A group of 13 health children and adolescents participated in a study designed to analyze the relationship between age (AGE in years) and average total sleep time (ATST in minutes). To obtain a measure for ATST, recordings were taken on each subject on three consecutive nights and then averaged . The results obtained are given below along with the corresponding scatter plot. AGE ATST 1. 4.40 586.00 2. 14.00 461.75 3. 10.10 491.10 4. 6.70 565.00 5. 11.50 462.00 6. 9.60 532.10 7. 12.40 477.60 8. 8.90 515.20 9. 11.10 493.00 10. 7.75 528.30 11. 5.50 575.90 12. 8.60 532.50 13. 7.20 530.50 A simple linear regression model was fit to the data in R. The results are given below. Call: lm(formula = ATST ~ AGE) Residuals: Min 1Q Median 3Q Max -23.011 -9.365 2.372 6.770 20.411 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 646.483 12.918 50.05 2.49e-14 * AGE -14.041 1.368 -10.26 5.70e-07 * --- Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 13.15 on 11 degrees of freedom Multiple R-squared: 0.9054, Adjusted R-squared: 0.8968 F-statistic: 105.3 on 1 and 11 DF, p-value: 5.7e-07 - Write the formula for the estimated regression line.

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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A group of 13 health children and adolescents participated in a study designed to analyze the relationship between age (AGE in years) and average total sleep time (ATST in minutes). To obtain a measure for ATST, recordings were taken on each subject on three consecutive nights and then averaged . The results obtained are given below along with the corresponding scatter plot.

AGE ATST

1. 4.40 586.00

2. 14.00 461.75

3. 10.10 491.10

4. 6.70 565.00

5. 11.50 462.00

6. 9.60 532.10

7. 12.40 477.60

8. 8.90 515.20

9. 11.10 493.00

10. 7.75 528.30

11. 5.50 575.90

12. 8.60 532.50

13. 7.20 530.50

A simple linear regression model was fit to the data in R. The results are given below.

Call:

lm(formula = ATST ~ AGE)

Residuals:

Min 1Q Median 3Q Max

-23.011 -9.365 2.372 6.770 20.411

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 646.483 12.918 50.05 2.49e-14 ***

AGE -14.041 1.368 -10.26 5.70e-07 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 13.15 on 11 degrees of freedom

Multiple R-squared: 0.9054, Adjusted R-squared: 0.8968

F-statistic: 105.3 on 1 and 11 DF, p-value: 5.7e-07

- Write the formula for the estimated regression line.

The image shows a line graph illustrating the increasing trend of living things changing over a timeline. The y-axis represents the quantity or degree of change in living things, while the x-axis indicates time, divided into four sections labeled A, B, C, and D.

Section A shows a gradual increase, indicating a slow change or development in living things. Section B depicts a sharper upward trend, suggesting a faster rate of change. In section C, the graph shows a more significant jump, indicating a rapid transformation or evolution. Finally, section D shows a tapering off or stabilization, suggesting a plateau in change.

Overall, the graph demonstrates how living organisms have evolved or changed at varying rates across different time periods.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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