Using scatter plots to Identify Relationships MAP4C Unit 3 Note 2 Using scatter plots to Identify Relationships

Independent and dependent Variables Scatter plots represent two-variable data as points. Scatter plots may reveal relationships between 2 variables. One variable is dependent on the other variable, because its value changes according to the value of the independent variable. Example: your height changes with your age, getting taller, reaching a maximum and even shrinking as we get older. The independent variable goes on the x-axis, the dependent variable goes on the y-axis.

Create a Scatter plot Collect data from at least 10 classmates: the distance from the elbow to the outstretched tip of the middle finger, the distance from the knee to the ankle. Graph this data on a scatter plot. Describe the results. Do you think the two are related? Why?

Correlation A correlation is a relationship between 2 variables. Scatter plots may show correlations. A positive correlation describes a situation in which both variables increase together. (The points go up and to the right in a positive slope). A negative correlation describes a situation where one variable increases because another one decreases. (The points go down and to the right in a negative slope).

Cause and Effect Observing a relationship between 2 variables does not necessarily mean that one affects the other. Other factors could be involved, or it could be a coincidence. Cause and effect is challenging to prove conclusively requiring analysis and statistics. The causes of global warming are hard to pinpoint as so many factors are involved.

Example 1 Jay researched estimates for a job painting his house and plots his results on a scatter plot. Which is the dependent variable? Justify your choice. Which 2 companies will take the longest? Which of these is cheaper? Which 2 companies charge the same amount? Why might you pick Company E? B? Time required Cost C B A D E

Example 2 Leg length (in cm) was measured with how long (in seconds) it takes that person to walk 100 m. Data: (80, 66), (73, 74), (60, 83), (64, 62), (63, 75), (78, 76), (83, 64), (54, 81), (73, 70), (78, 76). Graph the data. Is there a relationship? Describe it. Use your graph to estimate how long it would take someone with 85 cm long legs to walk 100 m. Explain. How might the experiment be improved to be more reliable?

Example 3 State whether each claim is reasonable: A negative correlation between aerobic exercise and blood pressure was found. It claimed the cause of the decrease in blood pressure was due to the increase in aerobic exercise. Carbon dioxide has been steadily increasing. Crime rates have also been increasing. Does an increase in carbon dioxide cause more people to commit crimes? A positive correlation between gasoline prices and average monthly temperature was found. Does temperature affect the gas price?

Text work Page 409 #2, 3, 4, 7, 13 Page 420 #3 Page 424 #1, 2abce, 3c