The following Minitab display gives information regarding the relationship between the body weight of a child (in kilograms) and the metabolic rate of the child (in 100 kcal/ 24 hr). Predictor Coef SE Coef P Constant 0.8462 0.4148 2.06 0.84 Weight 0.39917 0.02978 13.52 0.000 S - 0.517508 R-Sq = 94.4% (a) Write out the least-squares equation. = (b) For each 1 kilogram increase in weight, how much does the metabolic rate of a child increase? (Use 5 decimal places.) (c) What is the value of the correlation coefficient r? (Use 3 decimal places.)
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![The following Minitab display gives information regarding the relationship between the body weight of a child (in kilograms) and the metabolic rate of the child (in 100 kcal/24 hr).
| Predictor | Coef | SE Coef | T | P |
|-----------|--------|---------|-------|-------|
| Constant | 0.8462 | 0.4148 | 2.06 | 0.84 |
| Weight | 0.39917| 0.02978 | 13.52 | 0.000 |
- **S = 0.517508 R-Sq = 94.4%**
Questions:
(a) Write out the least-squares equation.
- \( \hat{y} = \_\_\_\_\_ + \_\_\_\_\_ \times \)
(b) For each 1 kilogram increase in weight, how much does the metabolic rate of a child increase? (Use 5 decimal places.)
- \_\_\_\_\_
(c) What is the value of the correlation coefficient \( r \)? (Use 3 decimal places.)
- \_\_\_\_\_](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4c5a3da-f5e3-4bbf-bd48-b9865949dfc0%2Ff21d29b5-cdf7-42ff-8600-6e65b1cd0938%2Fpgob2qh_processed.png&w=3840&q=75)
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