# Randomly distributed residuals or not?

Using Minitab I have checked for regression assumptions. Here I can see that the residuals (errors) of x4 are distributed normally. (y is response). However, are they distributed randomly? Looking at the "Versus Fits" graph they seem to be distributed normally, however I'm not very sure. What do you think?

Regression Analysis: y versus x4

The regression equation is
y = 62,1 + 4,98 x4

Predictor    Coef  SE Coef     T      P    VIF
Constant   62,125    9,683  6,42  0,000
x4          4,979    2,634  1,89  0,063  1,000

S = 11,5115   R-Sq = 5,5%   R-Sq(adj) = 4,0%

PRESS = 8703,56   R-Sq(pred) = 0,00%

Analysis of Variance

Source          DF      SS     MS     F      P
Regression       1   473,5  473,5  3,57  0,063
Residual Error  61  8083,3  132,5
Lack of Fit    3   638,8  212,9  1,66  0,186
Pure Error    58  7444,6  128,4
Total           62  8556,9

1 rows with no replicates

Unusual Observations

Obs    x4      y    Fit  SE Fit  Residual  St Resid
35  3,00  49,00  77,06    2,21    -28,06     -2,48R
56  2,00  60,00  72,08    4,54    -12,08     -1,14 X

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

Durbin-Watson statistic = 2,22949


Durbin-Watson is 2.22. Close to 2. So it means that the (standardized?) residuals are randomly and independently distributed?

• Evidently $x4$ is categorical with four categories. There's a marked lack of goodness of fit for one of its categories where the fit is near $77$. The problem is due to one low outlier (observation 35). There are two other problems called out by the warning messages. With three such issues in $62$ records it seems premature to be looking at normality of residuals: deal with the warnings first and then examine the residuals more closely.
– whuber
May 8, 2013 at 17:47