The following problem is based on information taken from the pediatrics section of The Merck Manual (a commonly used reference in medical schools and nursing programs). Let x be the body weight of a child (in kilograms), and let y be the metabolic rate of the child (in 100 kcal/24 h).x 13.0 24.0 25.0 24.0 19.0 14.0 6.0 18.0y 1.7 7.2 6.7 7.3 5.6 2.0 1.6 2.4Σx = 143; Σy = 34.5; Σx2 = 2863; Σy2 = 196.59; Σxy = 724.8 (a) Find Se. (Round your answer to three decimal places.) (b) Find r. (Round your answer to three decimal places.) Test that ρ is positive. Use α = 0.01. (Round your answers to three decimal places.)t = critical t = Conclusion:At the 1% level of significance, there is sufficient evidence to conclude that the population correlation coefficient is greater than zero.At the 1% level of significance, there is insufficient evidence to conclude that the population correlation coefficient is greater than zero. (c) Find b. (Round your answer to three decimal places.) Test that β is positive. Use α = 0.01. (Round your answers to three decimal places.)t = critical t = Conclusion:At the 1% level of significance, there is sufficient evidence to conclude that the slope of the population least-squares line is positive.At the 1% level of significance, there is insufficient evidence to conclude that the slope of the population least-squares line is positive. (d) Find the equation for the least-squares line ŷ. (Round your answers to three decimal places.)ŷ = + x Find a 90% confidence interval for the predicted metabolic rate for a child weighing 10 kg. (Round your answers to three decimal places.)to
Unitary Method
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The following problem is based on information taken from the pediatrics section of The Merck Manual (a commonly used reference in medical schools and nursing programs). Let x be the body weight of a child (in kilograms), and let y be the metabolic rate of the child (in 100 kcal/24 h).
x 13.0 24.0 25.0 24.0 19.0 14.0 6.0 18.0
y 1.7 7.2 6.7 7.3 5.6 2.0 1.6 2.4
Σx = 143; Σy = 34.5; Σx2 = 2863; Σy2 = 196.59; Σxy = 724.8
(a) Find Se. (Round your answer to three decimal places.)
(b) Find r. (Round your answer to three decimal places.)
Test that ρ is positive. Use α = 0.01. (Round your answers to three decimal places.)
t =
critical t =
Conclusion:
At the 1% level of significance, there is sufficient evidence to conclude that the population
At the 1% level of significance, there is insufficient evidence to conclude that the population correlation coefficient is greater than zero.
(c) Find b. (Round your answer to three decimal places.)
Test that β is positive. Use α = 0.01. (Round your answers to three decimal places.)
t =
critical t =
Conclusion:
At the 1% level of significance, there is sufficient evidence to conclude that the slope of the population least-squares line is positive.
At the 1% level of significance, there is insufficient evidence to conclude that the slope of the population least-squares line is positive.
(d) Find the equation for the least-squares line ŷ. (Round your answers to three decimal places.)
ŷ =
+
x
Find a 90% confidence interval for the predicted metabolic rate for a child weighing 10 kg. (Round your answers to three decimal places.)
to
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