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. 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

Hey, since there are multiple subparts posted, we will answer first three subparts. If you want any specific subpart to be answered then please submit that subpart only or specify the subpart in your message. d. The least square equation is y^=a+bx Step-by-step procedure to draw the fitted line plot using Excel: In Excel sheet, enter and select Age in one column and enter Height in one column. In Insert, select Scatter with only markers under Scatter. Right click the points in the graph and select Add trend line. Select Linear in Trend/Regression Type. Click Display Equation. Click Ok. Output obtained using Excel is given below: Thus , the equation is y^=65.088+7.095xe. Step-by-step procedure to find the correlation using Excel: In Excel sheet, enter Age in one column and enter height in one column. In Data, select Data Analysis and choose Correlation In Input Range, select the data Click Labels. Click Ok. Output obtained using Excel is given below: From the output, the correlation coefficient r=0.9761 Thus, the correlation coefficient r is 0.9761 Hypothesis: H0: ρ=0H1: ρ≠0 The test statistic is obtained as below: t=r×n-21-r2=0.9761×7-21-0.97612=2.18260.2173t=10.0442 Thus, the test statistic is 10.0442Degrees of freedom: df=n-2=7-2=5 p value: The P-value is obtained Excel function “=TDIST(x, degrees of freedom, tails)”. Output obtained using Excel is as follows: From the output, the value of p is 0.0002 Decision Rule: If p value < significance level, Reject null hypothesis. otherwise failed to reject null hypothesis. Here, 0.0002<0.05, thus null hypothesis is rejected. Thus, the correlation coefficient r is significant.f. The estimated average height for one year old is obtained as below: y^=65.088+7.095xput x=1y^=65.088_7.0951=65.088+7.095=72.1830 Thus, the estimated average height for one year old is 72.2 cm The estimated average height for seven year old is obtained as below: y^=65.088+7.095xput x=7y^=65.088_7.0957=65.088+49.6550=114.7530 Thus, the estimated average height for seven year old is 114.8 cm

Math

Statistics

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.)

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

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter2: Solving Equations

Section2.6: Solving Equations Using Multiplication Or Division

Problem 47E

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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

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.

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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