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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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