10 Σχι = 285, i=1 b) c) 10 10 10 10 Σx = 8205, Σνι = 78.4, Σv = 6279, Σ×i = 2264.7 i=1 i=1 i=1 i=1 a) What is the best-fitting regression line relating mean thyroxine level to gestational age? Interpret the meaning of the slope b in this problem. Is there a significant association between mean thyroxine level and gestational age? Report a p-valu (Hint: Test whether p-value < 0.001)
10 Σχι = 285, i=1 b) c) 10 10 10 10 Σx = 8205, Σνι = 78.4, Σv = 6279, Σ×i = 2264.7 i=1 i=1 i=1 i=1 a) What is the best-fitting regression line relating mean thyroxine level to gestational age? Interpret the meaning of the slope b in this problem. Is there a significant association between mean thyroxine level and gestational age? Report a p-valu (Hint: Test whether p-value < 0.001)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
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![### Investigating the Relationship Between Gestational Age and Thyroxine Levels in Premature Infants
#### Study Background
A study was conducted to determine whether hypothyroxinemia in premature infants is a cause of subsequent motor and cognitive abnormalities. The following dataset was produced:
| Gestational Age, \(x\) (weeks) | Mean Thyroxine Levels, \(y\) (µg/dL) |
|--------------------------------|-------------------------------------|
| ≤ 24 | 6.5 |
| 25 | 7.1 |
| 26 | 7.0 |
| 27 | 7.1 |
| 28 | 7.2 |
| 29 | 7.1 |
| 30 | 8.1 |
| 31 | 8.7 |
| 32 | 9.5 |
| 33 | 10.1 |
Additional summations helpful for analysis are given below:
\[ \sum_{i=1}^{10} x_i = 285, \]
\[ \sum_{i=1}^{10} x_i^2 = 8205, \]
\[ \sum_{i=1}^{10} y_i = 78.4, \]
\[ \sum_{i=1}^{10} y_i^2 = 627.9, \]
\[ \sum_{i=1}^{10} x_i y_i = 2264.7. \]
#### Questions and Analysis:
##### a) What is the best-fitting regression line relating mean thyroxine level to gestational age?
The best-fitting regression line can be determined using the linear regression formula:
\[ y = a + bx \]
Where the slope \( b \) and intercept \( a \) are calculated as follows:
\[ b = \frac{n\sum (xy) - (\sum x)(\sum y)}{n\sum x^2 - (\sum x)^2} \]
\[ a = \frac{\sum y - b\sum x}{n} \]
Using the given data:
\[ n = 10 \]
\[ \sum x = 285 \]
\[ \sum y = 78.4 \]
\[ \sum x^2 = 8205 \]
\[ \sum xy = 2264.7 \]
\[ b = \frac{10](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F499a9e14-0786-40cc-ba10-b77b2d83817e%2F81a215d0-097c-4b31-8110-d1f56824db20%2Flnj8kr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Investigating the Relationship Between Gestational Age and Thyroxine Levels in Premature Infants
#### Study Background
A study was conducted to determine whether hypothyroxinemia in premature infants is a cause of subsequent motor and cognitive abnormalities. The following dataset was produced:
| Gestational Age, \(x\) (weeks) | Mean Thyroxine Levels, \(y\) (µg/dL) |
|--------------------------------|-------------------------------------|
| ≤ 24 | 6.5 |
| 25 | 7.1 |
| 26 | 7.0 |
| 27 | 7.1 |
| 28 | 7.2 |
| 29 | 7.1 |
| 30 | 8.1 |
| 31 | 8.7 |
| 32 | 9.5 |
| 33 | 10.1 |
Additional summations helpful for analysis are given below:
\[ \sum_{i=1}^{10} x_i = 285, \]
\[ \sum_{i=1}^{10} x_i^2 = 8205, \]
\[ \sum_{i=1}^{10} y_i = 78.4, \]
\[ \sum_{i=1}^{10} y_i^2 = 627.9, \]
\[ \sum_{i=1}^{10} x_i y_i = 2264.7. \]
#### Questions and Analysis:
##### a) What is the best-fitting regression line relating mean thyroxine level to gestational age?
The best-fitting regression line can be determined using the linear regression formula:
\[ y = a + bx \]
Where the slope \( b \) and intercept \( a \) are calculated as follows:
\[ b = \frac{n\sum (xy) - (\sum x)(\sum y)}{n\sum x^2 - (\sum x)^2} \]
\[ a = \frac{\sum y - b\sum x}{n} \]
Using the given data:
\[ n = 10 \]
\[ \sum x = 285 \]
\[ \sum y = 78.4 \]
\[ \sum x^2 = 8205 \]
\[ \sum xy = 2264.7 \]
\[ b = \frac{10
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