QQ plot age residuals

[Florian Maissan]

Hi guys,

I'm trying to construct a QQ-plot for age and residuals using the following code:

gen residuals=HRQoL-HRQoL_predicted
qqplot age residuals

This gives me a normal looking QQ plot with a positively distributed population BUT there is something weird about the plot: the reference line (45 degrees normally?) is nowehere close to the QQ plot itself. It is a horizontal line which lies just above the x-axis.. Does anybody now how to solve this problem?

Thanks for the help!
Florian

[Andrew Musau]

I really do not know what you expect given a qqplot of residuals and age. Look at the following example

webuse auto
qui reg price mpg weight
predict r, residual

In a number of cases, the residual is normally distributed with mean 0. A variable like "age" will have a non-zero mean and in most cases will not be normally distributed. Now the only time you would get the dots coinciding with the reference line is if you were to do a qqplot of a variable and itself. For example

qqplot r r

However, all bets are off if you attempt to a qqplot of the residual, say with a variable like "length" in the auto dataset. Also, if you plot the 0-mean variable on the y-axis, the reference line will be horizontal at 0 (so check which variable is in the y-axis).

qqplot length r

qqplot r length

[Joseph Coveney]

That plot is to compare distributions. The example in the user's manual is the distribution of weights of automobiles made in the U.S. to that of those manufactured elsewhere.

Is there a reason why you would expect age to be distributed identically with residuals of some regression model of health-related quality of life survey scores?

[Florian Maissan]

Hello,

Thank you very much for your answers! I'm sorry if i was not clear with my question. Maybe with the plot shown (below) it makes more sense. I do not expect age to be distributed identically with residuals ( I know it is skewed to the right for example). I'm just confused that the reference line in my plot is nowhere the same like shown in the plots of Andrew. Also when i do the QQ plot the other way around (residuals on x axis and age on y axis) no normal plot is shown.

[Andrew Musau]

I suspect that there is nothing wrong with the plot above. You will see this if you ask Stata to summarize the two variables

sum age
sum residuals

At no point do the values of age and residuals intersect. It appears that the mean of residuals is close to zero and the range does not depart much from zero. I can create the same behavior in your graph by generating a variable with a mean and range that does not depart much from zero.

webuse auto
qui reg price mpg weight
gen r_2= rnormal(.01, 0.001)
qqplot length r_2

. sum r_2

Variable | Obs   Mean     Std. Dev.  Min       Max
-------------+--------------------------------------------------------
r_2      | 74    .0100943  .0010237   .0077693   .0130819



. sum length

Variable | Obs   Mean      Std. Dev.   Min   Max
-------------+--------------------------------------------------------
length   | 74    187.9324  22.26634    142   233

Now, let us increase the variance of r_2 so that some values are in the range 142 - 233 (but same mean)

gen r_3= rnormal(.01, 200)

. sum r_3

Variable | Obs    Mean      Std. Dev.   Min       Max
-------------+--------------------------------------------------------
r_3      | 74    -7.938616  201.4918   -547.6382  463.7131

. count if r_3> 142
18

qqplot length r_3

[Joseph Coveney]

Also when i do the QQ plot the other way around (residuals on x axis and age on y axis) no normal plot is shown.

No normal plot will be shown regardless of what you do with qqplot. Are you looking for qnorm?