Write the formula for the estimated regression line and interpret the slope of the estimated regression line, the intercept of the estimated regression line- Is it meaningful?, and the estimated R2.Based on the fitted regression model, what is the predicted ATST for a child who is 7 years old?What is the correlation between AGE and ATST?Does the residual plot suggest that the fitted regression line is inappropriate for these data? Explain why or why not. Suppose that a new subject is added to the study data and that subject is 12.5 years old with an ATST of 580 minutes. If the regression model were to be refit with this additional data point, would the new slope be greater than or less than -14.041? Justify your response. 8. 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 oneach subject on three consecutive nights and then averaged. The results obtained are given below along with thecorresponding scatter plot.AGEATST4.40 586.0014.00 461.7510.10 491.106.70 565.0011.50 462.009.60 532.1012.40 477.608.90 515.209 11.10 493.0010 7.75 528.30115.50 575.90128.60 532.5013 7.20 530.5072381456ATST (min/24hr)09960055050045005AGE (years)1015 A simple linear regression model was fit to the data in R. The results are given below.Call:m(formula = ATSTResiduals:MinCoefficients:10 Median3QMax-23.011 -9.365 2.372 6.770 20.411Estimate Std. Error t value (|t|)12.918 50.05 2.49e-14 ***1.368 -10.26 5.70e-07 ***Signif. codes: 0 **** 0.001** 0.01 * 0.05.' 0.1 1Residual standard error: 13.15 on 11 degrees of freedomMultiple R-squared: 0.9054, Adjusted R-squared:F-statistic: 105.3 on 1 and 11 DF, p-value: 5.7e-070.8968AGE(Intercept) 646.483-14.041ResidualsBelow is a plot of the model residuals vs. AGE.20~10AGE)0-10206810AGE (years)O1214

Question

Write the formula for the estimated regression line and interpret the slope of the estimated regression line, the intercept of the estimated regression line- Is it meaningful?, and the estimated R2.Based on the fitted regression model, what is the predicted ATST for a child who is 7 years old?What is the correlation between AGE and ATST?Does the residual plot suggest that the fitted regression line is inappropriate for these data? Explain why or why not. Suppose that a new subject is added to the study data and that subject is 12.5 years old with an ATST of 580 minutes. If the regression model were to be refit with this additional data point, would the new slope be greater than or less than -14.041?  Justify your response. 8. 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 oneach subject on three consecutive nights and then averaged. The results obtained are given below along with thecorresponding scatter plot.AGEATST4.40 586.0014.00 461.7510.10 491.106.70 565.0011.50 462.009.60 532.1012.40 477.608.90 515.209 11.10 493.0010 7.75 528.30115.50 575.90128.60 532.5013 7.20 530.5072381456ATST (min/24hr)09960055050045005AGE (years)1015 A simple linear regression model was fit to the data in R. The results are given below.Call:m(formula = ATSTResiduals:MinCoefficients:10 Median3QMax-23.011 -9.365 2.372 6.770 20.411Estimate Std. Error t value (>|t|)12.918 50.05 2.49e-14 ***1.368 -10.26 5.70e-07 ***Signif. codes: 0 **** 0.001** 0.01 * 0.05.' 0.1 1Residual standard error: 13.15 on 11 degrees of freedomMultiple R-squared: 0.9054, Adjusted R-squared:F-statistic: 105.3 on 1 and 11 DF, p-value: 5.7e-070.8968AGE(Intercept) 646.483-14.041ResidualsBelow is a plot of the model residuals vs. AGE.20~10AGE)0-10206810AGE (years)O1214

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