Lesson 7
The Correlation Coefficient
Problem 1
Select all the values for \(r\) that indicate a positive slope for the line of best fit.
1
-1
0.5
-0.5
0
0.8
-0.8
Solution
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Problem 2
The correlation coefficient, \(r\), is given for several different data sets. Which value for \(r\) indicates the strongest correlation?
0.01
-0.34
-0.82
-0.95
Solution
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Problem 3
Which of the values is the best estimate of the correlation coefficient for the line of best fit shown in the scatter plot?
-0.9
-0.4
0.4
0.9
Solution
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Problem 4
Technology required.
A study investigated the relationship between the amount of daily food waste measured in pounds and the number of people in a household. The data in the table displays the results of the study.
| number of people in household, \( x\) | food waste (pounds), \(y\) |
|---|---|
| 2 | 3.4 |
| 3 | 2.5 |
| 4 | 8.9 |
| 4 | 4.7 |
| 4 | 3.5 |
| 4 | 4 |
| 5 | 5.3 |
| 5 | 4.6 |
| 5 | 7.8 |
| 6 | 3.2 |
| 8 | 12 |
Use graphing technology to create the line of best fit for the data in the table.
- What is the equation of the line of best fit for this data? Round numbers to two decimal places.
- What is the slope of the line of best fit? What does it mean in this situation? Is this realistic?
- What is the \(y\)-intercept of the line of best fit? What does it mean in this situation? Is this realistic?
Solution
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(From Unit 3, Lesson 5.)Problem 5
A table of values and the plot of the residuals for the line of best fit are shown.
| \(x\) | \(y\) |
|---|---|
| 1 | 10 |
| 2 | 8 |
| 2.5 | 9.5 |
| 4 | 8 |
| 5 | 8 |
| 6 | 7.5 |
| 7.2 | 7 |
| 8.5 | 6 |
- Which point does the line estimate the best?
- Which point does the line estimate the worst?
Solution
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(From Unit 3, Lesson 6.)Problem 6
Tyler creates a scatter plot that displays the relationship between the grams of food a hamster eats, \(x\), and the total number of rotations that the hamster’s wheel makes, \(y\). Tyler creates a line of best fit and finds that the residual for the point \((1.4, 1250)\) is -132. The point \((1.2, 1364)\) has a residual of 117. Interpret the meaning of 117 in the context of the problem.
Solution
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(From Unit 3, Lesson 6.)