Slope Formula Continued...

[Allen]

Thanks to all who provided input on my initial inquiry about a compute
function in SPSS which would calculate a slope (simple regression
slope using an X and Y value). I had started some code to calculate
it and for the experience decided to finish it.

The code calcuates the slope formula - Sigma(Y-Ymean)*(X-Xmean)/
Sigma(X-Xmean)squared

I have a time series of 10 data points (years in this case) and I want
to calculate a slope using years 1 to 5,
2 to 6, 3 to 7, etc. so I end up with 6 calculated slopes. The code
below works fine, however, I couldn't figure
out how to calculate the slope in one step, I had to do the numerator
first, denominator second and then divide
them. Any help would be appreciated.

data list list (",")/ @2001 @2002 @2003 @2004 @2005 @2006 @2007 @2008
@2009 @2010.
begin data
48.75,52.71,52.79,58.31,55.86,55.05,54.78,49.55,42.79,46.24
42.25,36.07,42.95,33.52,44.83,40.76,27.47,27.26,25.36,29.97
end data.
exe.

numeric Ymean1 to Ymean6 (f2.1).
vector A=@2001 to @2010/D=Ymean1 to Ymean6.
loop #F=1 to 10.
compute D(#F)=mean(A(#F),A(#F+1),A(#F+2),A(#F+3),A(#F+4)).
end loop if #F+4 eq 10.
exe.

numeric Yr1 to Yr10 (f1.0).
exe.
vector H=Yr1 to Yr10.
loop #I=1 to 10.
compute H(#I)=1.
end loop.
exe.

compute Xmean=3.
exe.

***************************Numerator Of The Slope
Formula*******************************************

numeric NSlopeYr1 to NSlopeYr6 (f3.2).
vector A=@2001 to @2010/B=Ymean1 to Ymean6/C=Yr1 to Yr10/D=NSlopeYr1
to NSlopeYr6.
loop #E=1 to 10.
compute D(#E)=(A(#E)-B(#E))*(C(#E)-Xmean)+(A(#E+1)-B(#E))*((C(#E)
+1)-Xmean)+(A(#E+2)-B(#E))*((C(#E)+2)-Xmean)+
(A(#E+3)-B(#E))*((C(#E)+3)-Xmean)+(A(#E+4)-B(#E))*((C(#E)+4)-
Xmean).
end loop if (#E+4)=10.
exe.

*************************Denominator Of The Slope
Formula****************************************

numeric DSlopeYr1 to DSlopeYr6 (f3.2).
vector A=@2001 to @2010/B=Ymean1 to Ymean6/C=Yr1 to Yr10/D=DSlopeYr1
to DSlopeYr6.
loop #E=1 to 10.
compute D(#E)=((C(#E)-Xmean)**2+((C(#E+1)+1)-Xmean)**2)+(((C(#E+2)+2)-
Xmean)**2)+(((C(#E+3)+3)-Xmean)**2)+(((C(#E+4)+4)-Xmean)**2).
end loop if (#E+4)=10.
exe.

************************Numerator Divided By The Denominator For
Slope**************************

numeric SlopeYr1 to SlopeYr6 (f3.2).
vector A=NSlopeYr1 to NSlopeYr6/B=DSlopeYr1 to DSlopeYr6/C=SlopeYr1 to
SlopeYr6.
loop #D=1 to 6.
compute C(#D)=(A(#D)/B(#D)).
end loop.
exe.

[David]

Alan,
You are making this **MUCH** more difficult than it is!
**Noting the following:
* SUM(X-Xbar)**2 = Sum(X**2)-(Sum(X)**2)/N
* SUM[(X-Xbar)*(Y-Ybar)]=Sum(X*Y)-Sum(X)*Sum(Y)/N
Since X is always 1...5, The Sum(X) always=15, Sum(X**2)=55 etc
55-(15**2)/5=55-255/5=55-45=10
ie Your denominator is *ALWAYS* 10!!!!!!!!!!!!
-----
It is as simple as the following:

data list list (",")/ @2001 @2002 @2003 @2004 @2005 @2006 @2007 @2008
@2009 @2010.
begin data
48.75,52.71,52.79,58.31,55.86,55.05,54.78,49.55,42.79,46.24
42.25,36.07,42.95,33.52,44.83,40.76,27.47,27.26,25.36,29.97
end data.

VECTOR data=@2001 TO @2010 /#XY(6) /#X(6) / Slope(6).
LOOP #=1 TO 6.
COMPUTE #XY(#)=0.
COMPUTE #X(#) =0.
COMPUTE #TIME=1.
+ LOOP ##=# TO #+4.
+ COMPUTE #XY(#)=SUM(#XY(#),data(##)*#TIME).
+ COMPUTE #X(#) =SUM(#X(#),data(##)).
+ COMPUTE #TIME=#TIME+1.
+ END LOOP.
+ COMPUTE Slope(#)=(#XY(#)- #X(#)*3 )/ 10.
END LOOP.
FORMATS SLOPE1 TO SLOPE6 (F5.3).
LIST SLOPE1 TO SLOPE6.
-----------------------

[Allen]

> > exe.- Hide quoted text -
>
> - Show quoted text -

David:

Thank you!

This is a thing of beauty, now I need to figure out the mechanics
\logistics of the use of the vectors and loops
so that I can apply them to other problems. It is sad that this
excites me almost as much as beer.

[Bruce Weaver]

On 13/02/2012 9:58 AM, Allen wrote:

>
> David:
>
> Thank you!
>
> This is a thing of beauty, now I need to figure out the mechanics
> \logistics of the use of the vectors and loops
> so that I can apply them to other problems. It is sad that this
> excites me almost as much as beer.

What brand of beer are you drinking? It might be time to switch to
something better. :-|

--
Bruce Weaver
bwe...@lakeheadu.ca
http://sites.google.com/a/lakeheadu.ca/bweaver/Home
"When all else fails, RTFM."

[David]

On Feb 13, 1:29 pm, Bruce Weaver <bwea...@lakeheadu.ca> wrote:
> On 13/02/2012 9:58 AM, Allen wrote:
>
>
>
> > David:
>
> > Thank you!
>
> > This is a thing of beauty, now I need to figure out the mechanics
> > \logistics of the use of the vectors and loops
> > so that I can apply them to other problems.  It is sad that this
> > excites me almost as much as beer.
>
> What brand of beer are you drinking?  It might be time to switch to
> something better.  :-|
>
> --
> Bruce Weaver

> bwea...@lakeheadu.cahttp://sites.google.com/a/lakeheadu.ca/bweaver/Home

> "When all else fails, RTFM."

Ah Bruce, Yer just jaded ;-)