Cardiorespiratory fitness is w
Cardiorespiratory fitness is widely recognized as a majorcomponent of overall physical well-being. Direct measurement ofmaximal oxygen uptake (VO2max) is the single best measure of suchfitness, but direct measurement is time-consuming and expensive. Itis therefore desirable to have a prediction equation for VO2max interms of easily obtained quantities. A sample is taken andvariables measured are age (years), time necessary to walk 1 mile(mins), and heart rate at the end of the walk (bpm) in addition tothe VO2 max uptake. The equation from a multiple regression is(V02) = 0.017*(age) – 0.028*(HR) + 0.017*(time) + 3.483. If aperson is 29 years old, blood pressure of 130 bpm, and a walkingtime of 13 minutes, what is his/her expected maximum oxygenuptake?
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Suppose that a researcher studying the weight of female collegeathletes wants to predict the weights based on height, measured ininches, and the percentage of body fat of an athlete. Theresearcher calculates the regression equation as (weight) =3.979*(height) + 0.85*(percent body fat) – 87.814. If a femaleathlete is 67 inches tall and has a 20 percentage of body fat, whatis her expected weigh
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A trucking company considered a multiple regression model forrelating the dependent variable of total daily travel time for oneof its drivers (hours) to the predictors distance traveled (miles)and the number of deliveries of made. After taking a random sample,a multiple regression was performed and the equation is (time) =0.076*(distance) + 0.579*(deliveries) – 0.466. Suppose for a givendriver’s day, he is scheduled to drive 58.908 miles and make 10.97stops. Suppose it took him 14.302 hours to complete the trip. Whatis the residual based on the regression model?
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Suppose that a researcher studying the weight of female collegeathletes wants to predict the weights based on height, measured ininches, the percentage of body fat of an athlete, and age. Theresearcher calculates the regression equation as (weight) =4.08*(height) + 1.103*(percent body fat) – 0.995*(age) – 82.074. Ifa female athlete is 68.575 inches tall, has a 23.901 percentage ofbody fat, is 22.696 years old, and has a weight of 167.763, theresidual is -33.7293. Choose the correct interpretation of theresidual.
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Answer:
Part A
We are given
(VO2) = 0.017*age – 0.028*HR + 0.017*time + 3.483
Age = 29
HR = 130
Time = 13
(VO2) = 0.017*29 – 0.028*130 + 0.017*13 + 3.483
(VO2) = 0.557
Correct Answer: 1) 0.557
Part B
We are given
(Weight) = 3.979*(height) + 0.85*(percent body fat) – 87.814
Height = 67
Percent body fat = 20%
(Weight) = 3.979*67 + 0.85*20 – 87.814
(Weight) = 195.779
Correct Answer: 2) 195.779
Part C
Regression equation is given as below:
(time) = 0.076*(distance) + 0.579*(deliveries) – 0.466
We are given
Distance = 58.908
Deliveries = 10.97
Observed time = 14.302 hours
Predicted time = 0.076*(distance) + 0.579*(deliveries) -0.466
Predicted time = 0.076*58.908 + 0.579*10.97 – 0.466
Predicted time = 10.36264
Residual = Observed value – Predicted value
Residual = 14.302 – 10.36264 = 3.93936
Residual = 3.9394
Correct Answer: 2) 3.9394
Part D
Correct Answer: 3) The weight of the athlete is 33.7293 poundsless than what we would expect.
Explanation: We know that the residual is the difference betweenobserved values and predicted or expected value. A negative valueof residual indicates a less observed value than what we wouldexpect.