Quadratic formula doesn't add up (SPSS)

#1
Hello,
SPSS will draw a quadratic fit line on a scatterplot if requested and provide the formula (see attached).

I have typed out the quadratic formula below; see any errors?
y = (-5870) + 6.11x + (-.00157)x^2

The problem is that when I work out y by hand or use a graphing calculator (e.g., Desmos), I get values that don't jibe with the data. For instance, the graph shows x=1960, y~95 whereas by hand and a graphing calculator show x=1960,y~74.

What could I be doing wrong?

Thanks!
Hans

PS-I'm off to bed, so I'll check this tomorrow. Thanks!
 

Dason

Ambassador to the humans
#2
Change the -.00157 to -.00156 and you get something like 112. It isn't printing out all of the digits of the estimates which makes your 'by hand' version imprecise. If you center your X's first that will help.
 
#3
Change the -.00157 to -.00156 and you get something like 112. It isn't printing out all of the digits of the estimates which makes your 'by hand' version imprecise. If you center your X's first that will help.
Thank you, Dason, that's absolutely the issue. Sadly, I can't find any way to expand the number of digits for the estimates on the scatterplot.
 
#4
Another method for getting the estimates (at greater precision) for the quadratic is running SPSS Curve Estimation. I am interested in comparing both linear and quadratic because quadratic is marginally better (R-sq = .04 vs. .06). However, due to multicollinearity among terms (x and x^2), SPSS is excluding one of the variables, so as far as I can tell, I can't actually use SPSS to get a precise estimate for the quadratic model. Very frustrating, as Loess suggests that the relationship is not linear and I would like other options for estimating Y (and maybe the trend).

Any further ideas for how I should proceed would be appreciated!
 
#7
Thanks! I'll give it a shot and report back later today.
Yep, knowing that SPSS's rounding had a profound effect and centering would take care of multicollinearity fixed everything. I'm kicking myself for not remembering the role of centering from grad school!

Thanks much, Dason and spunky!
 

Dason

Ambassador to the humans
#8
Multi collinearity really isn't anything to worry about here. The centering is mainly to help you get a better way to get the estimates in a more accurate fashion although SPSS internally shouldn't have any need for you to do the centering if you use it to do the predictions for you.
 

Dragan

Super Moderator
#9
The "rounding issue" should not be a problem. All you need to do is when you get the SPSS results is "double click" on the output - and then "double click" again on the numerical result you are concerned with and will it give the numerical result in double precision i.e. 16 places to the right of the decimal point.
 
#10
Multi collinearity really isn't anything to worry about here. The centering is mainly to help you get a better way to get the estimates in a more accurate fashion although SPSS internally shouldn't have any need for you to do the centering if you use it to do the predictions for you.
Thank you. I agree, and I wonder why SPSS bothers to exclude variables, even if there is extreme multicollinearity. Seems like a warning would be useful instead.

Regarding the "rounding issue," when you add a fit line to a scatterplot, it provides the formula on the graph and in the pop-out window with graph options. Unfortunately, it does not have the option to expand the number of digits as one would find in output tables.

Thanks again!