A kinesiology major wanted to predict VO2max based on the one-mile run. To develop the regression equation, she obtained VO2max values (ml/kg/min) in the exercise physiology laboratory on 18 students. Two days later, she measured the same 18 students on the one-mile run with scores reported as total time in seconds. The data are as follows: X Y r = -.94 Subject One-mile run time (seconds) VO2 max (ml/kg/min) 1 250 60.3 2 315 57.2 3 420 55.4 4 410 51.4 5 436 52.5 6 511 45.6 7 460 38.4 8 510 41.5 9 530 39.6 10 586 33.2 11 591 37.7 12 600 40.1 13 626 32.0 14 643 35.4 15 650 33.7 16 675 35.9 17 710 27.4 18 720 25.3 Calculate means for one-mile run and VO2 = = Calculate the slope of the line (b) using this formula: Interpret your answer: Calculate the y-intercept (a) using this formula: What is the regression equation? EstimateVO2max for a person who runs the mile in 540 seconds.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
A kinesiology major wanted to predict VO2max based on the one-mile run. To develop the regression equation, she obtained VO2max values (ml/kg/min) in the exercise physiology laboratory on 18 students. Two days later, she measured the same 18 students on the one-mile run with scores reported as total time in seconds. The data are as follows:
|
|
X |
Y |
r = -.94
|
|
Subject |
One-mile run time (seconds) |
VO2 max (ml/kg/min) |
|
|
1 |
250 |
60.3 |
|
|
2 |
315 |
57.2 |
|
|
3 |
420 |
55.4 |
|
|
4 |
410 |
51.4 |
|
|
5 |
436 |
52.5 |
|
|
6 |
511 |
45.6 |
|
|
7 |
460 |
38.4 |
|
|
8 |
510 |
41.5 |
|
|
9 |
530 |
39.6 |
|
|
10 |
586 |
33.2 |
|
|
11 |
591 |
37.7 |
|
|
12 |
600 |
40.1 |
|
|
13 |
626 |
32.0 |
|
|
14 |
643 |
35.4 |
|
|
15 |
650 |
33.7 |
|
|
16 |
675 |
35.9 |
|
|
17 |
710 |
27.4 |
|
|
18 |
720 |
25.3 |
- Calculate means for one-mile run and VO2
- =
- =
- Calculate the slope of the line (b) using this formula:
- Interpret your answer:
- Calculate the y-intercept (a) using this formula:
- What is the regression equation?
- EstimateVO2max for a person who runs the mile in 540 seconds.
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