Air Force servicemen and servicewomen were tested for maximal oxygen use in a 12 min distance run versus a 1.5 mile run. The participant runs on a level terrain for the prescribed distance. The technicians records the participant’s time to the closet second, the heart rate for 15 s immediately after the participant crosses the finish line and then estimate the VO2 max consumption using a Wilmore and Bergfeld fitness table. Below is listed the data for both the 12 min and the 1.5 mile run with the corresponding VO2 maximum oxygen levels
Data 12 Min Distance (n=25) | |
x | y |
Miles | VO2Max(ml/kg.min) |
1.1 | 23.2 |
1.15 | 30 |
1.2 | 30 |
1.15 | 32.5 |
1.25 | 36.3 |
1.26 | 37 |
1.28 | 40 |
1.31 | 32.3 |
1.3 | 35 |
1.38 | 40 |
1.4 | 45.1 |
1.43 | 47.5 |
1.45 | 50 |
1.5 | 46.2 |
1.6 | 41 |
1.65 | 46.4 |
1.67 | 49 |
1.67 | 50 |
1.7 | 48 |
1.8 | 47.5 |
1.85 | 51.5 |
1.9 | 59.8 |
2 | 49.8 |
2.15 | 60 |
2.2 | 59 |
Data Two: 12 Min distance vs. VO2 Consumed
Make a scatter diagram for these pairs of data. Sketch below.
According to the scatter plot, as the distance increases, what happens to the oxygen consumed? _________
Does this indicate a positive or negative correlation? ________________
Complete the steps to find the correlation coefficient, the line of fit and the values for the linear regression equation.
1)
select data -> insert -> scatterplot
2)
The scatterplot shows an upward trend. thus, as the distance
increases, oxygen consumed also increases.
3)
The scatterplot shows an upward trend. thus there is a
positive correlation
4)
x | y | x^2 | y^2 | xy |
1.1 | 23.2 | 1 | 538 | 26 |
1.15 | 30 | 1 | 900 | 35 |
1.2 | 30 | 1 | 900 | 36 |
1.15 | 32.5 | 1 | 1056 | 37 |
1.25 | 36.3 | 2 | 1318 | 45 |
1.26 | 37 | 2 | 1369 | 47 |
1.28 | 40 | 2 | 1600 | 51 |
1.31 | 32.3 | 2 | 1043 | 42 |
1.3 | 35 | 2 | 1225 | 46 |
1.38 | 40 | 2 | 1600 | 55 |
1.4 | 45.1 | 2 | 2034 | 63 |
1.43 | 47.5 | 2 | 2256 | 68 |
1.45 | 50 | 2 | 2500 | 73 |
1.5 | 46.2 | 2 | 2134 | 69 |
1.6 | 41 | 3 | 1681 | 66 |
1.65 | 46.4 | 3 | 2153 | 77 |
1.67 | 49 | 3 | 2401 | 82 |
1.67 | 50 | 3 | 2500 | 84 |
1.7 | 48 | 3 | 2304 | 82 |
1.8 | 47.5 | 3 | 2256 | 86 |
1.85 | 51.5 | 3 | 2652 | 95 |
1.9 | 59.8 | 4 | 3576 | 114 |
2 | 49.8 | 4 | 2480 | 100 |
2.15 | 60 | 5 | 3600 | 129 |
2.2 | 59 | 5 | 3481 | 130 |
sum x | sum y | sum x^2 | sum y^2 | sum xy | n |
38.35 | 1087.1 | 61 | 49559 | 1734 | 25 |
slope, b1= {n*sum(xy) - sum(x)*sum(y)} / {n*sum(x^2)
- [sum(x)]^2 }
b1 = {25*1734.353 - 38.35*1087.1} / {25*61.2367 -
[38.35]^2 }
b1 = 27.7189
intercept, bo= {sum(y)*sum(x^2) - sum(x)*sum(xy)} /
{n*sum(X^2) - [sum(X)]^2}
bo = {1087.1*61.2367 - 38.35*1734.353} / {25*61.2367 -
[38.35]^2}
bo = 1.0
regression equation:
y = bo + b1*x
y = 0.9632 + 27.7189*x
corr coef, r = (n*sum(XY) - sum(X)*sum(Y)) / (
sqrt(n*sum(x^2)-[sum(x)]^2) * sqrt(n*sum(y^2)-[sum(y)]^2) )
corr coef, r = (25*1734.353-38.35*1087.1) / (
sqrt(25*61.2367-[38.35]^2) * sqrt(25*49558.71-[1087.1]^2) )
corr coef, r = 0.899351
Air Force servicemen and servicewomen were tested for maximal oxygen use in a 12 min distance...
Air Force servicemen and servicewomen were tested for maximal oxygen use in a 12 min distance run versus a 1.5 mile run. The participant runs on a level terrain for the prescribed distance. The technicians records the participant’s time to the closet second, the heart rate for 15 s immediately after the participant crosses the finish line and then estimate the VO2 max consumption using a Wilmore and Bergfeld fitness table. Below is listed the data for both the 12...
Air Force servicemen and servicewomen were tested for maximal oxygen use in a 12 min distance run versus a 1.5 mile run. The participant runs on a level terrain for the prescribed distance. The technicians records the participant’s time to the closet second, the heart rate for 15 s immediately after the participant crosses the finish line and then estimate the VO2 max consumption using a Wilmore and Bergfeld fitness table. Below is listed the data for both the 12...
Air Force servicemen and servicewomen were tested for maximal oxygen use in a 12 min distance run versus a 1.5 mile run. The participant runs on a level terrain for the prescribed distance. The technicians records the participant’s time to the closet second, the heart rate for 15 s immediately after the participant crosses the finish line and then estimate the VO2 max consumption using a Wilmore and Bergfeld fitness table. Data 1.5 Mile Run (n=29) X y Time...
Air Force servicemen and servicewomen were tested for maximal oxygen use in a 12 min distance run versus a 1.5 mile run. The participant runs on a level terrain for the prescribed distance. The technicians records the participant’s time to the closet second, the heart rate for 15 s immediately after the participant crosses the finish line and then estimate the VO2 max consumption using a Wilmore and Bergfeld fitness table. Data 1.5 Mile Run (n=29) X y Time...