Example 5. Multiple Linear Regression: Health Club Data

The data consists of health records of 30 employees who were regular members of a company's health club. The variables are described below:
Y: Time in a one-mile run (in seconds)
X1: Weight (in pounds)
X2: Resting pulse rate per minute
X3: Arm and leg strength (no. of pounds a subject was able to lift)
X4: Time in a 1/4-mile run (in seconds)

Source: Chatterjee, S. and Hadi, A.S. (1988). Sensitivity Analysis in Linear Regression. John Wiley & Sons: New York.

Table 5: Health Club Data

 No.     Y    X1   X2    X3   X4
   1   481   217   67   270   91
   2   292   141   52   190   66
   3   338   152   58   203   68
   4   357   153   56   183   70
   5   396   180   66   170   77
   6   429   193   71   178   82
   7   345   162   65   160   74
   8   469   180   80   170   84
   9   425   205   77   188   83
  10   358   168   74   170   79
  11   393   232   65   220   72
  12   346   146   68   158   68
  13   279   173   51   243   56
  14   311   155   64   198   59
  15   401   212   66   220   77
  16   267   138   70   180   62
  17   404   147   54   150   75
  18   442   197   76   228   88
  19   368   165   59   188   70
  20   295   125   58   160   66
  21   391   161   52   190   69
  22   264   132   62   163   59
  23   487   257   64   313   96
  24   481   236   72   225   84
  25   374   149   57   173   68
  26   309   161   57   173   65
  27   367   198   59   220   62
  28   469   245   70   218   69
  29   252   141   63   193   60
  30   338   177   53   183   75

Questions:

1. Fit a multiple regression model to the data. Assess the goodness of fit.
   
   
2. Define and discuss correlation, multiple correlation, partial correlation.
   
   
3. Discuss residual analyses, including partial residual plots.
   
   
4. Carry out partial F-tests and discuss them.

Keywords: Matrix plots, multiple correlation, partial correlation, residual plots