Ryan Smith MATH-131-DE03A 9/14/16 Lab 1 Stroke Rates in Relation to Life Expectancy Around the Globe 1. This lab studies the correlation between stroke rates and life expectancy in a random selection of countries from all over the world. In this study I hope to find a noticeable trend between these two variables. I expect to see a negative correlation when in which the stroke rates increase life expectancy decreases. 2. My population is the 196 countries in the world. 3. V1, Qualitative Variable - Continent V2, Quantitative Variable - Stroke Rates per 100,000 V3, Quantitative Variable - Life Expectancy 4. I used the simple random sampling method to select the countries of observation. I used an online generator called \"Randomlist.com\" to randomly selected the 40 countries in my study. I personally found this to be a much easier route rather than sampling the percentages. 5. Raw data in Table on next page... NAME 1. Iraq 2. Armenia 3. Turkey 4. Hait 5. Morocco 6. Austria V1 - Continent Asia Asia Asia Americas Africa Europe V2 - Stroke Rates per 10,000 81 133 117 150 62 26 V3 - Life Expectancy 71 74 73 71 74 73 7. Netherlands 8. Syria 9. Egypt 10. Chad 11. Jamaica 12. Venezuela 13. Mexico 14. Norway 15. Lebanon 16. Iceland 17. Thailand 18. Barbados 19. Guinea 20. Mongolia 21. Yemen 22. Estonia 23. Chile 24. Germany 25. Botswana 26. United States 27. Uganda 28. Vietnam 29. Dominica 30. Denmark 31. Benin 32. Malta 33. Saint Lucia 34. Spain 35. Nigeria 36. Saudi Arabia 37. Croata 38. Switzerland 39. United Kingdom 40. Georgia Europe Asia Africa Africa Americas Americas Americas Europe Europe Europe Asia Americas Africa Asia Asia Europe Americas Europe Africa Americas Africa Asia Americas Europe Africa Europe Americas Europe Africa Asia Europe Europe Europe Asia 22 112 110 163 63 54 39 33 53 29 23 41 166 151 84 58 45 31 112 163 151 173 87 39 148 44 68 29 149 50 89 22 37 169 63 77 80 81 69 73 49 73 74 75 82 77 81 74 75 60 69 65 74 78 88 54 80 59 73 77 79 61 80 77 81 82 80 76 MATH 131 Lab 7 8/16 The goal of this lab is to test the linear correlation between the two Quantitative Variables from Lab 1; to find the equation of the regression line for the variables; and to use the line for prediction. Important Note: The interpretation of computer output is part of this lab, but the output itself is not sufficient to complete this lab. You may use the scatter plot from the computer but it must be titled and labeled appropriately. Answers must be given in complete sentences. (1 point each) 1. Consider the relationship between the two quantitative variables from Lab 1. The data can be represented as ordered pairs (x, y) where x is the independent or explanatory variable and y is the dependent or response variable. When you choose x and y, consider if changes in one variable explain or even cause changes in the second variable? Call the explanatory (predictor) variable x and the response variable y. If you don't see such a relationship, choose V2 for x and V3 for y. Use Statcrunch or Minitab to construct a scatter plot for your 40 ordered pairs of data. Clearly label your graph and attach to this lab. 2. Comment about the information shown in the scatter plot, in terms of any apparent linear correlation. Do you think the correlation is positive, negative or close to 0? Explain. 3. Find the value for r, the linear correlation coefficient, using Statcrunch or Minitab. 4. Perform a hypothesis test of the significance of r (Use =0.05 ), the linear correlation coefficient. Clearly state the null and alternative hypothesis. State your conclusion clearly and completely. Does your answer agree with your response to #2 above? 5. Regardless of the significance of the correlation coefficient from #3 above, write the equation of the regression line, using Statcrunch or Minitab. Should you use this line for prediction purposes? Why or why not? 1 MATH 131 Lab 7 8/16 6. What is the slope of your regression line? ______________________________________ Write a statement interpreting the meaning of the slope for your data. [For example, if the slope is 4.5 and x is number of terms served by a U.S. senator and y is the age of the senator, you could say that for every increase of 1 term, you predict the average age of the US senator increases by 4.5 years.] 7. What is the y - intercept of your line? _________________________________________ Write a statement interpreting the meaning of the y-intercept for your data. For your data set, does this y-intercept make sense? Explain. 8. Find 3 ordered pairs that could be on the regression line. Specify the x values that you've chosen for the points (Make sure that you choose appropriate x values.) and show your calculations for ^y Locate these 3 points on your scatter plot. Connect these 3 points and draw the regression line on the scatter plot from #1 above. x Calculation for ^y ^y 9. Use one of the 3 points from #8 above to write a statement of prediction. Follow Example 3. [For example, if you chose x = 2 and computed ^y =58.4 , write the statement as "I predict a senator who has served 2 terms will have an average age of 58.4 years old."] 2 MATH 131 Lab 7 8/16 10. Summarize your results of this lab for someone who is not familiar with statistical terminology but might be interested in your data. In other words, what kind of a general relationship did you find, if any, between these 2 variables? Statcrunch Minitab Graph Select Graph Select Scatter Plot Choose the correct column for your x-variable Choose the correct column for your y-variable Select Compute Select Graph from the main bar. Select Scatterplot from the subdirectory and choose Simple. Click on OK. In the Y variables box, Click one of the variables in left-hand box to be your y. Select. In the X variables box, Click one of the variables in left-hand box to be your x. Select. Click on OK. Correlation Select Stat Select Summary Stats Select Correlation Highlight both columns containing your quantitative data. Select Compute Select Stat from the main menu. Select Basic Statistics from the subdirectory and Select correlation. List the columns that contain the data. Click on OK. Regression Select Select Stat Select Regression Select Simple Linear Identify columns for x and y variables Select Compute Select Stat from the main menu. Select Regression from the subdirectory and Select regression. Response is your y and Predictor is your x. Click on Result and select Regression equation. Click on OK twice. 3 Ryan Smith MATH-131-DE03A 9/14/16 Lab 1 Stroke Rates in Relation to Life Expectancy Around the Globe 1. This lab studies the correlation between stroke rates and life expectancy in a random selection of countries from all over the world. In this study I hope to find a noticeable trend between these two variables. I expect to see a negative correlation when in which the stroke rates increase life expectancy decreases. 2. My population is the 196 countries in the world. 3. V1, Qualitative Variable - Continent V2, Quantitative Variable - Stroke Rates per 100,000 V3, Quantitative Variable - Life Expectancy 4. I used the simple random sampling method to select the countries of observation. I used an online generator called \"Randomlist.com\" to randomly selected the 40 countries in my study. I personally found this to be a much easier route rather than sampling the percentages. 5. Raw data in Table on next page... NAME 1. Iraq 2. Armenia 3. Turkey 4. Hait 5. Morocco 6. Austria V1 - Continent Asia Asia Asia Americas Africa Europe V2 - Stroke Rates per 10,000 81 133 117 150 62 26 V3 - Life Expectancy 71 74 73 71 74 73 7. Netherlands 8. Syria 9. Egypt 10. Chad 11. Jamaica 12. Venezuela 13. Mexico 14. Norway 15. Lebanon 16. Iceland 17. Thailand 18. Barbados 19. Guinea 20. Mongolia 21. Yemen 22. Estonia 23. Chile 24. Germany 25. Botswana 26. United States 27. Uganda 28. Vietnam 29. Dominica 30. Denmark 31. Benin 32. Malta 33. Saint Lucia 34. Spain 35. Nigeria 36. Saudi Arabia 37. Croata 38. Switzerland 39. United Kingdom 40. Georgia Europe Asia Africa Africa Americas Americas Americas Europe Europe Europe Asia Americas Africa Asia Asia Europe Americas Europe Africa Americas Africa Asia Americas Europe Africa Europe Americas Europe Africa Asia Europe Europe Europe Asia 22 112 110 163 63 54 39 33 53 29 23 41 166 151 84 58 45 31 112 163 151 173 87 39 148 44 68 29 149 50 89 22 37 169 63 77 80 81 69 73 49 73 74 75 82 77 81 74 75 60 69 65 74 78 88 54 80 59 73 77 79 61 80 77 81 82 80 76 MATH 131 Lab 7 8/16 The goal of this lab is to test the linear correlation between the two Quantitative Variables from Lab 1; to find the equation of the regression line for the variables; and to use the line for prediction. Important Note: The interpretation of computer output is part of this lab, but the output itself is not sufficient to complete this lab. You may use the scatter plot from the computer but it must be titled and labeled appropriately. Answers must be given in complete sentences. (1 point each) 1. Consider the relationship between the two quantitative variables from Lab 1. The data can be represented as ordered pairs (x, y) where x is the independent or explanatory variable and y is the dependent or response variable. When you choose x and y, consider if changes in one variable explain or even cause changes in the second variable? Call the explanatory (predictor) variable x and the response variable y. If you don't see such a relationship, choose V2 for x and V3 for y. Use Statcrunch or Minitab to construct a scatter plot for your 40 ordered pairs of data. Clearly label your graph and attach to this lab. 2. Comment about the information shown in the scatter plot, in terms of any apparent linear correlation. Do you think the correlation is positive, negative or close to 0? Explain. 3. Find the value for r, the linear correlation coefficient, using Statcrunch or Minitab. 4. Perform a hypothesis test of the significance of r (Use =0.05 ), the linear correlation coefficient. Clearly state the null and alternative hypothesis. State your conclusion clearly and completely. Does your answer agree with your response to #2 above? 5. Regardless of the significance of the correlation coefficient from #3 above, write the equation of the regression line, using Statcrunch or Minitab. Should you use this line for prediction purposes? Why or why not? 1 MATH 131 Lab 7 8/16 6. What is the slope of your regression line? ______________________________________ Write a statement interpreting the meaning of the slope for your data. [For example, if the slope is 4.5 and x is number of terms served by a U.S. senator and y is the age of the senator, you could say that for every increase of 1 term, you predict the average age of the US senator increases by 4.5 years.] 7. What is the y - intercept of your line? _________________________________________ Write a statement interpreting the meaning of the y-intercept for your data. For your data set, does this y-intercept make sense? Explain. 8. Find 3 ordered pairs that could be on the regression line. Specify the x values that you've chosen for the points (Make sure that you choose appropriate x values.) and show your calculations for ^y Locate these 3 points on your scatter plot. Connect these 3 points and draw the regression line on the scatter plot from #1 above. x Calculation for ^y ^y 9. Use one of the 3 points from #8 above to write a statement of prediction. Follow Example 3. [For example, if you chose x = 2 and computed ^y =58.4 , write the statement as "I predict a senator who has served 2 terms will have an average age of 58.4 years old."] 2 MATH 131 Lab 7 8/16 10. Summarize your results of this lab for someone who is not familiar with statistical terminology but might be interested in your data. In other words, what kind of a general relationship did you find, if any, between these 2 variables? Statcrunch Minitab Graph Select Graph Select Scatter Plot Choose the correct column for your x-variable Choose the correct column for your y-variable Select Compute Select Graph from the main bar. Select Scatterplot from the subdirectory and choose Simple. Click on OK. In the Y variables box, Click one of the variables in left-hand box to be your y. Select. In the X variables box, Click one of the variables in left-hand box to be your x. Select. Click on OK. Correlation Select Stat Select Summary Stats Select Correlation Highlight both columns containing your quantitative data. Select Compute Select Stat from the main menu. Select Basic Statistics from the subdirectory and Select correlation. List the columns that contain the data. Click on OK. Regression Select Select Stat Select Regression Select Simple Linear Identify columns for x and y variables Select Compute Select Stat from the main menu. Select Regression from the subdirectory and Select regression. Response is your y and Predictor is your x. Click on Result and select Regression equation. Click on OK twice. 3 Ryan Smith MATH-131-DE03A 9/14/16 Lab 1 Stroke Rates in Relation to Life Expectancy Around the Globe 1. This lab studies the correlation between stroke rates and life expectancy in a random selection of countries from all over the world. In this study I hope to find a noticeable trend between these two variables. I expect to see a negative correlation when in which the stroke rates increase life expectancy decreases. 2. My population is the 196 countries in the world. 3. V1, Qualitative Variable - Continent V2, Quantitative Variable - Stroke Rates per 100,000 V3, Quantitative Variable - Life Expectancy 4. I used the simple random sampling method to select the countries of observation. I used an online generator called \"Randomlist.com\" to randomly selected the 40 countries in my study. I personally found this to be a much easier route rather than sampling the percentages. 5. Raw data in Table on next page... NAME 1. Iraq 2. Armenia 3. Turkey 4. Hait 5. Morocco 6. Austria V1 - Continent Asia Asia Asia Americas Africa Europe V2 - Stroke Rates per 10,000 81 133 117 150 62 26 V3 - Life Expectancy 71 74 73 71 74 73 7. Netherlands 8. Syria 9. Egypt 10. Chad 11. Jamaica 12. Venezuela 13. Mexico 14. Norway 15. Lebanon 16. Iceland 17. Thailand 18. Barbados 19. Guinea 20. Mongolia 21. Yemen 22. Estonia 23. Chile 24. Germany 25. Botswana 26. United States 27. Uganda 28. Vietnam 29. Dominica 30. Denmark 31. Benin 32. Malta 33. Saint Lucia 34. Spain 35. Nigeria 36. Saudi Arabia 37. Croata 38. Switzerland 39. United Kingdom 40. Georgia Europe Asia Africa Africa Americas Americas Americas Europe Europe Europe Asia Americas Africa Asia Asia Europe Americas Europe Africa Americas Africa Asia Americas Europe Africa Europe Americas Europe Africa Asia Europe Europe Europe Asia 22 112 110 163 63 54 39 33 53 29 23 41 166 151 84 58 45 31 112 163 151 173 87 39 148 44 68 29 149 50 89 22 37 169 63 77 80 81 69 73 49 73 74 75 82 77 81 74 75 60 69 65 74 78 88 54 80 59 73 77 79 61 80 77 81 82 80 76 MATH 131 Lab 7 8/16 The goal of this lab is to test the linear correlation between the two Quantitative Variables from Lab 1; to find the equation of the regression line for the variables; and to use the line for prediction. Important Note: The interpretation of computer output is part of this lab, but the output itself is not sufficient to complete this lab. You may use the scatter plot from the computer but it must be titled and labeled appropriately. Answers must be given in complete sentences. (1 point each) 1. Consider the relationship between the two quantitative variables from Lab 1. The data can be represented as ordered pairs (x, y) where x is the independent or explanatory variable and y is the dependent or response variable. When you choose x and y, consider if changes in one variable explain or even cause changes in the second variable? Call the explanatory (predictor) variable x and the response variable y. If you don't see such a relationship, choose V2 for x and V3 for y. Use Statcrunch or Minitab to construct a scatter plot for your 40 ordered pairs of data. Clearly label your graph and attach to this lab. 2. Comment about the information shown in the scatter plot, in terms of any apparent linear correlation. Do you think the correlation is positive, negative or close to 0? Explain. 3. Find the value for r, the linear correlation coefficient, using Statcrunch or Minitab. 4. Perform a hypothesis test of the significance of r (Use =0.05 ), the linear correlation coefficient. Clearly state the null and alternative hypothesis. State your conclusion clearly and completely. Does your answer agree with your response to #2 above? 5. Regardless of the significance of the correlation coefficient from #3 above, write the equation of the regression line, using Statcrunch or Minitab. Should you use this line for prediction purposes? Why or why not? 1 MATH 131 Lab 7 8/16 6. What is the slope of your regression line? ______________________________________ Write a statement interpreting the meaning of the slope for your data. [For example, if the slope is 4.5 and x is number of terms served by a U.S. senator and y is the age of the senator, you could say that for every increase of 1 term, you predict the average age of the US senator increases by 4.5 years.] 7. What is the y - intercept of your line? _________________________________________ Write a statement interpreting the meaning of the y-intercept for your data. For your data set, does this y-intercept make sense? Explain. 8. Find 3 ordered pairs that could be on the regression line. Specify the x values that you've chosen for the points (Make sure that you choose appropriate x values.) and show your calculations for ^y Locate these 3 points on your scatter plot. Connect these 3 points and draw the regression line on the scatter plot from #1 above. x Calculation for ^y ^y 9. Use one of the 3 points from #8 above to write a statement of prediction. Follow Example 3. [For example, if you chose x = 2 and computed ^y =58.4 , write the statement as "I predict a senator who has served 2 terms will have an average age of 58.4 years old."] 2 MATH 131 Lab 7 8/16 10. Summarize your results of this lab for someone who is not familiar with statistical terminology but might be interested in your data. In other words, what kind of a general relationship did you find, if any, between these 2 variables? Statcrunch Minitab Graph Select Graph Select Scatter Plot Choose the correct column for your x-variable Choose the correct column for your y-variable Select Compute Select Graph from the main bar. Select Scatterplot from the subdirectory and choose Simple. Click on OK. In the Y variables box, Click one of the variables in left-hand box to be your y. Select. In the X variables box, Click one of the variables in left-hand box to be your x. Select. Click on OK. Correlation Select Stat Select Summary Stats Select Correlation Highlight both columns containing your quantitative data. Select Compute Select Stat from the main menu. Select Basic Statistics from the subdirectory and Select correlation. List the columns that contain the data. Click on OK. Regression Select Select Stat Select Regression Select Simple Linear Identify columns for x and y variables Select Compute Select Stat from the main menu. Select Regression from the subdirectory and Select regression. Response is your y and Predictor is your x. Click on Result and select Regression equation. Click on OK twice. 3