Section 4 1 Exploring Associations between Two Quantitative

Section 4. 1 Exploring Associations between Two Quantitative Variables?

Example: n Is there, on a national scale, an association between TV watching and obesity? n What do you think? n What does the data Show?

Country Data: The average hours of TV watched by adults in 18 industrialized countries and the Obesity rate of adults in those countries. Does there seem to be a associated? Lets look at a bar graph and see if that helps. TV Viewing Hours Obesity Rate Australia 3. 25 24. 35 Austria 2. 72 20. 75 Belgium 3. 68 11. 35 Canada 3. 09 23. 45 Denmark 2. 87 8. 85 Finland 2. 87 18. 35 Ireland 2. 58 9. 7 Italy 3. 98 12. 75 Japan 3. 73 1. 65 Korea 3. 19 7. 1 New Zealand 2. 82 27. 3 Portugal 3. 41 14. 95 Spain 3. 82 15. 7 Sweden 2. 47 11. 4 Switzerland 2. 47 15. 55 Turkey United Kingdom 4. 33 21. 65 3 22. 9 United States 7. 97 39. 15

Data: TV vs. Obesity TV Viewing Hours Obesity Rate

New Tool: Scatter Plot: n To build a scatter plot treat your explanatory variable as x, and your response variable as y, and plot your data on an (x , y) plane. Height Weight Jim 68 145 Jill 65 130 Frank 71 173 Mark 73 205 Eric 66 143 Zach 70 166

New Tool: Scatter Plot: n We look at three things on a scatter Plot: n Is there a linear association? n What is the direction? n How strong is the association?

Correlation. n Correlation is a numerical value that summarizes the direction and strength of the association between two quantitative variables. n Properties: n Denoted r. n Positive r indicated a positive association n Negative r indicated a negative association n Values fall within the interval [-1, 1] n The closer to r = zero the weaker the association.

Correlation Would you expect a positive association, a negative association or no association between the age of the car and the mileage on the odometer? a) Positive association b) Negative association c) No association

New Tool: Scatter Plot: n What would we expect as the r value for the scatter plot below?

Questions

Calculating Correlation. Height Weight Jim 68 145 Jill 65 130 Frank 71 173 Mark 73 205 Eric 66 143 Zach 70 166

Country Remember the TV thing: r = 0. 5378 TV Viewing Hours Obesity Rate Australia 3. 25 24. 35 Austria 2. 72 20. 75 Belgium 3. 68 11. 35 Canada 3. 09 23. 45 Denmark 2. 87 8. 85 Finland 2. 87 18. 35 Ireland 2. 58 9. 7 Italy 3. 98 12. 75 Japan 3. 73 1. 65 Korea 3. 19 7. 1 New Zealand 2. 82 27. 3 Portugal 3. 41 14. 95 Spain 3. 82 15. 7 Sweden 2. 47 11. 4 Switzerland 2. 47 15. 55 Turkey United Kingdom 4. 33 21. 65 3 22. 9 United States 7. 97 39. 15

Country Remember the TV thing: r = 0. 0884 TV Viewing Hours Obesity Rate Australia 3. 25 24. 35 Austria 2. 72 20. 75 Belgium 3. 68 11. 35 Canada 3. 09 23. 45 Denmark 2. 87 8. 85 Finland 2. 87 18. 35 Ireland 2. 58 9. 7 Italy 3. 98 12. 75 Japan 3. 73 1. 65 Korea 3. 19 7. 1 New Zealand 2. 82 27. 3 Portugal 3. 41 14. 95 Spain 3. 82 15. 7 Sweden 2. 47 11. 4 Switzerland 2. 47 15. 55 Turkey United Kingdom 4. 33 21. 65 3 22. 9 United States 7. 97 39. 15

Questions