Example:  Electrical Consumption vs. Temperature

Linear Regression


 

Regression Analysis: electric versus temp

The regression equation is
electric = 24.4 + 0.514 temp
 

Predictor    Coef  SE Coef     T      P
Constant    24.42    10.57  2.31  0.029
temp       0.5139   0.1603  3.21  0.004
 

S = 13.5273   R-Sq = 29.1%   R-Sq(adj) = 26.3%
 

Analysis of Variance
Source          DF      SS      MS      F      P
Regression       1  1880.7  1880.7  10.28  0.004
Residual Error  25  4574.7   183.0
Total           26  6455.5
 

Unusual Observations
Obs  temp  electric    Fit  SE Fit  Residual  St Resid
  1  35.0     72.16  42.40    5.32     29.76      2.39R

R denotes an observation with a large standardized residual.
 
 
 
 
 
 

Quadratic Regression

Regression Analysis: electric versus temp, temp2

The regression equation is
electric = 213 - 5.83 temp + 0.0499 temp**2

Predictor      Coef   SE Coef       T      P
Constant     212.93     13.47   15.81  0.000
temp        -5.8278    0.4411  -13.21  0.000
temp**2    0.049854  0.003443   14.48  0.000

S = 4.42475   R-Sq = 92.7%   R-Sq(adj) = 92.1%

Analysis of Variance

Source          DF      SS      MS       F      P
Regression       2  5985.6  2992.8  152.86  0.000
Residual Error  24   469.9    19.6
Total           26  6455.5

Source  DF  Seq SS
temp     1  1880.7
temp2    1  4104.8
 

Unusual Observations
Obs  temp  electric     Fit  SE Fit  Residual  St Resid
  1  35.0    72.164  70.032   2.582     2.132      0.59 X
 22  81.0    79.468  67.974   1.243    11.494      2.71R
 23  83.0    82.469  72.671   1.369     9.798      2.33R
 27  91.0    87.265  95.445   2.356    -8.180     -2.18R

R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large influence.