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Lesson 9 Practice Problems
Problem Statement
Priya creates a scatter plot showing the relationship between the number of steps she takes and her heart rate. The correlation coe cient of the line of best t is 0.88.
a. Are they correlated? Explain your reasoning.
b. Do either of the variables cause the other to change? Explain your reasoning.
Solution
a. They are strongly correlated because the correlation coe cient is close to one. When Priya’s steps increase, her heart rate increases.
b. Sample response: It is likely that the type of exercise is the cause of both variables. For example, running on a treadmill would increase both the number of steps Priya takes as well as her heart rate. A long, slow walk would probably not raise her heart rate in the same way that a short, fast run would even if the number of steps were the same.
Problem Statement
Noah creates a scatter plot showing the relationship between number of free throws made in a basketball game and the number of points scored. The correlation coe cient for the line of best t is 0.76.
a. Are they correlated? Explain your reasoning.
b. Do either of the variables cause the other to change? Explain your reasoning.
Solution
a. The correlation coe cient shows that there is a positive correlation. When the number of free throws made increases, the number of points scored increases.
b. Sample response: Although there are other factors involved, increasing the number of free throws made does cause the number of points scored to increase.
Problem Statement
Kiran creates a scatter plot showing the relationship between number of students attending drama club and the number of students attending poetry club each week. The correlation coe cient for the line of best t is -0.36.
a. Are they correlated? Explain your reasoning.
b. Do either of the variables cause the other to change? Explain your reasoning.
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Teacher Guide
Algebra