Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 131 to 194 cm and weights of 38 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.55 cm, y = 81.42 kg, r = 0.192, P-value = 0.056, and y = - 107+ 1.12x. Find the best predicted value of y (weight) given an adult male who is 155 cm tall. Use a 0.01 significance level. Click the icon to view the critical values of the Pearson correlation coefficient r. The best predicted value of y for an adult male who is 155 cm tall is (Round to two decimal places as needed.) kg.
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 131 to 194 cm and weights of 38 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.55 cm, y = 81.42 kg, r = 0.192, P-value = 0.056, and y = - 107+ 1.12x. Find the best predicted value of y (weight) given an adult male who is 155 cm tall. Use a 0.01 significance level. Click the icon to view the critical values of the Pearson correlation coefficient r. The best predicted value of y for an adult male who is 155 cm tall is (Round to two decimal places as needed.) kg.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Predicting Weight Based on Height of Adult Males
#### Problem Statement
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males. Heights range from 131 cm to 194 cm, and weights range from 38 kg to 150 kg. Let the predictor variable \( x \) be the first variable given (height).
The 100 paired measurements yield:
- Mean height \(\bar{x} = 167.55\) cm
- Mean weight \(\bar{y} = 81.42\) kg
- Correlation coefficient \(r = 0.192\)
- P-value = 0.056
The regression equation for predicting weight (\(\hat{y}\)) from height (\(x\)) is:
\[
\hat{y} = -107 + 1.12x
\]
#### Task
Find the best predicted value of \(\hat{y}\) (weight) given an adult male who is 155 cm tall. Use a 0.01 significance level.
#### Instructions
Click the icon below to view the critical values of the Pearson correlation coefficient.
{Icon}
#### Calculation
The best predicted value of \(\hat{y}\) for an adult male who is 155 cm tall is \(\boxed{\ \ \ \ }\) kg.
(Round to two decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39618134-6ceb-48ac-ab5a-e0c16873beed%2F33c6f1a0-c30a-44ef-8a74-9bc2bcd76d14%2Fl2drl6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Predicting Weight Based on Height of Adult Males
#### Problem Statement
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males. Heights range from 131 cm to 194 cm, and weights range from 38 kg to 150 kg. Let the predictor variable \( x \) be the first variable given (height).
The 100 paired measurements yield:
- Mean height \(\bar{x} = 167.55\) cm
- Mean weight \(\bar{y} = 81.42\) kg
- Correlation coefficient \(r = 0.192\)
- P-value = 0.056
The regression equation for predicting weight (\(\hat{y}\)) from height (\(x\)) is:
\[
\hat{y} = -107 + 1.12x
\]
#### Task
Find the best predicted value of \(\hat{y}\) (weight) given an adult male who is 155 cm tall. Use a 0.01 significance level.
#### Instructions
Click the icon below to view the critical values of the Pearson correlation coefficient.
{Icon}
#### Calculation
The best predicted value of \(\hat{y}\) for an adult male who is 155 cm tall is \(\boxed{\ \ \ \ }\) kg.
(Round to two decimal places as needed.)
Transcribed Image Text:### Critical Values of the Pearson Correlation Coefficient \( r \)
| \( n \) | \( \alpha = 0.05 \) | \( \alpha = 0.01 \) |
|----------|--------------------|--------------------|
| 4 | 0.950 | 0.990 |
| 5 | 0.878 | 0.959 |
| 6 | 0.811 | 0.917 |
| 7 | 0.754 | 0.875 |
| 8 | 0.707 | 0.834 |
| 9 | 0.666 | 0.798 |
| 10 | 0.632 | 0.765 |
| 11 | 0.602 | 0.735 |
| 12 | 0.576 | 0.708 |
| 13 | 0.553 | 0.684 |
| 14 | 0.532 | 0.661 |
| 15 | 0.514 | 0.641 |
| 16 | 0.497 | 0.623 |
| 17 | 0.482 | 0.606 |
| 18 | 0.468 | 0.590 |
| 19 | 0.456 | 0.575 |
| 20 | 0.444 | 0.561 |
| 25 | 0.396 | 0.505 |
| 30 | 0.361 | 0.463 |
| 35 | 0.335 | 0.430 |
| 40 | 0.312 | 0.402 |
| 45 | 0.294 | 0.378 |
| 50 | 0.279 | 0.361 |
| 60 | 0.254 | 0.330 |
| 70 | 0.236 | 0.305 |
| 80 | 0.220 | 0.286 |
| 90 | 0
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