Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.

Exercise - Estimating the bicarbonate concentration in mineral waters

The amount of solid residues and the concentration of bicarbonate in mineral water are highly correlated. Use the data set WATERRESID to set up a straight line regression model for the estimation of the bicarbonate content from the amount of solid residues in the water. Try to answer the following questions:

  • Is the slope of the regression significant?
  • What about a parabolic model as an alternative to the straight line?
  • Try to apply the regression model to two "unknown" mineral water brands (see below), and compare the regression results with the true values.
  • If you set up another regression model, including the two unknown samples, how does the model change? Discuss the results.
  • What are the 95 % confidence intervals for the estimated unknowns?

Here are the measurements of the two "unknown" brands of mineral water ("Fonte Guizza", and "Radkersburger"):

                   HCO3     Solid
                   Conc.    Residues
                  [mg/l]    [mg]
  Fonte Guizza    256.2     230
  Radkersburger   2111      2850

You may go now directly to the  DataLab  in order to experiment with the data.