The data below are the final exam scores of 10 randomly selected calculus students and the number of hours they slept the night before the exam. Compute the linear correlation coefficient, rounding to three decimal places. Hours, x Scores, y A. 0.761 B. 0.991 C. 0.847 D. 0.654 6 62 8 77 5 57 11 85 5 63 7 75 7 82 8 87 9 87 6- 68

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The data below are the final exam scores of 10 randomly selected calculus students and the number of hours they slept the night before the exam. Compute the linear correlation coefficient, rounding to three decimal places.

| Hours, x | 6 | 8 | 5 | 11 | 5 | 7 | 7 | 8 | 9 | 6 |
|----------|---|---|---|----|---|---|---|---|---|---|
| Scores, y| 62| 77| 57| 85 | 63| 75| 82| 87| 87| 68|

Options for the linear correlation coefficient:
- A. 0.761
- B. 0.991
- C. 0.847
- D. 0.654
Transcribed Image Text:The data below are the final exam scores of 10 randomly selected calculus students and the number of hours they slept the night before the exam. Compute the linear correlation coefficient, rounding to three decimal places. | Hours, x | 6 | 8 | 5 | 11 | 5 | 7 | 7 | 8 | 9 | 6 | |----------|---|---|---|----|---|---|---|---|---|---| | Scores, y| 62| 77| 57| 85 | 63| 75| 82| 87| 87| 68| Options for the linear correlation coefficient: - A. 0.761 - B. 0.991 - C. 0.847 - D. 0.654
The least-square regression line for the given data is \( \hat{y} = -0.206x + 2.097 \). Determine the residual of a data point for which \( x = 1 \) and \( y = -3 \), rounding to three decimal places.

**Data:**

- \( x \): -5, -3, 4, 1, -1, -2, 0, 2, 3, -4
- \( y \): 11, -6, 8, -3, -2, 1, 5, -5, 6, 7

**Options:**

- A. \(-4.891\)
- B. \(-1.715\)
- C. \(-1.109\)
- D. \(1.891\)

To solve, use the regression line equation to estimate \(\hat{y}\) for \(x = 1\):

\[
\hat{y} = -0.206(1) + 2.097 = 1.891
\]

The residual is:

\[
\text{Residual} = y - \hat{y} = -3 - 1.891 = -4.891
\]

Correct Answer: A. \(-4.891\)
Transcribed Image Text:The least-square regression line for the given data is \( \hat{y} = -0.206x + 2.097 \). Determine the residual of a data point for which \( x = 1 \) and \( y = -3 \), rounding to three decimal places. **Data:** - \( x \): -5, -3, 4, 1, -1, -2, 0, 2, 3, -4 - \( y \): 11, -6, 8, -3, -2, 1, 5, -5, 6, 7 **Options:** - A. \(-4.891\) - B. \(-1.715\) - C. \(-1.109\) - D. \(1.891\) To solve, use the regression line equation to estimate \(\hat{y}\) for \(x = 1\): \[ \hat{y} = -0.206(1) + 2.097 = 1.891 \] The residual is: \[ \text{Residual} = y - \hat{y} = -3 - 1.891 = -4.891 \] Correct Answer: A. \(-4.891\)
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