I have 3 independent variables (Mined area, Reclamation age and reclaimed forest area) and 1 observed variable (conductivity). I ran multiple regression analysis with spss but I am not sure how to interpret the results. - I have standard error 236.175 is it too high? - On coefficient section RF(reclaimed forest) and AvgRecAge(reclamation age) is not significant Can I still include them in the model? Thanks!

Here is link for data.

And results here enter image description here

  • $\begingroup$ You have 4 variables and 62 observations. That's small enough a dataset to post here as text (using some format readable by people using different software). On questions just asking for interpretation, please see stats.meta.stackexchange.com/questions/3175/… on what interpretation means precisely. Here I guess wildly that you are regressing conductivity of water leaving drainage basins (catchments, watersheds) on basin properties. $\endgroup$
    – Nick Cox
    Dec 15, 2017 at 19:10
  • $\begingroup$ Mined area seems to work well as a predictor but (a) in my experience conductivity is often better modelled on logarithmic scale (b) watch out for blobs i.e. a contrast between non-mined and mined areas. $\endgroup$
    – Nick Cox
    Dec 15, 2017 at 19:11
  • $\begingroup$ Yes @Nick Cox these are results from samples taken from different watershed exits. what is the reason I need logarithmic transformation ? and you mean log based on 10 $\endgroup$
    – Amadeus
    Dec 15, 2017 at 19:37

1 Answer 1


Thanks for posting the data.

The original data look in good and surprisingly simple shape for environmental data. What sampling or selection process underlines what we see here? Nor is there any obvious need for transformation to capture nonlinearity or other awkwardness.

I have ignored the missing values in your data.

A scatter plot matrix suggests that Mined A is likely to be the best predictor, and then Rec. Age. That picture could be complicated by the relationships between different predictors.

enter image description here

I'd suggest that a two-predictor regression is a much better choice than your three-predictor model. It would not a good idea to force RecF into the model: its relationship with Rec. Age just muddies the waters if both are included. Presumably the results from Stata here will match what you can get from SPSS. The story from $R^2$, $P$-values and residual and added variable plots (not shown here) all support stopping with two predictors.

An RMSE can't be interpreted without knowing the units of measurement and the original SD of the outcome variable.

Substantive interpretation remains the responsibility of the researcher. Does the sign of each coefficient match what you think is happening?

. regress cond mineda recage

      Source |       SS           df       MS      Number of obs   =        64
-------------+----------------------------------   F(2, 61)        =    112.08
       Model |  12431284.1         2  6215642.07   Prob > F        =    0.0000
    Residual |  3382839.29        61  55456.3818   R-squared       =    0.7861
-------------+----------------------------------   Adj R-squared   =    0.7791
       Total |  15814123.4        63  251017.832   Root MSE        =    235.49

        cond |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
      mineda |   17.22542   1.576469    10.93   0.000     14.07308    20.37777
      recage |  -24.43057   6.293212    -3.88   0.000    -37.01462   -11.84651
       _cons |   526.0784   143.6132     3.66   0.001      238.906    813.2508
  • $\begingroup$ Thank you so much @Nick Cox ! It helped me a lot to understand what I have. Constant is higher than expected but the coefficients for other variables looks good. Probably I did not find all control factors. $\endgroup$
    – Amadeus
    Dec 16, 2017 at 18:50

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