Below are the average heights for American boys in 1990. Age (years) Height (cm) birth 50.8 2 83.8 3 91.4 106.6 119.3 10 137.1 14 157.5 O Part (a) O Part (b) O Part (c) O Part (d) Calculate the least squares line. Put the equation in the form of: ý = a + bx. (Round your answers to three decimal places.)

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
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Author:HOLT MCDOUGAL
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Chapter2: Solving Equations
Section2.6: Solving Equations Using Multiplication Or Division
Problem 47E
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Please label each part

## Part (i)

**Task:** 
Use the least squares line to estimate the average height for a sixty-five-year-old man. (Use your equation from part (d). Round your answer to one decimal place.)

- Estimated average height: _______ cm

**Question:** 
Do you think that your answer is reasonable? Why or why not?

- Options:
  - ( ) Yes, because the answer is positive.
  - (●) No, because 65 is outside the domain of the least squares line.

## Part (j)

**Task:** 
What is the slope of the least squares (best-fit) line? (Round your answer to three decimal places.)

- Slope: _______

**Interpretation:** 
Interpret the slope. (Round your answer to three decimal places.)

- As age increases by one year, the average height **increases** by _______ centimeters.
Transcribed Image Text:## Part (i) **Task:** Use the least squares line to estimate the average height for a sixty-five-year-old man. (Use your equation from part (d). Round your answer to one decimal place.) - Estimated average height: _______ cm **Question:** Do you think that your answer is reasonable? Why or why not? - Options: - ( ) Yes, because the answer is positive. - (●) No, because 65 is outside the domain of the least squares line. ## Part (j) **Task:** What is the slope of the least squares (best-fit) line? (Round your answer to three decimal places.) - Slope: _______ **Interpretation:** Interpret the slope. (Round your answer to three decimal places.) - As age increases by one year, the average height **increases** by _______ centimeters.
Below are the average heights for American boys in 1990.

| Age (years) | Height (cm) |
|-------------|-------------|
| birth       | 50.8        |
| 2           | 83.8        |
| 3           | 91.4        |
| 5           | 106.6       |
| 7           | 119.3       |
| 10          | 137.1       |
| 14          | 157.5       |

- **Part (a)**
- **Part (b)**
- **Part (c)**
- **Part (d)**
  
  Calculate the least squares line. Put the equation in the form of:  
  \(\hat{y} = a + bx\). (Round your answers to three decimal places.)
  
  \(\hat{y} = \_\_\_\_\_\_\_\_\_\_\_\_ + \_\_\_\_\_\_\_\_\_\_\_\_ x\)

- **Part (e)**
  
  Find the correlation coefficient \(r\). (Round your answer to four decimal places.)
  
  \(r = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \)

  Is it significant?
  
  - [ ] Yes
  - [ ] No ✔

- **Part (f)**
  
  Find the estimated average height for a one-year-old. (Use your equation from part (d). Round your answer to one decimal place.)
  
  \_\_\_\_\_\_\_\_\_ cm

  Find the estimated average height for an eleven-year-old. (Use your equation from part (d). Round your answer to two decimal places.)
  
  \_\_\_\_\_\_\_\_\_ cm
Transcribed Image Text:Below are the average heights for American boys in 1990. | Age (years) | Height (cm) | |-------------|-------------| | birth | 50.8 | | 2 | 83.8 | | 3 | 91.4 | | 5 | 106.6 | | 7 | 119.3 | | 10 | 137.1 | | 14 | 157.5 | - **Part (a)** - **Part (b)** - **Part (c)** - **Part (d)** Calculate the least squares line. Put the equation in the form of: \(\hat{y} = a + bx\). (Round your answers to three decimal places.) \(\hat{y} = \_\_\_\_\_\_\_\_\_\_\_\_ + \_\_\_\_\_\_\_\_\_\_\_\_ x\) - **Part (e)** Find the correlation coefficient \(r\). (Round your answer to four decimal places.) \(r = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \) Is it significant? - [ ] Yes - [ ] No ✔ - **Part (f)** Find the estimated average height for a one-year-old. (Use your equation from part (d). Round your answer to one decimal place.) \_\_\_\_\_\_\_\_\_ cm Find the estimated average height for an eleven-year-old. (Use your equation from part (d). Round your answer to two decimal places.) \_\_\_\_\_\_\_\_\_ cm
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