Example 4. Multiple Linear Regression: Steam Data

The data shows observations taken at intervals from a steam plant which is part of a large industry. The variables are:
Y: Monthly use of steam (in pounds)
X1: Real fatty acid in storage per month (in pounds)
X2: Crude glycerin produced (in pounds)
X3: Average wind velocity (mph)
X4: Calendar days per month
X5: Operating days per month
X6: Days below 32 degrees F
X7: Average atmospheric temperature (in degrees F)
X8: Average wind velocity squared
X9: Number of start-ups

Source: Draper, N.R. and Smith, H. (1998). Applied Regression Analysis, Appendix 1, 3rd edition. John Wiley & Sons: New York.

Table 4: Steam Data

 Obs      Y     X1     X2     X3   X4   X5   X6     X7     X8   X9
   1  10.98   5.20   0.61    7.4   31   20   22   35.3   54.8    4
   2  11.13   5.12   0.64    8.0   29   20   25   29.7   64.0    5
   3  12.51   6.19   0.78    7.4   31   23   17   30.8   54.8    4
   4   8.40   3.89   0.49    7.5   30   20   22   58.8   56.3    4
   5   9.27   6.28   0.84    5.5   31   21    0   61.4   30.3    5
   6   8.73   5.76   0.74    8.9   30   22    0   71.3   79.2    4
   7   6.36   3.45   0.42    4.1   31   11    0   74.4   16.8    2
   8   8.50   6.57   0.87    4.1   31   23    0   76.7   16.8    5
   9   7.82   5.69   0.75    4.1   30   21    0   70.7   16.8    4
  10   9.14   6.14   0.76    4.5   31   20    0   57.5   20.3    5
  11   8.24   4.84   0.65   10.3   30   20   11   46.4  106.1    4
  12  12.19   4.88   0.62    6.9   31   21   12   28.9   47.6    4
  13  11.88   6.03   0.79    6.6   31   21   25   28.1   43.6    5
  14   9.57   4.55   0.60    7.3   28   19   18   39.1   53.3    5
  15  10.94   5.71   0.70    8.1   31   23    5   46.8   65.6    4
  16   9.58   5.67   0.74    8.4   30   20    7   48.5   70.6    4
  17  10.09   6.72   0.85    6.1   31   22    0   59.3   37.2    6
  18   8.11   4.95   0.67    4.9   30   22    0   70.0   24.0    4
  19   6.83   4.62   0.45    4.6   31   11    0   70.0   21.2    3
  20   8.88   6.60   0.95    3.7   31   23    0   74.5   13.7    4
  21   7.68   5.01   0.64    4.7   30   20    0   72.1   22.1    4
  22   8.47   5.68   0.75    5.3   31   21    1   58.1   28.1    6
  23   8.86   5.28   0.70    6.2   30   20   14   44.6   38.4    4
  24  10.36   5.36   0.67    6.8   31   20   22   33.4   46.2    4
  25  11.08   5.87   0.70    7.5   31   22   28   28.6   56.3    5

Questions:

1. Fit a suitable multiple regression model.
   
   
2. Use t-tests and F-tests to verify adequacy of the model fit.
   
   
3. How do you use this model for prediction?

Keywords: Partial regression coefficients, coefficient of determination, correlation matrix of predictors, residual analyses, ANOVA table