Lesson 9
Causal Relationships
Problem 1
Priya creates a scatter plot showing the relationship between the number of steps she takes and her heart rate. The correlation coefficient for the data is 0.88.
- Are they correlated? Explain your reasoning.
- Do either of the variables cause the other to change? Explain your reasoning.
Solution
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Problem 2
Kiran creates a scatter plot showing the relationship between the number of students attending drama club and the number of students attending poetry club each week. The correlation coefficient for the data is -0.36.
- Are they correlated? Explain your reasoning.
- Do either of the variables cause the other to change? Explain your reasoning.
Solution
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Problem 3
A news website shows a scatter plot with a negative relationship between the amount of sugar eaten and happiness levels. The headline reads, “Eating sugar causes happiness to decrease!”
- What is wrong with this claim?
- What is a better headline for this information?
Solution
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Problem 4
A group of 125 college students are surveyed about their note taking and study habits. Some results are represented in the table.
prefer writing notes by hand | prefer typing notes | don't take notes | |
---|---|---|---|
study for less than 1 hour | 22 | 8 | |
study for 1 hour or more | 38 | 28 | 3 |
How many students prefer typing notes and study for less than 1 hour?
Solution
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(From Unit 3, Lesson 1.)Problem 5
The number of miles driven, \(x\), and the number of gallons remaining in the gas tank, \(y\), have a strong negative relationship.
Explain what it means to have a strong negative relationship in this context.
Solution
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(From Unit 3, Lesson 8.)Problem 6
Technology required. Use a graphing calculator to answer the questions.
\(x\) | \(y\) |
---|---|
10.2 | 31 |
10.4 | 27 |
10.5 | 29 |
10.5 | 30 |
10.5 | 31 |
10.6 | 26 |
10.8 | 25 |
10.8 | 26 |
10.9 | 27 |
11 | 24 |
11.2 | 22 |
- What is an equation of the line of best fit?
- What is the value of the correlation coefficient?
Solution
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(From Unit 3, Lesson 8.)