1906 Sri Lanka 72 2277 Sudan 52 1974 Tanzania 51 2206 Thailand 69 2316 Togo 54 2214 Zaire 52 1991 Zambia 48 2077 Zimbabwe 60 2299 World Health Organization Infant Health Mortality Services 61 90 125 30 110 30 24 89 116 53 105 30 38 90 57 99 168 46 81 60 133 40 72 80 65 87 58 99 47 97 66 77 14 100 131 39 68 100 113 65 14 90 60 100 147 39 123 30 84 72 54 97 40 75 110 80 31 98 80 40 6 100 127 27 18 90 99 60 115 80 26 70 85 60 91 40 108 74 47 83 Safe Water 70 34 54 60 37 12 83 88 28 54 64 51 61 91 99 50 100 54 93 20 72 79 24 55 50 32 82 66 93 47 100 60 71 45 51 76 59 33 48 36 Sanitation 60 18 42 42 15 21 97 51 16 42 24 44 51 70 76 43 98 15 95 5 94 73 24 10 15 56 69 58 82 54 96 17 60 70 66 74 21 25 43 42