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.
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.
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