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# Regression analysis for oxygen consumption in R.

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Data is from a study carried out at NC State University in order to determine the relationship between oxygen consumption, a measure of aerobic fitness, and several other variables related to physical fitness among n=31 runners.

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Data is from a study carried out at NC State University in order to determine the relationship between oxygen consumption, a measure of aerobic fitness, and several other variables related to physical fitness among n=31 runners. (Source: Montgomery, Peck & Vining, Fourth Edition.)
Variables:
AGE = age in years
WEIGHT = weight in kilograms
OXY = oxygen consumption in volume per unit body weight per unit time
RUNTIME = time to run 1.5 miles
RSTPULSE = pulse rate at rest
RUNPULSE = pulse rate at end of run
MAXPULSE = maximum pulse rate during run
Examine a model that predicts oxygen consumption (OXY) based on age, weight, runtime, and at least one of the heart rate variables. For example, you can fit
fitness.lm <- lm(OXY ~ RUNTIME + AGE + WEIGHT + RUNPULSE + MAXPULSE, data=fitness)
Conduct a residual analysis of your model, explaining your choices.
Refer to the lab transcript and to chapter 7 in the text for guidelines.

Answer
The Estimated regression model has the form
OXY = 0+1*Age + 2*MaxPulse+ 3*RunPulse+4*RunTime+5*Weight. I represent the regression coefficient of the ith variable. The nature of relation ship between the variables can be examined using the matrix scatter plot.

Figure 1: Matrix Scatter Plot
The matrix scatter plot suggests that there is linear relationship between the OXY and other independent variables.
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 103.15159 12.28721 8.395 9.65e-09 ***
AGE -0.22485 0.09806 -2.293 0.03053 *
MAXPULSE 0.30361 0.13418 2.263 0.03259 *
RUNPULSE -0.37794 0.11701 -3.230 0.00345 **
RUNTIME -2.65182 0.34532 -7.679 4.91e-08 ***
WEIGHT -0.07293 0.05335 -1.367 0.18375
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.275 on 25 degrees of freedom
Multiple R-squared: 0.848,
Adjusted R-squared: 0.8176
F-statistic: 27.9 on 5 and 25 ...

#### Solution Summary

The solution provides step by step method for the calculation of regression analysis for oxygen consumption.. Formula for the calculation and Interpretations of the results are also included.

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