Example 14. Multicollinearity in Linear Regression: Manhours Data

The following data describes the manpower needs for operating a U.S. Navy bachelor officers' quarters, consisting of 25 establishments. The variables are described below and the data is given in the following table:
Y: Monthly manhours needed to operate an establishment
X1: Average daily occupancy
X2: Monthly average number of check-ins
X3: Weekly hours of service desk operation
X4: Common use area (in square feet)
X5: Number of building wings
X6: Operational berthing capacity
X7: Number of rooms

Source: Freund, R.J., and Littell, R.C. (1991). SAS System for Regression. SAS Institute Inc.

Table 14: Manhours Data

      Y      X1       X2     X3     X4   X5    X6    X7
 180.23    2.00     4.00    4.0   1.26    1     6     6
 182.61    3.00     1.58   40.0   1.25    1     5     5
 199.92    5.30     1.67   42.5   7.79    3    25    25
 284.55    7.00     2.37  168.0   1.00    1     7     8
 267.38   16.50     8.25  168.0   1.12    2    19    19
 164.38   16.60    23.78   40.0   1.00    1    13    13
 999.09   25.89     3.00   40.0   0.00    3    36    36
 931.84   31.92    40.80  168.0   5.52    6    47    47
 944.21   39.63    50.86   40.0  27.37   10    77    77
1103.24   44.42   159.75  168.0   0.60   18    48    48
1387.82   54.48   207.08   40.0   7.77    6    66    66
1489.50   56.63   373.42  168.0   6.03    4    36    37
1845.89   95.00   368.00  168.0  30.26    9   292   196
1891.70   96.67   206.67  168.0  17.86   14   120   120
1880.84   96.83   677.33  168.0  20.31   10   302   210
2268.06   97.33   255.08  168.0  19.00    6   165   130
3036.63  102.33   288.83  168.0  21.01   14   131   131
2628.32  110.24   410.00  168.0  20.05   12   115   115
3559.92  113.88   981.00  168.0  24.48    6   166   179
2227.76  134.32   145.82  168.0  25.99   12   192   192
3115.29  149.58   233.83  168.0  31.07   14   185   202
4804.24  188.74   937.00  168.0  45.44   26   237   237
5539.98  274.92   695.25  168.0  46.63   58   363   363
8266.77  384.50  1473.66  168.0   7.36   24   540   453
3534.49  811.08   714.33  168.0  22.76   17   242   242

Questions:

1. Are the explanatory variables, or some subset of them, collinear? How is this detected?
   
   
2. What are the consequences of ignoring multicollinearity on the model fit and prediction?

Keywords: Multicollinearity, correlation matrix of predictors, variance inflation factors