Re: linear regression results approximates to the mean of Y

Thank you!

I am not a researcher in mathematics and statistics. In my work,
Linear Regression is used to estimate human age when given a face
image.
That is, the "X" is features extracted from face image , Y is the
corresponding age.

I am not very sure if there's linear realtion between the X and Y. So
both linear and quadratic
regression is test and found that linear is better.
I have 25 images for each age, and the age range is from 20 to 60.
When all images are used the result is pleasing, the mean estimated
age of images at each age exhibits linearity: (in the image below the
read line is the real age,the blue line is the mean estimated ages:
http://hiphotos.baidu.com/bslnt/pic/item/1b85bf587ad439ca9d8204d9.jpg

but when images in a smaller age range is used , the means trends to
near the mean of the age range.( in this image, images aged from 30 to
50 is used to train the "local linear regression", its means at each
age is represented by the blue line, red line is still the real age
and green is that of the global regression when all images are used.
http://hi.baidu.com/bslnt/album/item/da168c44dedad396b3b7dcaa.html

I am not very sure what does this result mean. Could it be possible
that there is no local linearity? Or it means the real distrubution is
similar to the line below?
http://hi.baidu.com/bslnt/album/item/823733178d8632154a90a780.html

And I also want to know how to confirm the linear realationship
between two variables?

Thank you very much!
feilian
.

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