Example:  Temperature vs latitude and Elevation
 

 
 


 
Regression Analysis: temp versus lat, elev, lat**2, elev**2, lat*elev

The regression equation is
temp = 103 - 1.45 lat - 0.00227 elev - 0.0054 lat**2 + 0.000000 elev**2
       - 0.000007 lat*elev
 

Predictor        Coef     SE Coef      T      P
Constant       103.03       58.34   1.77  0.108
lat            -1.451       4.014  -0.36  0.725
elev        -0.002274    0.006011  -0.38  0.713
lat**2       -0.00541     0.06871  -0.08  0.939
elev**2    0.00000016  0.00000026   0.60  0.560
lat*elev   -0.0000069   0.0002051  -0.03  0.974

 

S = 0.945280   R-Sq = 99.1%   R-Sq(adj) = 98.6%

 

Analysis of Variance
Source          DF      SS      MS       F      P
Regression       5  933.00  186.60  208.83  0.000
Residual Error  10    8.94    0.89
Total           15  941.94

 

Unusual Observations
Obs   lat    temp     Fit  SE Fit  Residual  St Resid
  7  28.7  53.000  55.016   0.399    -2.016     -2.35R
R denotes an observation with a large standardized residual.


Regression Analysis: temp versus lat, elev, lat*elev

The regression equation is
temp = 110 - 1.85 lat - 0.00229 elev + 0.000014 lat*elev

Predictor        Coef     SE Coef       T      P
Constant      109.752       3.860   28.43  0.000
lat           -1.8487      0.1328  -13.92  0.000
elev        -0.002286    0.002068   -1.11  0.291
lat*elev   0.00001372  0.00006420    0.21  0.834

S = 0.883649   R-Sq = 99.0%   R-Sq(adj) = 98.8%

Analysis of Variance
Source          DF      SS      MS       F      P
Regression       3  932.57  310.86  398.11  0.000
Residual Error  12    9.37    0.78
Total           15  941.94
 
 
 

Regression Analysis: temp versus lat, elev

The regression equation is
temp = 109 - 1.83 lat - 0.00185 elev

Predictor        Coef    SE Coef       T      P
Constant      109.259      2.979   36.68  0.000
lat           -1.8322     0.1038  -17.65  0.000
elev       -0.0018463  0.0002188   -8.44  0.000

S = 0.850596   R-Sq = 99.0%   R-Sq(adj) = 98.8%

Analysis of Variance
Source          DF      SS      MS       F      P
Regression       2  932.53  466.27  644.45  0.000
Residual Error  13    9.41    0.72
Total           15  941.94

Source  DF  Seq SS
lat      1  881.00
elev     1   51.53

Unusual Observations
Obs   lat    temp     Fit  SE Fit  Residual  St Resid
  7  28.7  53.000  55.171   0.269    -2.171     -2.69R
R denotes an observation with a large standardized residual.